In [1]:

import numpy as np
import pandas as pd
import scipy as sp
import emcee 

from sklearn.pipeline import Pipeline
from sklearn.compose import TransformedTargetRegressor
from sklearn.neural_network import MLPRegressor
from sklearn.preprocessing import RobustScaler
from sklearn.ensemble import RandomForestRegressor
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import cross_val_score, ShuffleSplit, KFold

from scipy import stats

from math import *
import sys
import re
import os
from itertools import chain

%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt

from tqdm import tqdm_notebook as tqdm

In [2]:

np.random.seed(0) # for reproducibility 

In [3]:

import seaborn as sns
sns.set(style="ticks", palette="muted", rc={"xtick.bottom" : True, "ytick.left" : True})
plt.style.use('matplotlibrc')

In [4]:

import warnings
warnings.filterwarnings('ignore')

In [5]:

DF = pd.read_table('../regression/classical/models_cep.dat', sep='\t')
DF.drop(columns=['Mode'], inplace=True)
DF = DF[DF['M'] < 9]
pd.set_option('display.max_columns', 500)

DF['Period'] = np.log10(DF['Period'])
DF.rename(columns={'Period':'logP'}, inplace=True)

DF['W']  = DF['I_M0'] - 1.55 * (DF['V_M0'] - DF['I_M0'])
DF['VI'] = DF['V_M0'] - DF['I_M0']

DF['logR'] = np.log10(np.sqrt(10**DF['logL']) * (DF['Teff']/5777)**-2)

print(DF.columns)
DF

Index(['M', 'Z', 'logR', 'logL', 'Teff', 'logP', 'I_Amplitude', 'I_Skewness',
       'I_acuteness', 'I_R21', 'I_R31', 'I_M0', 'I_A1', 'I_A2', 'I_A3',
       'V_Amplitude', 'V_Skewness', 'V_acuteness', 'V_R21', 'V_R31', 'V_M0',
       'V_A1', 'V_A2', 'V_A3', 'W', 'VI'],
      dtype='object')

Out[5]:

	M	Z	logR	logL	Teff	logP	I_Amplitude	I_Skewness	I_acuteness	I_R21	I_R31	I_M0	I_A1	I_A2	I_A3	V_Amplitude	V_Skewness	V_acuteness	V_R21	V_R31	V_M0	V_A1	V_A2	V_A3	W	VI
0	4.6	0.008	1.477102	3.02	6000	0.466380	0.552	2.571	1.329	0.43929	0.15010	-3.38631	0.21697	0.09531	0.03257	0.882	2.368	1.830	0.44330	0.15349	-2.74358	0.34335	0.15220	0.05270	-4.382541	0.64273
1	4.6	0.008	1.477102	3.02	6000	0.466650	0.800	3.099	1.551	0.54260	0.26072	-3.36715	0.27487	0.14915	0.07166	1.298	2.969	2.134	0.54981	0.26784	-2.71277	0.43298	0.23806	0.11597	-4.381439	0.65438
2	4.6	0.008	1.491701	3.02	5900	0.490475	0.440	2.425	0.921	0.37955	0.11013	-3.40824	0.18830	0.07147	0.02074	0.678	2.087	1.341	0.38871	0.11579	-2.73952	0.29563	0.11492	0.03423	-4.444756	0.66872
3	4.6	0.008	1.491701	3.02	5900	0.490745	0.691	3.717	1.143	0.51889	0.22975	-3.39157	0.25519	0.13242	0.05863	1.085	2.496	1.791	0.52955	0.23697	-2.71144	0.39741	0.21045	0.09417	-4.445771	0.68013
4	4.6	0.008	1.506549	3.02	5800	0.514472	0.317	1.950	0.761	0.32980	0.13680	-3.42835	0.14776	0.04873	0.02021	0.501	3.309	1.088	0.34265	0.14114	-2.73490	0.23427	0.08027	0.03307	-4.503197	0.69345
5	4.6	0.008	1.506549	3.02	5800	0.515287	0.561	3.548	0.815	0.45976	0.19837	-3.41423	0.23158	0.10647	0.04594	0.863	3.032	1.273	0.47535	0.20595	-2.70878	0.35680	0.16960	0.07348	-4.507678	0.70545
6	4.6	0.008	1.521655	3.02	5700	0.539598	0.197	2.598	0.772	0.30496	0.13906	-3.44669	0.09311	0.02840	0.01295	0.336	2.448	1.139	0.31027	0.13521	-2.72857	0.15312	0.04751	0.02070	-4.559776	0.71812
7	4.6	0.008	1.521655	3.02	5700	0.540138	0.470	9.423	0.687	0.40808	0.20670	-3.43443	0.19822	0.08089	0.04097	0.744	8.712	1.184	0.42691	0.21526	-2.70324	0.30525	0.13032	0.06571	-4.567775	0.73119
8	4.6	0.008	1.537029	3.02	5600	0.565515	0.403	7.699	0.726	0.40512	0.24458	-3.45241	0.15827	0.06412	0.03871	0.638	7.132	1.252	0.42260	0.24895	-2.69574	0.24744	0.10457	0.06160	-4.625248	0.75667
9	4.6	0.008	1.552679	3.02	5500	0.590934	0.286	4.781	0.864	0.42011	0.24556	-3.46875	0.11408	0.04793	0.02801	0.461	2.677	1.398	0.41801	0.23619	-2.68691	0.18560	0.07758	0.04384	-4.680602	0.78184
10	4.6	0.008	1.587745	3.27	6100	0.654317	0.073	0.748	1.245	0.07664	0.06854	-4.01908	0.03354	0.00257	0.00230	0.111	0.742	1.162	0.07363	0.06663	-3.42357	0.05303	0.00390	0.00353	-4.942121	0.59551
11	4.6	0.008	1.602102	3.27	6000	0.679052	0.516	2.573	1.294	0.39981	0.12866	-4.01708	0.20772	0.08305	0.02673	0.822	2.637	1.575	0.39753	0.12860	-3.38021	0.32757	0.13022	0.04213	-5.004228	0.63687
12	4.6	0.008	1.602102	3.27	6000	0.679590	0.732	4.153	1.257	0.49614	0.23591	-4.00088	0.26395	0.13096	0.06227	1.170	3.740	1.635	0.49643	0.23806	-3.35500	0.41574	0.20638	0.09897	-5.001994	0.64588
13	4.6	0.008	1.616701	3.27	5900	0.703394	0.745	3.589	0.747	0.52244	0.21904	-4.01850	0.26619	0.13907	0.05830	1.176	3.221	1.248	0.52621	0.22176	-3.34266	0.41184	0.21671	0.09133	-5.066052	0.67584
14	4.6	0.008	1.616701	3.27	5900	0.703932	0.544	2.473	0.823	0.41532	0.10969	-4.03276	0.21271	0.08834	0.02333	0.851	2.585	1.173	0.41697	0.11089	-3.36541	0.33062	0.13786	0.03666	-5.067152	0.66735
15	4.6	0.008	1.631549	3.27	5800	0.729115	0.480	1.891	0.527	0.38483	0.11141	-4.05230	0.19198	0.07388	0.02139	0.736	2.030	0.725	0.39419	0.11619	-3.35633	0.29389	0.11585	0.03415	-5.131053	0.69597
16	4.6	0.008	1.631549	3.27	5800	0.729384	0.678	3.064	0.508	0.51588	0.16413	-4.03980	0.25118	0.12958	0.04123	1.044	3.150	0.704	0.52505	0.16800	-3.33552	0.38205	0.20060	0.06418	-5.131434	0.70428
17	4.6	0.008	1.646655	3.27	5700	0.754374	0.397	1.611	0.430	0.36775	0.16609	-4.07079	0.15964	0.05871	0.02651	0.595	1.793	0.490	0.38535	0.17103	-3.34747	0.24225	0.09335	0.04143	-5.191936	0.72332
18	4.6	0.008	1.646655	3.27	5700	0.754911	0.611	2.290	0.392	0.47613	0.14588	-4.05976	0.23014	0.10958	0.03357	0.898	2.413	0.448	0.49403	0.15279	-3.32798	0.34393	0.16991	0.05255	-5.194019	0.73178
19	4.6	0.008	1.662029	3.27	5600	0.780413	0.530	2.003	0.383	0.45236	0.16807	-4.07881	0.19704	0.08914	0.03312	0.776	2.105	0.421	0.47957	0.17550	-3.31934	0.29137	0.13973	0.05114	-5.255988	0.75947
20	4.6	0.008	1.677679	3.27	5500	0.806160	0.199	1.494	0.431	0.43636	0.08023	-4.10129	0.08647	0.03773	0.00694	0.320	1.681	0.474	0.45539	0.07596	-3.32157	0.13359	0.06084	0.01015	-5.309856	0.77972
21	4.6	0.008	1.677679	3.27	5500	0.806698	0.455	1.755	0.374	0.47853	0.12431	-4.09307	0.17331	0.08293	0.02154	0.681	1.907	0.415	0.51557	0.12541	-3.30416	0.25534	0.13165	0.03202	-5.315881	0.78891
22	4.6	0.008	1.693617	3.27	5400	0.832441	0.077	1.748	0.511	0.37569	0.03939	-4.11376	0.03565	0.01339	0.00140	0.132	1.916	0.618	0.36950	0.03674	-3.30635	0.05770	0.02132	0.00212	-5.365246	0.80741
23	4.6	0.008	1.693617	3.27	5400	0.832980	0.329	0.550	0.405	0.56023	0.08291	-4.10756	0.13184	0.07386	0.01093	0.498	2.509	0.443	0.59848	0.08684	-3.29059	0.19630	0.11748	0.01705	-5.373863	0.81697
24	4.6	0.008	1.709853	3.27	5300	0.859297	0.178	0.493	0.429	0.67353	0.12277	-4.12149	0.06807	0.04585	0.00836	0.288	3.000	0.495	0.68888	0.12505	-3.27754	0.10444	0.07194	0.01306	-5.429613	0.84395
25	4.6	0.008	1.726398	3.27	5200	0.888073	0.100	0.495	0.521	0.62750	0.11560	-4.13025	0.03581	0.02247	0.00414	0.150	0.546	0.509	0.59487	0.10824	-3.25549	0.05798	0.03449	0.00628	-5.486128	0.87476
26	4.6	0.008	1.743264	3.27	5100	0.915084	0.106	0.616	0.830	0.28357	0.07916	-4.13531	0.04535	0.01286	0.00359	0.168	0.618	0.740	0.25690	0.07211	-3.22846	0.07514	0.01930	0.00542	-5.540927	0.90685
27	4.7	0.008	1.492102	3.05	6000	0.481891	0.595	3.000	1.396	0.44053	0.16614	-3.45621	0.23044	0.10151	0.03829	0.948	2.322	1.867	0.44560	0.17041	-2.81648	0.36351	0.16198	0.06195	-4.447792	0.63973
28	4.7	0.008	1.506701	3.05	5900	0.509512	0.466	2.311	0.961	0.38518	0.12466	-3.48209	0.19809	0.07630	0.02469	0.720	2.311	1.376	0.39332	0.12888	-2.81304	0.31034	0.12207	0.04000	-4.519118	0.66905
29	4.7	0.008	1.506701	3.05	5900	0.509783	0.712	4.000	1.128	0.51291	0.23322	-3.46513	0.26203	0.13440	0.06111	1.122	3.877	1.811	0.52423	0.24029	-2.78482	0.40732	0.21353	0.09787	-4.519611	0.68031
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
361	6.8	0.008	1.957679	3.83	5500	1.183636	0.886	2.154	1.579	0.20728	0.16471	-5.46599	0.32597	0.06757	0.05369	1.437	2.096	2.270	0.22320	0.17183	-4.64929	0.50731	0.11323	0.08717	-6.731875	0.81670
362	6.8	0.008	1.957679	3.83	5500	1.184432	1.114	2.650	1.596	0.22364	0.14890	-5.44759	0.38111	0.08523	0.05675	1.791	2.611	2.596	0.24342	0.16026	-4.61944	0.58441	0.14226	0.09366	-6.731222	0.82815
363	6.8	0.008	1.973617	3.83	5400	1.212477	0.920	2.258	1.301	0.23926	0.12553	-5.47349	0.34199	0.08182	0.04293	1.485	2.205	1.828	0.25810	0.13166	-4.61694	0.52495	0.13549	0.06911	-6.801142	0.85655
364	6.8	0.008	1.973617	3.83	5400	1.214062	1.203	2.788	1.239	0.26035	0.10239	-5.45024	0.41240	0.10737	0.04223	1.924	2.760	1.865	0.28439	0.11656	-4.57804	0.62060	0.17649	0.07234	-6.802150	0.87220
365	6.8	0.008	1.989853	3.83	5300	1.240656	0.803	1.977	0.967	0.25822	0.10658	-5.48847	0.32696	0.08443	0.03485	1.284	1.994	1.414	0.27758	0.10772	-4.60073	0.49852	0.13838	0.05370	-6.864467	0.88774
366	6.8	0.008	1.989853	3.83	5300	1.242768	1.153	2.704	0.907	0.31810	0.04840	-5.46142	0.41673	0.13256	0.02017	1.835	2.717	1.449	0.34081	0.06403	-4.55209	0.61916	0.21101	0.03965	-6.870881	0.90933
367	6.8	0.008	2.006398	3.83	5200	1.267441	0.681	1.578	0.871	0.22987	0.08779	-5.50440	0.29649	0.06815	0.02603	1.081	2.355	1.139	0.25151	0.08919	-4.58942	0.45067	0.11335	0.04019	-6.922619	0.91498
368	6.8	0.008	2.023264	3.83	5100	1.294895	0.525	1.359	0.843	0.20046	0.06900	-5.51983	0.24876	0.04987	0.01716	0.882	2.205	1.149	0.22140	0.07261	-4.57853	0.37979	0.08409	0.02758	-6.978845	0.94130
369	6.8	0.008	2.023264	3.83	5100	1.299946	0.889	1.933	0.683	0.31191	0.03655	-5.49136	0.37241	0.11616	0.01361	1.409	3.238	0.906	0.33657	0.04903	-4.52189	0.54627	0.18386	0.02679	-6.994039	0.96947
370	6.8	0.008	2.040465	3.83	5000	1.317512	0.419	2.185	0.855	0.17097	0.07711	-5.53071	0.20354	0.03480	0.01570	0.707	1.986	1.134	0.19007	0.08158	-4.56796	0.31308	0.05951	0.02554	-7.022972	0.96275
371	6.8	0.008	2.040465	3.83	5000	1.322616	0.805	3.237	0.676	0.27379	0.02656	-5.50048	0.34945	0.09568	0.00928	1.314	3.201	0.927	0.29827	0.03968	-4.50717	0.51248	0.15286	0.02033	-7.040111	0.99331
372	6.8	0.008	2.058013	3.83	4900	1.356278	0.703	3.184	0.687	0.24726	0.04981	-5.50731	0.32061	0.07927	0.01597	1.162	3.099	0.946	0.27174	0.05936	-4.47620	0.47261	0.12843	0.02805	-7.105530	1.03111
373	6.8	0.008	2.075922	3.83	4800	1.384846	0.647	2.732	0.701	0.27153	0.10357	-5.50801	0.30338	0.08238	0.03142	1.079	2.704	0.983	0.29678	0.11335	-4.44144	0.44931	0.13334	0.05093	-7.161193	1.06657
374	6.8	0.008	2.094209	3.83	4700	1.408872	0.617	7.930	0.737	0.29407	0.15436	-5.50917	0.28010	0.08237	0.04323	1.012	2.559	1.051	0.31722	0.16223	-4.41539	0.41749	0.13244	0.06773	-7.204529	1.09378
375	6.8	0.008	2.112889	3.83	4600	1.440466	0.480	5.454	0.793	0.32401	0.20694	-5.51676	0.21084	0.06832	0.04363	0.744	2.125	1.220	0.33283	0.20419	-4.39404	0.32322	0.10758	0.06600	-7.256976	1.12272
376	7.4	0.008	1.871549	3.75	5800	0.999544	0.112	1.066	0.957	0.09761	0.00976	-5.27220	0.05552	0.00542	0.00054	0.178	1.155	0.996	0.09655	0.00960	-4.59290	0.08820	0.00852	0.00085	-6.325115	0.67930
377	7.4	0.008	1.886655	3.75	5700	1.024478	0.392	2.021	0.724	0.28949	0.07662	-5.27570	0.17777	0.05146	0.01362	0.624	1.907	0.801	0.29278	0.07780	-4.55784	0.27811	0.08142	0.02164	-6.388383	0.71786
378	7.4	0.008	1.898160	3.75	5625	1.045485	0.366	1.874	0.608	0.29035	0.08649	-5.28666	0.17343	0.05035	0.01500	0.582	2.136	0.673	0.29744	0.08939	-4.54461	0.26925	0.08009	0.02407	-6.436837	0.74205
379	7.4	0.008	1.902029	3.75	5600	1.052150	0.351	2.058	0.579	0.29170	0.09150	-5.29061	0.16803	0.04901	0.01538	0.556	1.959	0.638	0.30012	0.09492	-4.54076	0.26018	0.07809	0.02470	-6.452878	0.74985
380	7.4	0.008	1.905915	3.75	5575	1.058880	0.336	0.754	0.564	0.29242	0.09265	-5.29488	0.15900	0.04649	0.01473	0.513	1.907	0.594	0.30245	0.09832	-4.53759	0.24566	0.07430	0.02415	-6.468680	0.75729
381	7.4	0.008	1.909819	3.75	5550	1.065631	0.330	0.695	0.565	0.29660	0.09821	-5.29898	0.15049	0.04464	0.01478	0.487	0.733	0.572	0.30803	0.10282	-4.53393	0.23227	0.07155	0.02388	-6.484807	0.76505
382	7.4	0.008	1.913740	3.75	5525	1.072418	0.328	0.730	0.572	0.30550	0.10684	-5.30280	0.14292	0.04366	0.01527	0.487	0.703	0.578	0.31832	0.11169	-4.52989	0.22029	0.07012	0.02460	-6.500811	0.77291
383	7.4	0.008	1.917679	3.75	5500	1.079215	0.334	0.736	0.582	0.31916	0.12414	-5.30612	0.13851	0.04421	0.01719	0.500	0.718	0.589	0.33295	0.12903	-4.52506	0.21331	0.07102	0.02752	-6.516763	0.78106
384	7.4	0.008	1.925612	3.75	5450	1.094013	0.405	0.805	0.623	0.35188	0.19739	-5.30969	0.15201	0.05349	0.03000	0.615	0.767	0.627	0.36482	0.20261	-4.51013	0.23407	0.08539	0.04743	-6.549008	0.79956
385	7.4	0.008	1.933617	3.75	5400	1.108081	0.554	0.930	1.500	0.35229	0.30542	-5.30784	0.19413	0.06839	0.05929	0.853	0.919	0.641	0.35845	0.31091	-4.48608	0.29871	0.10707	0.09287	-6.581568	0.82176
386	7.4	0.008	1.949853	3.75	5300	1.137560	0.764	1.288	1.083	0.22873	0.39911	-5.30261	0.26173	0.05987	0.10446	1.194	1.237	1.019	0.21560	0.39844	-4.43437	0.40258	0.08680	0.16040	-6.648382	0.86824
387	7.4	0.008	1.966398	3.75	5200	1.166958	0.867	1.538	0.908	0.12127	0.35736	-5.30085	0.29690	0.03600	0.10610	1.375	1.519	1.070	0.10063	0.35018	-4.38986	0.45658	0.04594	0.15988	-6.712884	0.91099
388	7.4	0.008	1.983264	3.75	5100	1.195275	0.932	1.802	1.063	0.11461	0.25094	-5.30022	0.31343	0.03592	0.07865	1.500	1.770	1.434	0.11973	0.23962	-4.34934	0.48510	0.05808	0.11624	-6.774084	0.95088
389	7.5	0.008	2.000465	3.75	5000	1.223979	0.447	2.846	1.634	0.39164	0.18668	-5.08193	0.17022	0.06666	0.03178	0.710	2.690	3.072	0.44466	0.25849	-3.97067	0.22353	0.09939	0.05778	-6.804383	1.11126
390	7.5	0.008	2.018013	3.75	4900	1.250225	0.225	1.564	1.501	0.23606	0.07483	-5.18131	0.09739	0.02299	0.00729	0.394	1.404	2.794	0.33403	0.15767	-4.09747	0.14173	0.04734	0.02235	-6.861262	1.08384

391 rows × 26 columns

In [6]:

y_columns = ['logP', 
       'I_Amplitude', 'I_Skewness', 'I_acuteness', 
       'V_Amplitude', 'V_Skewness', 'V_acuteness', 
       'I_A1', 'I_A2', 'I_A3', 
       'V_A1', 'V_A2', 'V_A3']

X_columns = ['M', 'logR', 'logL', 'Teff', 'I_M0', 'V_M0', 'VI', 'W']

In [ ]:

Visualize grid of models

In [7]:

#sns.pairplot(DF[y_columns])
fig, ax = plt.subplots(3, 4, squeeze=True, figsize=(6.64306*2,4.10318716*2))
for i, ax_row in enumerate(ax):
    for j, axes in enumerate(ax_row):
        axes.plot(DF['logP'], DF[y_columns].iloc[:,1+3*i+j], '.')

In [8]:

plt.suptitle('Cepheid H–R Diagram', y=0.99)
plt.scatter(DF['Teff'], DF['logL'], c=DF['M'])
plt.xlabel('$T_{\mathrm{eff}}/K$')
plt.ylabel('$\log\;L/$L$_\odot$')
plt.colorbar(label='$M/$M$_\odot$')
plt.xlim([6200, 4550])

plt.savefig('HR.pdf', bbox_inches='tight')
plt.show()

In [9]:

plt.suptitle('Cepheid P–M Relation', y=0.99)
plt.scatter(DF['logP'], DF['M'], c=DF['logR'])
plt.xlabel('$\log\;P/$days')
plt.ylabel('$M/$M$_\odot$')
plt.colorbar(label='$\log\;R/$R$_\odot$')

plt.savefig('PMR.pdf', bbox_inches='tight')
plt.show()

In [10]:

plt.suptitle('Cepheid P–R Relation', y=0.99)
plt.scatter(DF['logP'], DF['logR'], c=DF['M'])
plt.ylabel('$\log\;R/$R$_\odot$')
plt.xlabel('$\log\;P/$days')
plt.colorbar(label='$M/$M$_\odot$')

plt.savefig('PRM.pdf', bbox_inches='tight')
plt.show()

In [11]:

plt.suptitle('Cepheid P–L Relation', y=0.99)
plt.scatter(DF['logP'], DF['logL'], c=DF['logR'])
plt.ylabel('$\log\;L/$L$_\odot$')
plt.xlabel('$\log\;P/$days')
plt.colorbar(label='$\log\;R/$R$_\odot$')

plt.savefig('PL.pdf', bbox_inches='tight')
plt.show()

In [ ]:

Cross validation

In [12]:

np.random.seed(0) 
splits = KFold(n_splits=2, shuffle=True, random_state=0).split(DF)

ml = TransformedTargetRegressor(regressor=Pipeline(
            [('scaler', RobustScaler()), 
             ('mlp', MLPRegressor(hidden_layer_sizes=(100, 100), 
                                  max_iter=2000, activation='relu', solver='lbfgs', tol=1e-7))]),
         transformer=RobustScaler())
lm = LinearRegression()

ml_preds = {} 
lm_preds = {} 

for split in splits:
    training_idx, testing_idx = split
    
    ml.fit(DF.iloc[training_idx][y_columns], DF.iloc[training_idx][X_columns])
    ml_pred = ml.predict(DF.iloc[testing_idx][y_columns].values)
    
    lm.fit(DF.iloc[training_idx][['logP']],  DF.iloc[training_idx][X_columns])
    lm_pred = lm.predict(DF.iloc[testing_idx]['logP'].values.reshape(-1, 1))
    
    for ii in range(len(testing_idx)):
        ml_preds[testing_idx[ii]] = ml_pred[ii]
        lm_preds[testing_idx[ii]] = lm_pred[ii]

ml_pred = np.array([ml_preds[ii] for ii in range(len(DF))])
lm_pred = np.array([lm_preds[ii] for ii in range(len(DF))])

In [13]:

for penalty in [0, 0.00001, 0.0001, 0.001, 0.01]:
    ml = TransformedTargetRegressor(regressor=Pipeline(
        [('scaler', RobustScaler()), 
         ('mlp', MLPRegressor(hidden_layer_sizes=(100, 100), 
                              max_iter=2000, activation='relu', solver='lbfgs', tol=1e-7,
                              alpha=penalty))]),
         transformer=RobustScaler())
    print(penalty, cross_val_score(ml, DF[y_columns], DF[X_columns], cv=KFold(n_splits=2, shuffle=True, random_state=0)))

0 [0.89920164 0.84726445]
1e-05 [0.90443243 0.84731028]
0.0001 [0.91943472 0.8606015 ]
0.001 [0.8964787  0.84558117]
0.01 [0.90326339 0.86531132]

In [ ]:

Compute R^2, standard deviations, and percentages of improved estimates

In [14]:

all_r2s = []
all_sds = []

for pred in (ml_pred, lm_pred):
    
    r2s = []
    sds = []
    
    for idx, name in enumerate(X_columns):
        std = np.array(np.array(pred[:,idx]) - DF[name]).std()
        sds += [std]
        
        SS_tot = np.sum((DF[name] - DF[name].mean())**2)
        SS_res = np.sum((pred[:,idx] - DF[name].values)**2)
        R2 = 1-SS_res/SS_tot
        
        r2s += [R2]
    
    all_r2s += [r2s]
    all_sds += [sds]

all_r2s = np.array(all_r2s)
all_sds = np.array(all_sds)

In [15]:

ml_err = []
lm_err = []

for idx, name in enumerate(X_columns):
    ml_errs = abs(np.array(ml_pred[:,idx]) - DF[name])
    lm_errs = abs(np.array(lm_pred[:,idx]) - DF[name])
    ml_err += [ml_errs]
    lm_err += [lm_errs]

ml_err = np.array(ml_err)
lm_err = np.array(lm_err)

In [16]:

for idx, name in enumerate(X_columns): 
    print(name, int(np.round(((lm_err[idx,:] >= ml_err[idx,:]).sum()) / lm_err.shape[1] * 100, 0))) 

M 74
logR 74
logL 81
Teff 85
I_M0 81
V_M0 82
VI 84
W 76

In [ ]:

In [17]:

labels = ['$M$', '$\log\;R$', '$\log\;L$', '$T_{\\rm{eff}}$', '$M_I$', '$M_V$', '$V-I$', '$W$']

plt.rcParams["font.size"] = 18
x = np.arange(len(labels))  # the label locations
width = 0.45  # the width of the bars

fig, ax = plt.subplots(figsize=(6.64306*2,4.10318716*0.9))
plt.suptitle('Cepheids', y=0.99)
rects1 = ax.bar(x - width/2, all_r2s[0,:], width, label='Machine learning')
rects2 = ax.bar(x + width/2, all_r2s[1,:], width, label='Linear model')

plt.axhline(1, c='gray', linewidth=1.25, linestyle='--')

ax.set_ylabel('$R^2$')
ax.set_xticks(x)
ax.set_xticklabels(labels)
ax.set_ylim([0, 1.15])
ax.legend(loc='lower right')

def autolabel(rects):
    """Attach a text label above each bar in *rects*, displaying its height."""
    for rect in rects:
        height = rect.get_height()
        ax.annotate('%.3f' % height,
                    xy=(rect.get_x() + rect.get_width() / 2, height),
                    xytext=(0, 3),  # 3 points vertical offset
                    textcoords="offset points",
                    ha='center', va='bottom')

plt.rcParams["font.size"] = 12
autolabel(rects1)
autolabel(rects2)
plt.rcParams["font.size"] = 18
#autolabel(rects3)

plt.savefig('R2-ML-LM.pdf')
plt.show()

In [18]:

labels = ['$M$', '$\log\;R$', '$\log\;L$', '$T_{\\rm{eff}}$', '$M_I$', '$M_V$', '$V-I$', '$W$']

x = np.arange(len(labels))
width = 0.45

fig, ax = plt.subplots(figsize=(6.64306*2,4.10318716*0.9))
plt.suptitle('Cepheids', y=0.99)
rects1 = ax.bar(x, (all_sds[1,:] - all_sds[0,:])/all_sds[1,:], width)

ax.set_ylabel('Accuracy improvement\n$(\sigma_{\\rm{LM}} - \sigma_{\\rm{ML}}) / \sigma_{\\rm{LM}}$')
ax.set_xticks(x)
ax.set_xticklabels(labels)

ax.set_ylim([0, 0.8])
ax.set_yticks([0, 0.2, 0.4, 0.6, 0.8])
locs, labels = plt.yticks()
ax.set_yticklabels([str(int(loc*100)) + '%' for loc in locs])

def autolabel(rects):
    for rect in rects:
        height = rect.get_height()
        ax.annotate('%.1f' % (height*100) + '%',
                    xy=(rect.get_x() + rect.get_width() / 2, height),
                    xytext=(0, 3), 
                    textcoords="offset points",
                    ha='center', va='bottom')

autolabel(rects1)

plt.savefig('sds-ML-LM.pdf')
plt.show()

In [ ]:

In [19]:

ml_stds = []
ml_r2s = []

for idx, name in enumerate(X_columns):
    std = np.array(np.array(ml_pred[:,idx]) - DF[name]).std()
    print(name, 'std: %.3f' % std)
    ml_stds += [std]
    
    SS_tot = np.sum((DF[name] - DF[name].mean())**2)
    SS_res = np.sum((ml_pred[:,idx] - DF[name].values)**2)
    R2 = 1-SS_res/SS_tot
    ml_r2s += [R2]
    
    print(name, 'R2: %.3f' % R2)

M std: 0.350
M R2: 0.799
logR std: 0.011
logR R2: 0.994
logL std: 0.044
logL R2: 0.961
Teff std: 107.694
Teff R2: 0.885
I_M0 std: 0.101
I_M0 R2: 0.969
V_M0 std: 0.131
V_M0 R2: 0.936
VI std: 0.033
VI R2: 0.909
W std: 0.065
W R2: 0.991

In [20]:

lm_stds = []
lm_r2s = []

for idx, name in enumerate(X_columns):
    std = np.array(np.array(lm_pred[:,idx]) - DF[name]).std()
    print(name, 'std: %.3f' % std)
    lm_stds += [std]
    
    SS_tot = np.sum((DF[name] - DF[name].mean())**2)
    SS_res = np.sum((lm_pred[:,idx] - DF[name].values)**2)
    R2 = 1-SS_res/SS_tot
    lm_r2s += [R2]
    
    print(name, 'R2: %.3f' % R2)

M std: 0.564
M R2: 0.479
logR std: 0.017
logR R2: 0.986
logL std: 0.084
logL R2: 0.860
Teff std: 209.088
Teff R2: 0.568
I_M0 std: 0.193
I_M0 R2: 0.886
V_M0 std: 0.258
V_M0 R2: 0.754
VI std: 0.070
VI R2: 0.605
W std: 0.105
W R2: 0.976

In [ ]:

In [21]:

var = 'M'
lims = [4, 8]

plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Machine Learning: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)], c=DF['logL'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted Mass [M$_\odot$]')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='$\log\;L/$L$_\odot$', pad=0.02)
plt.text(7, 4.1, '$R^2$: %.3f' % ml_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.axhline(0, c='k', ls='--', linewidth=1.25)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)] - DF[var], c=DF['logL'])
plt.xlabel('Model Mass [M$_\odot$]')
plt.ylabel('Errors [M$_\odot$]')
plt.colorbar(label='$\log\;L/$L$_\odot$', pad=0.02)
plt.xlim(lims)
plt.ylim([-1.5, 1.5])
ax2.set_yticks([-1, 0, 1])
ax2.set_yticklabels([-1, 0, 1])
plt.text(6.35, -1.4, 'St. dev: %.2f M$_\odot$' % ml_stds[X_columns.index(var)])

plt.savefig('CEP-ML-mass.pdf')#, bbox_inches='tight')
plt.show()

In [22]:

var = 'logR'
lims = [1.4, 2.2]

fig = plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Linear Model: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], lm_pred[:,X_columns.index(var)], c=DF['M'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted Radius [$\log$ R$_\odot$]')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='Mass [M$_\odot$]', pad=0.02)
plt.text(1.98, 1.43, '$R^2$: %.3f' % lm_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.plot([lims[0], lims[1]], [0, 0], 'k--', zorder=0, linewidth=1.25)
plt.scatter(DF[var], lm_pred[:,X_columns.index(var)] - DF[var], c=DF['M'])
plt.colorbar(label='Mass [M$_\odot$]', pad=0.02)
plt.xlabel('Model Radius [$\log$ R$_\odot$]')
plt.ylabel('Errors [$\log$ R$_\odot$]')
plt.xlim(lims)
plt.ylim([-0.05, 0.05])
plt.text(1.42, -0.045, 'St. dev: %.3f $\log$ R$_\odot$' % lm_stds[X_columns.index(var)])

plt.savefig('CEP-LM-radius.pdf')#, bbox_inches='tight')
plt.show()

In [23]:

var = 'logR'
lims = [1.4, 2.2]

plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Machine Learning: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)], c=DF['M'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted Radius [$\log$ R$_\odot$]')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='Mass [M$_\odot$]', pad=0.02)
plt.text(1.98, 1.43, '$R^2$: %.3f' % ml_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.plot([lims[0], lims[1]], [0, 0], 'k--', zorder=0, linewidth=1.25)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)] - DF[var], c=DF['M'])
plt.colorbar(label='Mass [M$_\odot$]', pad=0.02)
plt.xlabel('Model Radius [$\log$ R$_\odot$]')
plt.ylabel('Errors [$\log$ R$_\odot$]')
plt.xlim(lims)
plt.ylim([-0.05, 0.05])
plt.text(1.42, -0.045, 'St. dev: %.3f $\log$ R$_\odot$' % ml_stds[X_columns.index(var)])

plt.savefig('CEP-ML-radius.pdf')#, bbox_inches='tight')
plt.show()

In [24]:

var = 'logL'
lims = [2.9, 4.05]

fig = plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Linear Model: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], lm_pred[:,X_columns.index(var)], c=DF['Teff'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted Luminosity [$\log$ L$_\odot$]')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.text(3.73, 2.93, '$R^2$: %.3f' % lm_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.plot([lims[0], lims[1]], [0, 0], 'k--', zorder=0, linewidth=1.25)
plt.scatter(DF['logL'], lm_pred[:,X_columns.index(var)] - DF['logL'], c=DF['Teff'])
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.xlabel('Model Luminosity [$\log$ L$_\odot$]')
plt.ylabel('Errors [$\log$ L$_\odot$]')
plt.xlim(lims)
plt.ylim([-0.3, 0.3])
plt.text(2.93, -0.28, 'St. dev: %.3f $\log$ L$_\odot$' % lm_stds[X_columns.index(var)])

plt.savefig('CEP-LM-luminosity.pdf')#, bbox_inches='tight')
plt.show()

In [25]:

lims = [2.9, 4.05]

plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Machine Learning: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)], c=DF['Teff'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted Luminosity [$\log$ L$_\odot$]')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.text(3.73, 2.93, '$R^2$: %.3f' % ml_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.plot([lims[0], lims[1]], [0, 0], 'k--', zorder=0, linewidth=1.25)
plt.scatter(DF['logL'], ml_pred[:,X_columns.index(var)] - DF['logL'], c=DF['Teff'])
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.xlabel('Model Luminosity [$\log$ L$_\odot$]')
plt.ylabel('Errors [$\log$ L$_\odot$]')
plt.xlim(lims)
plt.ylim([-0.3, 0.3])
plt.text(2.93, -0.28, 'St. dev: %.3f $\log$ L$_\odot$' % ml_stds[X_columns.index(var)])

plt.savefig('CEP-ML-luminosity.pdf')#, bbox_inches='tight')
plt.show()

In [26]:

var = 'W'
lims = [-4, -8]

fig = plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Linear Model: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], lm_pred[:,X_columns.index(var)], c=DF['Teff'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted Wesenheit Index')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.text(-6.9, -4.1, '$R^2$: %.3f' % lm_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.plot([lims[0], lims[1]], [0, 0], 'k--', zorder=0, linewidth=1.25)
plt.scatter(DF[var], lm_pred[:,X_columns.index(var)] - DF[var], c=DF['Teff'])
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.xlabel('Model Wesenheit Index')
plt.ylabel('Errors [mag]')
plt.xlim(lims)
plt.ylim([-0.4, 0.4])
plt.text(-4.1, -0.37, 'St. dev: %.2f mag' % lm_stds[X_columns.index(var)])

plt.savefig('CEP-LM-W.pdf')#, bbox_inches='tight')
plt.show()

In [27]:

var = 'W'
lims = [-4, -8]

fig = plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Machine Learning: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)], c=DF['Teff'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted Wesenheit Index')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.text(-6.9, -4.1, '$R^2$: %.3f' % ml_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.plot([lims[0], lims[1]], [0, 0], 'k--', zorder=0, linewidth=1.25)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)] - DF[var], c=DF['Teff'])
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.xlabel('Model Wesenheit Index')
plt.ylabel('Errors [mag]')
plt.xlim(lims)
plt.ylim([-0.4, 0.4])
plt.text(-4.1, -0.37, 'St. dev: %.3f mag' % ml_stds[X_columns.index(var)])

plt.savefig('CEP-ML-W.pdf')#, bbox_inches='tight')
plt.show()

In [28]:

var = 'V_M0'
lims = [-2.5, -5]

fig = plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Linear Model: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], lm_pred[:,X_columns.index(var)], c=DF['Teff'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted $M_V$')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.text(-4.3, -2.56, '$R^2$: %.3f' % lm_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.plot([lims[0], lims[1]], [0, 0], 'k--', zorder=0, linewidth=1.25)
plt.scatter(DF[var], lm_pred[:,X_columns.index(var)] - DF[var], c=DF['Teff'])
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.xlabel('Model $M_V$')
plt.ylabel('Errors [mag]')
plt.xlim(lims)
plt.ylim([-0.8, 0.8])
plt.text(-2.57, -0.75, 'St. dev: %.2f mag' % lm_stds[X_columns.index(var)])

plt.savefig('CEP-LM-V_M0.pdf')#, bbox_inches='tight')
plt.show()

In [29]:

var = 'V_M0'
lims = [-2.5, -5]

fig = plt.figure(figsize=(6.64306,4.10318716*2))
plt.suptitle('Machine Learning: Cepheids', y=0.995)

ax = plt.subplot(2,1,1)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)], c=DF['Teff'])
plt.plot([lims[0],lims[1]], [lims[0],lims[1]], 'k--', alpha=0.75, zorder=0)
plt.ylabel('Predicted $M_V$')
plt.xlim(lims)
plt.ylim(lims)
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.text(-4.3, -2.56, '$R^2$: %.3f' % ml_r2s[X_columns.index(var)])

ax2 = plt.subplot(2,1,2, sharex=ax)
plt.plot([lims[0], lims[1]], [0, 0], 'k--', zorder=0, linewidth=1.25)
plt.scatter(DF[var], ml_pred[:,X_columns.index(var)] - DF[var], c=DF['Teff'])
plt.colorbar(label='$T_{\\rm{eff}}/$K', pad=0.02)
plt.xlabel('Model $M_V$')
plt.ylabel('Errors [mag]')
plt.xlim(lims)
plt.ylim([-0.8, 0.8])
plt.text(-2.57, -0.75, 'St. dev: %.2f mag' % ml_stds[X_columns.index(var)])

plt.savefig('CEP-ML-V_M0.pdf')#, bbox_inches='tight')
plt.show()

In [ ]:

Significance testing

In [30]:

# (neural network with log P and lightcurve) vs (linear model with log P) with the Wilcoxon test 

for name in X_columns: 
    ml_err = abs(DF[name] - ml_pred[:,X_columns.index(name)])
    lm_err = abs(DF[name] - lm_pred[:,X_columns.index(name)])
    print(name, sp.stats.wilcoxon(lm_err, ml_err).pvalue)

M 4.8226885861573445e-28
logR 1.2904685567980838e-25
logL 7.410398478671702e-40
Teff 2.768046944534012e-45
I_M0 2.3024578991353531e-38
V_M0 2.873842493932314e-41
VI 4.765730830885012e-46
W 1.8762776320162059e-28

In [ ]:

In [31]:

# (neural network with log P and lightcurve) vs (linear model with log P) with 5x2 cv test 

np.random.seed(0) 

ml = TransformedTargetRegressor(regressor=Pipeline(
            [('scaler', RobustScaler()), 
             ('mlp', MLPRegressor(hidden_layer_sizes=(100, 100), 
                                  max_iter=2000, activation='relu', solver='lbfgs', tol=1e-7))]),
         transformer=RobustScaler())
lm = LinearRegression()

first_p1 = 0 
s2s = []

for ii in range(5):
    ml_scores = []
    lm_scores = []
    
    cv = ShuffleSplit(n_splits=2, random_state=ii, train_size=0.5, test_size=0.5)
    
    for train_index, test_index in cv.split(DF):
        ml.fit(DF.iloc[train_index][y_columns], DF.iloc[train_index][X_columns])
        lm.fit(DF.iloc[train_index][['logP']],  DF.iloc[train_index][X_columns])
        
        ml_predict = ml.predict(DF.iloc[test_index][y_columns])
        lm_predict = lm.predict(DF.iloc[test_index][['logP']])
        
        ml_scores_ = []
        lm_scores_ = []
        
        for idx, name in enumerate(X_columns):
            SS_tot = np.sum((DF.iloc[test_index][name] - DF.iloc[test_index][name].mean())**2)
            
            ml_SS_res = np.sum((ml_predict[:,idx] - DF.iloc[test_index][name].values)**2)
            ml_R2 = 1-ml_SS_res/SS_tot
            #ml_scores_ += [ml_R2]
            ml_scores_ += [ml_SS_res]
            
            lm_SS_res = np.sum((lm_predict[:,idx] - DF.iloc[test_index][name].values)**2)
            lm_R2 = 1-lm_SS_res/SS_tot
            #lm_scores_ += [lm_R2]
            lm_scores_ += [lm_SS_res]
        
        ml_scores += [ml_scores_]
        lm_scores += [lm_scores_]
    
    ml_scores = np.array(ml_scores)
    lm_scores = np.array(lm_scores)
    
    p1 = ml_scores[0,:] - lm_scores[0,:]
    p2 = ml_scores[1,:] - lm_scores[1,:]
    p_bar = (p1 + p2)/2
    s2 = (p1 - p_bar)**2 + (p2 - p_bar)**2
    
    if ii == 0:
        first_p1 = p1
    s2s += [s2]

first_p1 = np.array(first_p1)
s2s = np.array(s2s)

for idx, name in enumerate(X_columns):
    p = stats.t.sf(np.abs(first_p1[idx]) / np.sqrt(1/5. * sum(s2s[:,idx])), 5)*2.
    print(name, '%.2E' % p) # '%.10f' % p)

M 9.64E-05
logR 4.37E-03
logL 3.03E-06
Teff 6.29E-06
I_M0 3.67E-06
V_M0 4.78E-06
VI 4.82E-06
W 1.57E-04

In [32]:

# (neural network with log P and lightcurve) vs (linear model with log P) with Wilcoxon signed-rank test 

np.random.seed(0) 

ml = TransformedTargetRegressor(regressor=Pipeline(
            [('scaler', RobustScaler()), 
             ('mlp', MLPRegressor(hidden_layer_sizes=(100, 100), 
                                  max_iter=2000, activation='relu', solver='lbfgs', tol=1e-7))]),
         transformer=RobustScaler())
lm = LinearRegression()

cv = ShuffleSplit(n_splits=2, random_state=0, train_size=0.5, test_size=0.5)
train_set, test_set = list(cv.split(DF))[0]

ml.fit(DF.iloc[train_set][y_columns], DF.iloc[train_set][X_columns])
lm.fit(DF.iloc[train_set][['logP']],  DF.iloc[train_set][X_columns])

ml_predict = ml.predict(DF.iloc[test_set][y_columns])
lm_predict = lm.predict(DF.iloc[test_set][['logP']])

for idx, name in enumerate(X_columns):
    ml_SE = (ml_predict[:,idx] - DF.iloc[test_set][name].values)**2
    lm_SE = (lm_predict[:,idx] - DF.iloc[test_set][name].values)**2
    
    wil = sp.stats.wilcoxon(ml_SE, lm_SE)
    print(name, ml_SE.mean() < lm_SE.mean(), wil.pvalue/2.) # one sided test 

M True 4.1581837797536337e-13
logR True 3.63728908382849e-14
logL True 6.160719974907984e-21
Teff True 5.654911569738892e-24
I_M0 True 5.818796617528765e-20
V_M0 True 3.652754351987831e-21
VI True 2.108630817227543e-23
W True 6.818718841112479e-14

In [ ]:

In [33]:

# (neural network with log P and lightcurve) vs (linear model with log P and lightcurve) with 5x2cv test 

np.random.seed(0) 

ml = TransformedTargetRegressor(regressor=Pipeline(
            [('scaler', RobustScaler()), 
             ('mlp', MLPRegressor(hidden_layer_sizes=(100, 100), 
                                  max_iter=2000, activation='relu', solver='lbfgs', tol=1e-7))]),
         transformer=RobustScaler())
lm = LinearRegression()

first_p1 = 0 
s2s = []

for ii in range(5):
    ml_scores = []
    lm_scores = []
    
    cv = ShuffleSplit(n_splits=2, random_state=ii, train_size=0.5, test_size=0.5)
    
    for train_index, test_index in cv.split(DF):
        ml.fit(DF.iloc[train_index][y_columns], DF.iloc[train_index][X_columns])
        lm.fit(DF.iloc[train_index][y_columns], DF.iloc[train_index][X_columns])
        
        ml_predict = ml.predict(DF.iloc[test_index][y_columns])
        lm_predict = lm.predict(DF.iloc[test_index][y_columns])
        
        ml_scores_ = []
        lm_scores_ = []
        
        for idx, name in enumerate(X_columns):
            SS_tot = np.sum((DF.iloc[test_index][name] - DF.iloc[test_index][name].mean())**2)
            
            ml_SS_res = np.sum((ml_predict[:,idx] - DF.iloc[test_index][name].values)**2)
            ml_R2 = 1-ml_SS_res/SS_tot
            #ml_scores_ += [ml_R2]
            ml_scores_ += [ml_SS_res]
            
            lm_SS_res = np.sum((lm_predict[:,idx] - DF.iloc[test_index][name].values)**2)
            lm_R2 = 1-lm_SS_res/SS_tot
            #lm_scores_ += [lm_R2]
            lm_scores_ += [lm_SS_res]
        
        ml_scores += [ml_scores_]
        lm_scores += [lm_scores_]
    
    ml_scores = np.array(ml_scores)
    lm_scores = np.array(lm_scores)
    
    p1 = ml_scores[0,:] - lm_scores[0,:]
    p2 = ml_scores[1,:] - lm_scores[1,:]
    p_bar = (p1 + p2)/2
    s2 = (p1 - p_bar)**2 + (p2 - p_bar)**2
    
    if ii == 0:
        first_p1 = p1
    s2s += [s2]

first_p1 = np.array(first_p1)
s2s = np.array(s2s)

for idx, name in enumerate(X_columns):
    p = stats.t.sf(np.abs(first_p1[idx]) / np.sqrt(1/5. * sum(s2s[:,idx])), 5)/2. # one sided test 
    print(name, '%.2E' % p)

M 3.29E-04
logR 2.94E-03
logL 3.87E-04
Teff 3.76E-04
I_M0 6.87E-04
V_M0 5.52E-04
VI 2.97E-04
W 4.23E-04

In [34]:

# (neural network with log P and lightcurve) vs (linear model with log P and lightcurve) with Wilcoxon signed-rank test 

np.random.seed(0) 

ml = TransformedTargetRegressor(regressor=Pipeline(
            [('scaler', RobustScaler()), 
             ('mlp', MLPRegressor(hidden_layer_sizes=(100, 100), 
                                  max_iter=2000, activation='relu', solver='lbfgs', tol=1e-7))]),
         transformer=RobustScaler())
lm = LinearRegression()

cv = ShuffleSplit(n_splits=2, random_state=0, train_size=0.5, test_size=0.5)
train_set, test_set = list(cv.split(DF))[0]

ml.fit(DF.iloc[train_set][y_columns], DF.iloc[train_set][X_columns])
lm.fit(DF.iloc[train_set][y_columns], DF.iloc[train_set][X_columns])

ml_predict = ml.predict(DF.iloc[test_set][y_columns])
lm_predict = lm.predict(DF.iloc[test_set][y_columns])

for idx, name in enumerate(X_columns):
    ml_SE = (ml_predict[:,idx] - DF.iloc[test_set][name].values)**2
    lm_SE = (lm_predict[:,idx] - DF.iloc[test_set][name].values)**2
    
    wil = sp.stats.wilcoxon(ml_SE, lm_SE)
    print(name, ml_SE.mean() < lm_SE.mean(), wil.pvalue/2.) # one sided test 

M True 3.6221348278706677e-12
logR True 5.371970878763796e-13
logL True 3.3695494986483773e-16
Teff True 1.1229376543350066e-18
I_M0 True 1.880937254410796e-15
V_M0 True 2.497344286221803e-16
VI True 5.0889774862789716e-18
W True 8.964825529966717e-12

In [ ]:

Now train on all models and run on real data

In [35]:

np.random.seed(0) 

ml = TransformedTargetRegressor(regressor=Pipeline(
            [('scaler', RobustScaler()), 
             ('mlp', MLPRegressor(hidden_layer_sizes=(100, 100), 
                                  max_iter=2000, activation='relu', solver='lbfgs', tol=1e-7))]),
         transformer=RobustScaler())
lm = LinearRegression()

ml.fit(DF[y_columns], DF[X_columns])
lm.fit(DF[['logP']], DF[X_columns])

Out[35]:

LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,
         normalize=False)

In [36]:

import joblib
joblib.dump(ml, 'Cepheids.ann')

Out[36]:

['Cepheids.ann']

In [37]:

maxs = DF[y_columns].quantile(0.95)
mins = DF[y_columns].quantile(0.05)
print(maxs, '\n\n', mins)

logP           1.267723
I_Amplitude    0.949500
I_Skewness     4.636500
I_acuteness    1.587500
V_Amplitude    1.509000
V_Skewness     5.008500
V_acuteness    2.047500
I_A1           0.341895
I_A2           0.129675
I_A3           0.077520
V_A1           0.518150
V_A2           0.202490
V_A3           0.120370
Name: 0.95, dtype: float64 

 logP           0.553626
I_Amplitude    0.103000
I_Skewness     0.609000
I_acuteness    0.391500
V_Amplitude    0.159000
V_Skewness     0.722500
V_acuteness    0.454500
I_A1           0.044220
I_A2           0.010055
I_A3           0.002625
V_A1           0.073965
V_A2           0.016170
V_A3           0.004420
Name: 0.05, dtype: float64

In [38]:

X_maxs = DF[X_columns].max()
X_mins = DF[X_columns].min()
print(X_maxs, '\n\n', X_mins)

M          7.500000
logR       2.112889
logL       3.830000
Teff    6100.000000
I_M0      -3.367150
V_M0      -2.686910
VI         1.122720
W         -4.381439
dtype: float64 

 M          4.600000
logR       1.477102
logL       3.020000
Teff    4600.000000
I_M0      -5.530710
V_M0      -4.765800
VI         0.595510
W         -7.256976
dtype: float64

In [39]:

star_names = []
ests = []
e_ests = []
logPs = []

lm_ests = []
e_lm_ests = []

LMC_CEP_dir = '/scratch/seismo/bellinger/asteroseismology/regression/perturb/LMC_CEP'
for star_filename in tqdm(os.listdir(LMC_CEP_dir)):
    star_name = star_filename.split('_')[0]
    star_data = pd.read_table(os.path.join(LMC_CEP_dir, star_filename), sep='\s+')
    star_data['Period'] = np.log10(star_data['Period'])
    star_data.rename(columns={'Period':'logP'}, inplace=True)
    
    if np.any(star_data[y_columns] >= maxs) or np.any(star_data[y_columns] <= mins):
        #print('Skipping', star_name)
        continue 
    
    res = ml.predict(star_data[y_columns])
    
    if np.any([res_i >= X_maxs for res_i in res]) or \
       np.any([res_i <= X_mins for res_i in res]):
        #print('Skipping', star_name)
        continue
    
    ests += [res[0]]
    e_ests += [res.std(axis=0)]
    
    lm_res = lm.predict(star_data[['logP']])
    lm_ests += [lm_res[0]]
    e_lm_ests += [lm_res.std(axis=0)]
    
    star_names += [star_name]
    logPs += [star_data['logP'].iloc[0]]

logPs = np.array(logPs)

ests = np.array(ests)
e_ests = np.array(e_ests)

lm_ests = np.array(lm_ests)
e_lm_ests = np.array(e_lm_ests)

HBox(children=(IntProgress(value=0, max=2132), HTML(value='')))

In [40]:

ests.shape

Out[40]:

(325, 8)

In [41]:

e_ests_ = np.array([np.sqrt(e_ests[ii]**2 + np.array(ml_stds)**2) 
                    for ii in range(len(e_ests))])

In [42]:

ests_ = np.vstack(chain.from_iterable(((ests[:,ii], e_ests_[:,ii]) for ii in range(ests.shape[1])))).T

In [43]:

#ests_DF = pd.DataFrame(ests, columns=X_columns)
ests_DF = pd.DataFrame(ests_, columns=list(chain.from_iterable(zip(X_columns, ['e_'+X_col for X_col in X_columns]))))
ests_DF.insert(0, 'ID', star_names)
ests_DF

Out[43]:

	ID	M	e_M	logR	e_logR	logL	e_logL	Teff	e_Teff	I_M0	e_I_M0	V_M0	e_V_M0	VI	e_VI	W	e_W
0	OGLE-LMC-CEP-0033	5.981732	0.390032	1.756617	0.014038	3.513580	0.057473	5784.480902	137.084847	-4.660956	0.132794	-3.963571	0.174257	0.700211	0.044123	-5.748440	0.082892
1	OGLE-LMC-CEP-0050	6.166502	0.399251	1.780000	0.013875	3.541317	0.058653	5719.021219	139.354356	-4.744733	0.133739	-4.020167	0.177962	0.720711	0.045507	-5.862415	0.082405
2	OGLE-LMC-CEP-0057	6.871249	0.398144	1.861168	0.011742	3.693657	0.044538	5684.717505	110.927487	-5.148841	0.101086	-4.423182	0.131607	0.721185	0.034501	-6.260633	0.066180
3	OGLE-LMC-CEP-0078	5.699958	0.366346	1.749439	0.011992	3.493068	0.045377	5763.870880	109.680605	-4.608432	0.103839	-3.901637	0.134257	0.708586	0.034162	-5.707185	0.068343
4	OGLE-LMC-CEP-0103	6.330912	0.403360	1.760601	0.013788	3.570397	0.048609	5941.385137	109.314158	-4.794215	0.111991	-4.144789	0.141975	0.647057	0.034063	-5.795697	0.077433
5	OGLE-LMC-CEP-0107	5.980849	0.355053	1.799100	0.011692	3.584044	0.050546	5732.983831	122.383591	-4.840953	0.114402	-4.120565	0.150769	0.720462	0.038612	-5.961329	0.069967
6	OGLE-LMC-CEP-0123	5.826094	0.360087	1.736962	0.011951	3.461769	0.046147	5738.516324	111.949047	-4.529634	0.105788	-3.816418	0.137326	0.716085	0.035095	-5.639910	0.068627
7	OGLE-LMC-CEP-0155	6.250097	0.391777	1.835071	0.012150	3.702338	0.045001	5870.056191	109.880246	-5.143550	0.102843	-4.480868	0.132649	0.665213	0.034128	-6.182993	0.068784
8	OGLE-LMC-CEP-0158	5.487512	0.378884	1.735524	0.012837	3.476436	0.047695	5801.943364	111.430148	-4.557389	0.109506	-3.861329	0.140579	0.698613	0.034784	-5.643501	0.073200
9	OGLE-LMC-CEP-0162	5.465754	0.506745	1.647071	0.018590	3.367102	0.052835	6015.969035	108.031712	-4.252390	0.127329	-3.626834	0.153373	0.629550	0.033601	-5.230378	0.099812
10	OGLE-LMC-CEP-0169	5.528907	0.440518	1.673293	0.016346	3.328034	0.051738	5707.637170	111.208387	-4.201153	0.121787	-3.473906	0.150703	0.723450	0.034694	-5.320069	0.089202
11	OGLE-LMC-CEP-0177	5.548326	0.459980	1.600906	0.016786	3.215232	0.051782	5841.181651	108.523398	-3.899994	0.122690	-3.216864	0.151590	0.687223	0.033868	-4.966730	0.091349
12	OGLE-LMC-CEP-0189	5.360901	0.436592	1.677614	0.014538	3.383387	0.048328	5870.029253	108.519472	-4.311477	0.113080	-3.632315	0.141764	0.679045	0.033771	-5.362733	0.080284
13	OGLE-LMC-CEP-0212	5.827662	0.388543	1.878070	0.012839	3.678507	0.058507	5512.321224	136.168289	-5.110928	0.134717	-4.306381	0.175297	0.796622	0.043224	-6.345276	0.080668
14	OGLE-LMC-CEP-0250	5.810384	0.390116	1.705167	0.014125	3.381746	0.049315	5676.234659	110.116633	-4.344498	0.114007	-3.614058	0.143999	0.729551	0.034345	-5.471039	0.078992
15	OGLE-LMC-CEP-0264	5.340560	0.423963	1.564663	0.015050	3.136247	0.049791	5836.566834	108.575913	-3.702632	0.116724	-3.017599	0.146205	0.691011	0.033859	-4.779438	0.083818
16	OGLE-LMC-CEP-0269	5.223341	0.400990	1.565511	0.014293	3.165140	0.048471	5913.272544	108.283659	-3.755813	0.113094	-3.089476	0.142398	0.671343	0.033740	-4.801272	0.079445
17	OGLE-LMC-CEP-0291	5.214949	0.442964	1.556525	0.016287	3.109353	0.052164	5790.705025	108.936928	-3.643970	0.122596	-2.942489	0.151575	0.705261	0.033957	-4.738173	0.089745
18	OGLE-LMC-CEP-0306	6.141272	0.370203	1.737548	0.011800	3.485621	0.045800	5818.700016	110.334754	-4.580542	0.104712	-3.888373	0.135723	0.692407	0.034412	-5.653477	0.067836
19	OGLE-LMC-CEP-0316	5.399814	0.437950	1.557504	0.015657	3.109774	0.050749	5786.677530	108.652587	-3.643539	0.119598	-2.943436	0.148702	0.705220	0.033886	-4.737486	0.086755
20	OGLE-LMC-CEP-0329	5.237083	0.413132	1.567480	0.014386	3.134955	0.049245	5797.709739	108.553704	-3.704776	0.114282	-3.008118	0.143684	0.701122	0.033776	-4.793327	0.080557
21	OGLE-LMC-CEP-0356	6.021884	0.372840	1.892691	0.012304	3.672953	0.055787	5424.543155	129.241502	-5.087434	0.127832	-4.253778	0.166450	0.838968	0.040944	-6.382608	0.077124
22	OGLE-LMC-CEP-0377	6.608692	0.414287	1.732983	0.014289	3.521981	0.049051	5953.413965	110.958698	-4.647231	0.114633	-3.996031	0.144837	0.648584	0.034730	-5.650205	0.080014
23	OGLE-LMC-CEP-0458	5.281688	0.407069	1.562998	0.014325	3.119723	0.048912	5783.798184	108.395195	-3.669420	0.113737	-2.967387	0.143118	0.706554	0.033738	-4.766181	0.080090
24	OGLE-LMC-CEP-0482	5.727776	0.369432	1.749335	0.012144	3.501535	0.047825	5783.424213	114.584404	-4.631902	0.109061	-3.929575	0.141729	0.700820	0.036012	-5.712972	0.069977
25	OGLE-LMC-CEP-0492	5.020713	0.401435	1.636063	0.013508	3.320696	0.047238	5934.848049	108.239370	-4.143013	0.109388	-3.483671	0.138702	0.660544	0.033665	-5.165452	0.075554
26	OGLE-LMC-CEP-0505	5.297052	0.423142	1.583592	0.015286	3.160552	0.050114	5777.273315	108.396204	-3.772481	0.117093	-3.066106	0.146068	0.709262	0.033752	-4.871374	0.084179
27	OGLE-LMC-CEP-0520	6.116985	0.357136	1.793759	0.012131	3.572909	0.051777	5728.852765	121.591288	-4.811805	0.118213	-4.096073	0.154286	0.719826	0.038372	-5.930786	0.073430
28	OGLE-LMC-CEP-0542	5.487110	0.441655	1.647855	0.015728	3.299480	0.049094	5788.135818	108.023427	-4.113048	0.116194	-3.408498	0.144080	0.703619	0.033552	-5.200917	0.085542
29	OGLE-LMC-CEP-0561	5.972216	0.374926	1.872249	0.012086	3.630625	0.067437	5414.643974	165.521892	-4.988641	0.152511	-4.163650	0.201596	0.827615	0.051492	-6.270989	0.083603
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
295	OGLE-LMC-CEP-4153	5.840818	0.353542	1.794408	0.011735	3.557715	0.048026	5673.105028	114.058821	-4.781374	0.109741	-4.046425	0.142773	0.737870	0.035679	-5.928041	0.069112
296	OGLE-LMC-CEP-4176	5.858068	0.352757	1.780428	0.011477	3.562131	0.046822	5770.803045	112.524011	-4.787490	0.106400	-4.082022	0.138313	0.702135	0.035280	-5.874449	0.066939
297	OGLE-LMC-CEP-4194	5.867758	0.373700	1.774839	0.012186	3.558133	0.048747	5809.781229	115.554813	-4.772283	0.110597	-4.075753	0.144085	0.694995	0.036264	-5.853785	0.070912
298	OGLE-LMC-CEP-4211	5.988204	0.354018	1.788256	0.011704	3.568296	0.048561	5752.672642	116.005497	-4.803398	0.110395	-4.093041	0.143961	0.712956	0.036298	-5.910954	0.069196
299	OGLE-LMC-CEP-4249	5.439077	0.458192	1.578760	0.016903	3.188277	0.052242	5908.389470	108.758928	-3.822877	0.124137	-3.160218	0.153196	0.668875	0.033980	-4.865996	0.092401
300	OGLE-LMC-CEP-4257	5.182741	0.431018	1.585972	0.015937	3.222722	0.050965	5957.248740	108.606825	-3.893257	0.120344	-3.241180	0.149290	0.655313	0.033925	-4.912366	0.087613
301	OGLE-LMC-CEP-4274	5.462647	0.445767	1.653439	0.015338	3.316108	0.048316	5807.763804	108.420563	-4.156299	0.112773	-3.459070	0.140357	0.696064	0.033624	-5.235904	0.082794
302	OGLE-LMC-CEP-4281	5.340388	0.446426	1.658971	0.015163	3.332365	0.048060	5832.036830	108.814164	-4.192350	0.112551	-3.501848	0.140470	0.690884	0.033760	-5.264705	0.082117
303	OGLE-LMC-CEP-4287	5.793736	0.449801	1.714802	0.016004	3.429586	0.051858	5775.387942	110.786713	-4.445291	0.121385	-3.742566	0.151172	0.703409	0.034693	-5.531175	0.087689
304	OGLE-LMC-CEP-4293	5.492365	0.449147	1.592466	0.016686	3.209056	0.051575	5878.997746	108.585078	-3.877234	0.122038	-3.203930	0.150807	0.678308	0.033884	-4.932093	0.090383
305	OGLE-LMC-CEP-4316	5.319296	0.355738	1.742126	0.012140	3.453836	0.048886	5681.251473	115.139574	-4.526689	0.111408	-3.800150	0.144114	0.728685	0.036143	-5.654391	0.070567
306	OGLE-LMC-CEP-4317	6.067925	0.373260	1.844272	0.012223	3.671292	0.056455	5704.296014	135.006430	-5.077455	0.130387	-4.350499	0.169925	0.723217	0.043282	-6.206211	0.076856
307	OGLE-LMC-CEP-4319	5.800130	0.398842	1.706651	0.014260	3.416578	0.048475	5786.500997	111.576645	-4.409215	0.112284	-3.707509	0.142398	0.703287	0.034861	-5.500201	0.078638
308	OGLE-LMC-CEP-4330	5.330297	0.396520	1.634917	0.013571	3.267188	0.046495	5771.216637	107.889030	-4.036485	0.107953	-3.328429	0.136795	0.708039	0.033490	-5.132767	0.075235
309	OGLE-LMC-CEP-4396	5.481457	0.437013	1.613785	0.015762	3.232454	0.050284	5805.610560	108.370159	-3.948748	0.118420	-3.250918	0.147182	0.699603	0.033765	-5.031833	0.086105
310	OGLE-LMC-CEP-4402	5.875651	0.354651	1.788180	0.011433	3.571531	0.048785	5749.355273	120.686002	-4.816530	0.109742	-4.107320	0.144842	0.706930	0.038068	-5.911652	0.067039
311	OGLE-LMC-CEP-4409	5.636537	0.369849	1.702387	0.012642	3.360739	0.046654	5630.602752	108.162740	-4.299324	0.106931	-3.550974	0.136734	0.745008	0.033653	-5.445785	0.071585
312	OGLE-LMC-CEP-4414	5.853990	0.400237	1.682367	0.013374	3.362379	0.046351	5768.517908	108.623317	-4.277952	0.106947	-3.570380	0.135905	0.706007	0.033722	-5.371111	0.074175
313	OGLE-LMC-CEP-4440	5.423800	0.396749	1.629071	0.013535	3.256091	0.046498	5769.328847	107.860387	-4.008001	0.107730	-3.296252	0.136519	0.710061	0.033478	-5.105987	0.074993
314	OGLE-LMC-CEP-4465	5.335445	0.430254	1.567492	0.015697	3.135683	0.050066	5801.744938	108.267175	-3.702393	0.117825	-3.000760	0.146715	0.705030	0.033744	-4.795042	0.085713
315	OGLE-LMC-CEP-4470	5.353141	0.442194	1.577129	0.016293	3.181481	0.051488	5895.259448	108.828612	-3.808703	0.121953	-3.141582	0.151200	0.672580	0.033991	-4.856896	0.089570
316	OGLE-LMC-CEP-4474	5.457405	0.456051	1.662122	0.015783	3.333803	0.049024	5812.066895	108.743552	-4.200595	0.114823	-3.505129	0.142242	0.694569	0.033736	-5.278677	0.085169
317	OGLE-LMC-CEP-4475	5.313539	0.404938	1.584267	0.014311	3.170286	0.048585	5801.745285	108.321130	-3.791293	0.113218	-3.091693	0.142506	0.702613	0.033724	-4.880608	0.079589
318	OGLE-LMC-CEP-4476	5.390528	0.456553	1.654910	0.015396	3.340119	0.048401	5872.781626	108.754571	-4.202901	0.113889	-3.523501	0.141532	0.677572	0.033775	-5.254489	0.083236
319	OGLE-LMC-CEP-4484	5.213186	0.430378	1.647035	0.015256	3.274910	0.049997	5710.702515	108.826781	-4.067261	0.116416	-3.341477	0.145289	0.723262	0.033844	-5.184288	0.083809
320	OGLE-LMC-CEP-4504	5.313000	0.414688	1.594631	0.014793	3.208892	0.048698	5852.826370	108.104109	-3.878441	0.113918	-3.192993	0.142975	0.687920	0.033657	-4.944660	0.081253
321	OGLE-LMC-CEP-4512	6.109729	0.361390	1.793811	0.013051	3.569567	0.058209	5719.497818	133.394190	-4.809538	0.133576	-4.090534	0.174047	0.722550	0.042394	-5.929879	0.081163
322	OGLE-LMC-CEP-4524	5.377051	0.419763	1.603084	0.015022	3.203401	0.049523	5779.593970	108.407770	-3.877106	0.116135	-3.170269	0.145171	0.708462	0.033767	-4.972559	0.082994
323	OGLE-LMC-CEP-4544	4.861819	0.355307	1.752786	0.011574	3.439831	0.046230	5574.115821	113.031667	-4.508021	0.104629	-3.746073	0.136494	0.761896	0.035316	-5.689614	0.066140
324	OGLE-LMC-CEP-4600	6.015916	0.494931	1.887622	0.016501	3.646813	0.088076	5364.440289	201.291367	-5.039300	0.203981	-4.179848	0.268950	0.852019	0.065033	-6.357413	0.114394

325 rows × 17 columns

In [44]:

ests_DF.iloc[1:10].to_latex(longtable=False, index=False)

Out[44]:

'\\begin{tabular}{lrrrrrrrrrrrrrrrr}\n\\toprule\n                ID &         M &       e\\_M &      logR &    e\\_logR &      logL &    e\\_logL &         Teff &      e\\_Teff &      I\\_M0 &    e\\_I\\_M0 &      V\\_M0 &    e\\_V\\_M0 &        VI &      e\\_VI &         W &       e\\_W \\\\\n\\midrule\n OGLE-LMC-CEP-0050 &  6.166502 &  0.399251 &  1.780000 &  0.013875 &  3.541317 &  0.058653 &  5719.021219 &  139.354356 & -4.744733 &  0.133739 & -4.020167 &  0.177962 &  0.720711 &  0.045507 & -5.862415 &  0.082405 \\\\\n OGLE-LMC-CEP-0057 &  6.871249 &  0.398144 &  1.861168 &  0.011742 &  3.693657 &  0.044538 &  5684.717505 &  110.927487 & -5.148841 &  0.101086 & -4.423182 &  0.131607 &  0.721185 &  0.034501 & -6.260633 &  0.066180 \\\\\n OGLE-LMC-CEP-0078 &  5.699958 &  0.366346 &  1.749439 &  0.011992 &  3.493068 &  0.045377 &  5763.870880 &  109.680605 & -4.608432 &  0.103839 & -3.901637 &  0.134257 &  0.708586 &  0.034162 & -5.707185 &  0.068343 \\\\\n OGLE-LMC-CEP-0103 &  6.330912 &  0.403360 &  1.760601 &  0.013788 &  3.570397 &  0.048609 &  5941.385137 &  109.314158 & -4.794215 &  0.111991 & -4.144789 &  0.141975 &  0.647057 &  0.034063 & -5.795697 &  0.077433 \\\\\n OGLE-LMC-CEP-0107 &  5.980849 &  0.355053 &  1.799100 &  0.011692 &  3.584044 &  0.050546 &  5732.983831 &  122.383591 & -4.840953 &  0.114402 & -4.120565 &  0.150769 &  0.720462 &  0.038612 & -5.961329 &  0.069967 \\\\\n OGLE-LMC-CEP-0123 &  5.826094 &  0.360087 &  1.736962 &  0.011951 &  3.461769 &  0.046147 &  5738.516324 &  111.949047 & -4.529634 &  0.105788 & -3.816418 &  0.137326 &  0.716085 &  0.035095 & -5.639910 &  0.068627 \\\\\n OGLE-LMC-CEP-0155 &  6.250097 &  0.391777 &  1.835071 &  0.012150 &  3.702338 &  0.045001 &  5870.056191 &  109.880246 & -5.143550 &  0.102843 & -4.480868 &  0.132649 &  0.665213 &  0.034128 & -6.182993 &  0.068784 \\\\\n OGLE-LMC-CEP-0158 &  5.487512 &  0.378884 &  1.735524 &  0.012837 &  3.476436 &  0.047695 &  5801.943364 &  111.430148 & -4.557389 &  0.109506 & -3.861329 &  0.140579 &  0.698613 &  0.034784 & -5.643501 &  0.073200 \\\\\n OGLE-LMC-CEP-0162 &  5.465754 &  0.506745 &  1.647071 &  0.018590 &  3.367102 &  0.052835 &  6015.969035 &  108.031712 & -4.252390 &  0.127329 & -3.626834 &  0.153373 &  0.629550 &  0.033601 & -5.230378 &  0.099812 \\\\\n\\bottomrule\n\\end{tabular}\n'

In [45]:

def signif(x, digits=6):
    if x == 0 or not isfinite(x):
        return x
    digits -= ceil(log10(abs(x)))
    rounded = round(x, digits)
    if rounded > 10:
        rounded = int(rounded)
    return rounded

def formatter(val, unc):
    unc = str(signif(unc, 2))
    if len(unc) == 1:
        unc += '.0'
    if float(unc) < 10:
        if unc[-2] == '0' or (unc[-2] == '.' and unc[-3] == '0'):
            unc += '0'
        dec_places = len(unc.split('.')[1])
        val = str(val).split('.')
        val = val[0] + '.' + val[1][:dec_places]
    else:
        val = str(val).split('.')[0]
        if len(unc) > 2:
            val = val[:len(val) - len(unc) + 2] + '0'*(len(val) - len(unc))
    return [val, unc]

In [46]:

for index, row in ests_DF.iloc[0:10].iterrows():
    out_str = row['ID'].split('-')[-1]
    
    rest = row[1:]
    for ii in range(len(rest) - 1):
        if ii % 2 != 0: # every other column contains the uncertainty 
            continue
        
        val, unc = formatter(rest[ii], rest[ii+1])
        out_str += ' & ' + val + ' $\pm$ ' + unc
    
    out_str += r' \\'
    
    print(out_str)

0033 & 5.98 $\pm$ 0.39 & 1.756 $\pm$ 0.014 & 3.513 $\pm$ 0.057 & 5780 $\pm$ 140 & -4.66 $\pm$ 0.13 & -3.96 $\pm$ 0.17 & 0.700 $\pm$ 0.044 & -5.748 $\pm$ 0.083 \\
0050 & 6.16 $\pm$ 0.40 & 1.780 $\pm$ 0.014 & 3.541 $\pm$ 0.059 & 5710 $\pm$ 140 & -4.74 $\pm$ 0.13 & -4.02 $\pm$ 0.18 & 0.720 $\pm$ 0.046 & -5.862 $\pm$ 0.082 \\
0057 & 6.87 $\pm$ 0.40 & 1.861 $\pm$ 0.012 & 3.693 $\pm$ 0.045 & 5680 $\pm$ 110 & -5.14 $\pm$ 0.10 & -4.42 $\pm$ 0.13 & 0.721 $\pm$ 0.035 & -6.260 $\pm$ 0.066 \\
0078 & 5.69 $\pm$ 0.37 & 1.749 $\pm$ 0.012 & 3.493 $\pm$ 0.045 & 5760 $\pm$ 110 & -4.60 $\pm$ 0.10 & -3.90 $\pm$ 0.13 & 0.708 $\pm$ 0.034 & -5.707 $\pm$ 0.068 \\
0103 & 6.33 $\pm$ 0.40 & 1.760 $\pm$ 0.014 & 3.570 $\pm$ 0.049 & 5940 $\pm$ 110 & -4.79 $\pm$ 0.11 & -4.14 $\pm$ 0.14 & 0.647 $\pm$ 0.034 & -5.795 $\pm$ 0.077 \\
0107 & 5.98 $\pm$ 0.36 & 1.799 $\pm$ 0.012 & 3.584 $\pm$ 0.051 & 5730 $\pm$ 120 & -4.84 $\pm$ 0.11 & -4.12 $\pm$ 0.15 & 0.720 $\pm$ 0.039 & -5.961 $\pm$ 0.070 \\
0123 & 5.82 $\pm$ 0.36 & 1.736 $\pm$ 0.012 & 3.461 $\pm$ 0.046 & 5730 $\pm$ 110 & -4.52 $\pm$ 0.11 & -3.81 $\pm$ 0.14 & 0.716 $\pm$ 0.035 & -5.639 $\pm$ 0.069 \\
0155 & 6.25 $\pm$ 0.39 & 1.835 $\pm$ 0.012 & 3.702 $\pm$ 0.045 & 5870 $\pm$ 110 & -5.14 $\pm$ 0.10 & -4.48 $\pm$ 0.13 & 0.665 $\pm$ 0.034 & -6.182 $\pm$ 0.069 \\
0158 & 5.48 $\pm$ 0.38 & 1.735 $\pm$ 0.013 & 3.476 $\pm$ 0.048 & 5800 $\pm$ 110 & -4.55 $\pm$ 0.11 & -3.86 $\pm$ 0.14 & 0.698 $\pm$ 0.035 & -5.643 $\pm$ 0.073 \\
0162 & 5.46 $\pm$ 0.51 & 1.647 $\pm$ 0.019 & 3.367 $\pm$ 0.053 & 6010 $\pm$ 110 & -4.25 $\pm$ 0.13 & -3.62 $\pm$ 0.15 & 0.629 $\pm$ 0.034 & -5.23 $\pm$ 0.10 \\

In [47]:

out_str = '\t'.join(list(ests_DF.columns)) + '\n'
for index, row in ests_DF.iterrows():
    out_str += row['ID'] + '\t'
    
    rest = row[1:]
    for ii in range(len(rest) - 1):
        if ii % 2 != 0: # every other column contains the uncertainty 
            continue
        
        val, unc = formatter(rest[ii], rest[ii+1])
        out_str += val + '\t' + unc + '\t'
    
    out_str += '\n'
    
print(out_str)

out_file = open("ML-OGLE_LMC_CEP.dat", "w")
out_file.write(out_str)
out_file.close()

ID	M	e_M	logR	e_logR	logL	e_logL	Teff	e_Teff	I_M0	e_I_M0	V_M0	e_V_M0	VI	e_VI	W	e_W
OGLE-LMC-CEP-0033	5.98	0.39	1.756	0.014	3.513	0.057	5780	140	-4.66	0.13	-3.96	0.17	0.700	0.044	-5.748	0.083	
OGLE-LMC-CEP-0050	6.16	0.40	1.780	0.014	3.541	0.059	5710	140	-4.74	0.13	-4.02	0.18	0.720	0.046	-5.862	0.082	
OGLE-LMC-CEP-0057	6.87	0.40	1.861	0.012	3.693	0.045	5680	110	-5.14	0.10	-4.42	0.13	0.721	0.035	-6.260	0.066	
OGLE-LMC-CEP-0078	5.69	0.37	1.749	0.012	3.493	0.045	5760	110	-4.60	0.10	-3.90	0.13	0.708	0.034	-5.707	0.068	
OGLE-LMC-CEP-0103	6.33	0.40	1.760	0.014	3.570	0.049	5940	110	-4.79	0.11	-4.14	0.14	0.647	0.034	-5.795	0.077	
OGLE-LMC-CEP-0107	5.98	0.36	1.799	0.012	3.584	0.051	5730	120	-4.84	0.11	-4.12	0.15	0.720	0.039	-5.961	0.070	
OGLE-LMC-CEP-0123	5.82	0.36	1.736	0.012	3.461	0.046	5730	110	-4.52	0.11	-3.81	0.14	0.716	0.035	-5.639	0.069	
OGLE-LMC-CEP-0155	6.25	0.39	1.835	0.012	3.702	0.045	5870	110	-5.14	0.10	-4.48	0.13	0.665	0.034	-6.182	0.069	
OGLE-LMC-CEP-0158	5.48	0.38	1.735	0.013	3.476	0.048	5800	110	-4.55	0.11	-3.86	0.14	0.698	0.035	-5.643	0.073	
OGLE-LMC-CEP-0162	5.46	0.51	1.647	0.019	3.367	0.053	6010	110	-4.25	0.13	-3.62	0.15	0.629	0.034	-5.23	0.10	
OGLE-LMC-CEP-0169	5.52	0.44	1.673	0.016	3.328	0.052	5700	110	-4.20	0.12	-3.47	0.15	0.723	0.035	-5.320	0.089	
OGLE-LMC-CEP-0177	5.54	0.46	1.600	0.017	3.215	0.052	5840	110	-3.89	0.12	-3.21	0.15	0.687	0.034	-4.966	0.091	
OGLE-LMC-CEP-0189	5.36	0.44	1.677	0.015	3.383	0.048	5870	110	-4.31	0.11	-3.63	0.14	0.679	0.034	-5.362	0.080	
OGLE-LMC-CEP-0212	5.82	0.39	1.878	0.013	3.678	0.059	5510	140	-5.11	0.13	-4.30	0.18	0.796	0.043	-6.345	0.081	
OGLE-LMC-CEP-0250	5.81	0.39	1.705	0.014	3.381	0.049	5670	110	-4.34	0.11	-3.61	0.14	0.729	0.034	-5.471	0.079	
OGLE-LMC-CEP-0264	5.34	0.42	1.564	0.015	3.136	0.050	5830	110	-3.70	0.12	-3.01	0.15	0.691	0.034	-4.779	0.084	
OGLE-LMC-CEP-0269	5.22	0.40	1.565	0.014	3.165	0.048	5910	110	-3.75	0.11	-3.08	0.14	0.671	0.034	-4.801	0.079	
OGLE-LMC-CEP-0291	5.21	0.44	1.556	0.016	3.109	0.052	5790	110	-3.64	0.12	-2.94	0.15	0.705	0.034	-4.738	0.090	
OGLE-LMC-CEP-0306	6.14	0.37	1.737	0.012	3.485	0.046	5810	110	-4.58	0.10	-3.88	0.14	0.692	0.034	-5.653	0.068	
OGLE-LMC-CEP-0316	5.39	0.44	1.557	0.016	3.109	0.051	5780	110	-3.64	0.12	-2.94	0.15	0.705	0.034	-4.737	0.087	
OGLE-LMC-CEP-0329	5.23	0.41	1.567	0.014	3.134	0.049	5790	110	-3.70	0.11	-3.00	0.14	0.701	0.034	-4.793	0.081	
OGLE-LMC-CEP-0356	6.02	0.37	1.892	0.012	3.672	0.056	5420	130	-5.08	0.13	-4.25	0.17	0.838	0.041	-6.382	0.077	
OGLE-LMC-CEP-0377	6.60	0.41	1.732	0.014	3.521	0.049	5950	110	-4.64	0.11	-3.99	0.14	0.648	0.035	-5.650	0.080	
OGLE-LMC-CEP-0458	5.28	0.41	1.562	0.014	3.119	0.049	5780	110	-3.66	0.11	-2.96	0.14	0.706	0.034	-4.766	0.080	
OGLE-LMC-CEP-0482	5.72	0.37	1.749	0.012	3.501	0.048	5780	110	-4.63	0.11	-3.92	0.14	0.700	0.036	-5.712	0.070	
OGLE-LMC-CEP-0492	5.02	0.40	1.636	0.014	3.320	0.047	5930	110	-4.14	0.11	-3.48	0.14	0.660	0.034	-5.165	0.076	
OGLE-LMC-CEP-0505	5.29	0.42	1.583	0.015	3.160	0.050	5770	110	-3.77	0.12	-3.06	0.15	0.709	0.034	-4.871	0.084	
OGLE-LMC-CEP-0520	6.11	0.36	1.793	0.012	3.572	0.052	5720	120	-4.81	0.12	-4.09	0.15	0.719	0.038	-5.930	0.073	
OGLE-LMC-CEP-0542	5.48	0.44	1.647	0.016	3.299	0.049	5780	110	-4.11	0.12	-3.40	0.14	0.703	0.034	-5.200	0.086	
OGLE-LMC-CEP-0561	5.97	0.37	1.872	0.012	3.630	0.067	5410	170	-4.98	0.15	-4.16	0.20	0.827	0.051	-6.270	0.084	
OGLE-LMC-CEP-0576	5.67	0.42	1.645	0.015	3.292	0.049	5790	110	-4.09	0.12	-3.39	0.14	0.703	0.034	-5.184	0.083	
OGLE-LMC-CEP-0592	5.38	0.44	1.588	0.016	3.184	0.051	5820	110	-3.82	0.12	-3.13	0.15	0.693	0.034	-4.899	0.087	
OGLE-LMC-CEP-0599	5.67	0.43	1.664	0.015	3.334	0.048	5800	110	-4.20	0.11	-3.50	0.14	0.699	0.034	-5.287	0.080	
OGLE-LMC-CEP-0613	5.46	0.44	1.603	0.016	3.223	0.050	5840	110	-3.92	0.12	-3.23	0.15	0.688	0.034	-4.987	0.087	
OGLE-LMC-CEP-0625	5.22	0.42	1.557	0.015	3.118	0.050	5810	110	-3.66	0.12	-2.96	0.15	0.698	0.034	-4.747	0.084	
OGLE-LMC-CEP-0647	5.33	0.42	1.632	0.014	3.289	0.048	5850	110	-4.07	0.11	-3.39	0.14	0.684	0.034	-5.137	0.078	
OGLE-LMC-CEP-0655	5.93	0.37	1.892	0.012	3.670	0.055	5390	130	-5.09	0.12	-4.25	0.16	0.835	0.042	-6.391	0.075	
OGLE-LMC-CEP-0658	5.48	0.40	1.664	0.014	3.406	0.048	6020	110	-4.34	0.11	-3.71	0.14	0.630	0.034	-5.323	0.077	
OGLE-LMC-CEP-0669	5.89	0.37	1.770	0.011	3.507	0.047	5660	110	-4.65	0.11	-3.92	0.14	0.737	0.036	-5.806	0.067	
OGLE-LMC-CEP-0671	6.39	0.39	1.667	0.013	3.335	0.047	5800	110	-4.20	0.11	-3.51	0.14	0.693	0.034	-5.283	0.074	
OGLE-LMC-CEP-0683	6.20	0.38	1.932	0.012	3.720	0.059	5300	140	-5.23	0.14	-4.36	0.18	0.866	0.046	-6.573	0.077	
OGLE-LMC-CEP-0702	5.30	0.42	1.628	0.015	3.254	0.048	5770	110	-4.00	0.11	-3.29	0.14	0.707	0.034	-5.101	0.080	
OGLE-LMC-CEP-0708	5.76	0.39	1.836	0.012	3.650	0.060	5680	140	-5.02	0.14	-4.28	0.18	0.730	0.046	-6.154	0.079	
OGLE-LMC-CEP-0716	5.60	0.36	1.870	0.012	3.607	0.051	5340	120	-4.94	0.12	-4.09	0.15	0.847	0.039	-6.258	0.070	
OGLE-LMC-CEP-0741	6.18	0.37	1.857	0.012	3.730	0.053	5790	130	-5.21	0.12	-4.51	0.16	0.691	0.041	-6.292	0.074	
OGLE-LMC-CEP-0776	6.70	0.37	1.759	0.012	3.548	0.046	5870	110	-4.73	0.11	-4.06	0.14	0.671	0.035	-5.776	0.068	
OGLE-LMC-CEP-0800	5.56	0.38	1.875	0.012	3.620	0.062	5350	150	-4.97	0.14	-4.11	0.19	0.850	0.047	-6.287	0.082	
OGLE-LMC-CEP-0831	5.55	0.37	1.811	0.012	3.591	0.046	5660	120	-4.88	0.11	-4.14	0.14	0.734	0.037	-6.022	0.067	
OGLE-LMC-CEP-0837	5.43	0.38	1.675	0.012	3.255	0.048	5470	110	-4.04	0.11	-3.23	0.14	0.798	0.035	-5.272	0.073	
OGLE-LMC-CEP-0838	5.16	0.42	1.567	0.015	3.173	0.049	5920	110	-3.78	0.12	-3.12	0.14	0.664	0.034	-4.816	0.083	
OGLE-LMC-CEP-0843	5.79	0.35	1.776	0.011	3.551	0.047	5750	110	-4.76	0.11	-4.05	0.14	0.705	0.036	-5.856	0.066	
OGLE-LMC-CEP-0845	5.29	0.42	1.599	0.015	3.194	0.050	5770	110	-3.85	0.12	-3.14	0.15	0.709	0.034	-4.954	0.084	
OGLE-LMC-CEP-0846	6.08	0.35	1.815	0.011	3.597	0.048	5670	110	-4.87	0.11	-4.13	0.14	0.741	0.036	-6.029	0.068	
OGLE-LMC-CEP-0878	6.21	0.42	1.830	0.013	3.625	0.045	5660	110	-4.98	0.10	-4.23	0.13	0.733	0.035	-6.108	0.069	
OGLE-LMC-CEP-0884	5.79	0.37	1.761	0.012	3.534	0.048	5810	110	-4.70	0.11	-4.00	0.14	0.694	0.035	-5.782	0.070	
OGLE-LMC-CEP-0886	5.39	0.41	1.599	0.014	3.195	0.048	5770	110	-3.86	0.11	-3.15	0.14	0.705	0.034	-4.953	0.079	
OGLE-LMC-CEP-0888	6.42	0.39	1.828	0.012	3.610	0.045	5630	110	-4.94	0.10	-4.20	0.13	0.739	0.035	-6.087	0.066	
OGLE-LMC-CEP-0915	5.75	0.36	1.747	0.012	3.481	0.046	5730	110	-4.58	0.11	-3.87	0.14	0.716	0.034	-5.695	0.068	
OGLE-LMC-CEP-0919	5.53	0.43	1.632	0.015	3.275	0.049	5810	110	-4.05	0.11	-3.35	0.14	0.696	0.034	-5.128	0.082	
OGLE-LMC-CEP-0926	5.28	0.39	1.612	0.014	3.229	0.047	5790	110	-3.93	0.11	-3.23	0.14	0.704	0.034	-5.027	0.076	
OGLE-LMC-CEP-0927	5.85	0.35	1.800	0.011	3.593	0.046	5750	110	-4.86	0.10	-4.15	0.14	0.711	0.034	-5.972	0.067	
OGLE-LMC-CEP-0931	6.49	0.42	1.713	0.015	3.472	0.049	5930	110	-4.53	0.11	-3.87	0.14	0.653	0.034	-5.541	0.081	
OGLE-LMC-CEP-0936	5.99	0.35	1.787	0.011	3.541	0.046	5670	110	-4.74	0.10	-4.01	0.14	0.735	0.034	-5.891	0.066	
OGLE-LMC-CEP-0949	5.38	0.38	1.877	0.012	3.610	0.057	5300	130	-4.94	0.13	-4.06	0.17	0.870	0.043	-6.288	0.078	
OGLE-LMC-CEP-0963	5.96	0.35	1.797	0.012	3.569	0.048	5690	110	-4.80	0.11	-4.08	0.14	0.730	0.036	-5.945	0.068	
OGLE-LMC-CEP-0969	5.85	0.37	1.891	0.012	3.671	0.053	5400	130	-5.10	0.12	-4.26	0.16	0.825	0.041	-6.377	0.073	
OGLE-LMC-CEP-0973	5.23	0.36	1.821	0.012	3.491	0.053	5280	130	-4.65	0.12	-3.79	0.16	0.857	0.041	-5.983	0.070	
OGLE-LMC-CEP-0975	6.13	0.37	1.897	0.012	3.710	0.058	5480	140	-5.18	0.13	-4.38	0.17	0.797	0.044	-6.418	0.077	
OGLE-LMC-CEP-0990	5.35	0.43	1.563	0.015	3.130	0.049	5810	110	-3.69	0.12	-3.00	0.14	0.694	0.034	-4.773	0.084	
OGLE-LMC-CEP-1004	5.15	0.42	1.551	0.015	3.097	0.049	5780	110	-3.61	0.11	-2.91	0.14	0.706	0.034	-4.709	0.082	
OGLE-LMC-CEP-1011	5.25	0.41	1.587	0.015	3.191	0.049	5840	110	-3.83	0.11	-3.15	0.14	0.690	0.034	-4.907	0.081	
OGLE-LMC-CEP-1012	5.31	0.44	1.641	0.015	3.291	0.049	5790	110	-4.09	0.12	-3.39	0.14	0.699	0.034	-5.173	0.084	
OGLE-LMC-CEP-1019	5.24	0.44	1.612	0.016	3.227	0.050	5780	110	-3.93	0.12	-3.22	0.15	0.704	0.034	-5.025	0.086	
OGLE-LMC-CEP-1020	5.16	0.42	1.572	0.015	3.131	0.049	5750	110	-3.70	0.11	-2.99	0.14	0.715	0.034	-4.811	0.082	
OGLE-LMC-CEP-1045	5.35	0.42	1.619	0.015	3.236	0.048	5770	110	-3.95	0.11	-3.25	0.14	0.707	0.033	-5.054	0.082	
OGLE-LMC-CEP-1057	5.44	0.42	1.638	0.015	3.276	0.048	5770	110	-4.06	0.11	-3.35	0.14	0.706	0.034	-5.153	0.081	
OGLE-LMC-CEP-1073	5.85	0.39	1.657	0.013	3.304	0.048	5760	110	-4.13	0.11	-3.42	0.14	0.707	0.034	-5.231	0.076	
OGLE-LMC-CEP-1078	6.08	0.35	1.798	0.011	3.569	0.047	5680	120	-4.80	0.11	-4.08	0.14	0.730	0.036	-5.945	0.067	
OGLE-LMC-CEP-1094	5.95	0.37	1.737	0.012	3.475	0.045	5790	110	-4.55	0.10	-3.85	0.13	0.700	0.034	-5.645	0.066	
OGLE-LMC-CEP-1096	5.27	0.40	1.600	0.014	3.254	0.048	5960	110	-3.97	0.11	-3.32	0.14	0.650	0.034	-4.988	0.079	
OGLE-LMC-CEP-1109	6.06	0.37	1.876	0.012	3.639	0.060	5410	150	-5.01	0.14	-4.18	0.18	0.826	0.048	-6.292	0.077	
OGLE-LMC-CEP-1112	5.76	0.37	1.763	0.012	3.530	0.047	5800	110	-4.70	0.11	-4.00	0.14	0.696	0.035	-5.782	0.068	
OGLE-LMC-CEP-1115	6.26	0.39	1.830	0.012	3.617	0.044	5630	110	-4.96	0.10	-4.21	0.13	0.740	0.035	-6.103	0.066	
OGLE-LMC-CEP-1118	5.46	0.46	1.563	0.017	3.133	0.052	5820	110	-3.69	0.12	-3.01	0.15	0.690	0.034	-4.773	0.091	
OGLE-LMC-CEP-1120	5.46	0.37	1.863	0.012	3.566	0.057	5260	140	-4.84	0.13	-3.96	0.17	0.873	0.044	-6.198	0.075	
OGLE-LMC-CEP-1128	5.51	0.41	1.728	0.014	3.475	0.054	5840	120	-4.55	0.12	-3.86	0.16	0.685	0.039	-5.615	0.083	
OGLE-LMC-CEP-1129	5.45	0.39	1.678	0.014	3.334	0.049	5700	110	-4.22	0.11	-3.50	0.14	0.721	0.034	-5.340	0.079	
OGLE-LMC-CEP-1141	5.50	0.39	1.679	0.013	3.374	0.046	5820	110	-4.30	0.11	-3.60	0.14	0.688	0.034	-5.369	0.074	
OGLE-LMC-CEP-1166	5.78	0.39	1.905	0.012	3.674	0.057	5330	130	-5.10	0.13	-4.23	0.17	0.864	0.042	-6.442	0.078	
OGLE-LMC-CEP-1172	5.19	0.45	1.620	0.016	3.275	0.050	5890	110	-4.03	0.12	-3.36	0.15	0.673	0.034	-5.081	0.086	
OGLE-LMC-CEP-1180	6.23	0.37	1.939	0.012	3.731	0.053	5300	130	-5.25	0.12	-4.37	0.16	0.873	0.040	-6.605	0.073	
OGLE-LMC-CEP-1184	6.17	0.37	1.923	0.012	3.705	0.052	5310	120	-5.19	0.12	-4.32	0.15	0.862	0.039	-6.529	0.072	
OGLE-LMC-CEP-1190	5.33	0.41	1.594	0.015	3.204	0.049	5840	110	-3.86	0.11	-3.18	0.14	0.688	0.034	-4.938	0.082	
OGLE-LMC-CEP-1192	5.26	0.43	1.629	0.015	3.280	0.048	5840	110	-4.05	0.11	-3.36	0.14	0.687	0.034	-5.125	0.081	
OGLE-LMC-CEP-1200	5.78	0.37	1.727	0.012	3.457	0.046	5770	110	-4.51	0.11	-3.81	0.14	0.702	0.035	-5.603	0.070	
OGLE-LMC-CEP-1211	5.26	0.42	1.553	0.015	3.135	0.049	5880	110	-3.69	0.11	-3.02	0.14	0.673	0.034	-4.742	0.082	
OGLE-LMC-CEP-1214	5.84	0.35	1.794	0.011	3.554	0.046	5670	110	-4.77	0.10	-4.03	0.14	0.740	0.035	-5.925	0.066	
OGLE-LMC-CEP-1225	5.27	0.43	1.576	0.016	3.196	0.051	5940	110	-3.83	0.12	-3.17	0.15	0.660	0.034	-4.861	0.087	
OGLE-LMC-CEP-1233	6.04	0.35	1.786	0.011	3.583	0.047	5810	110	-4.83	0.11	-4.13	0.14	0.695	0.035	-5.914	0.067	
OGLE-LMC-CEP-1237	5.51	0.37	1.826	0.012	3.602	0.059	5600	140	-4.90	0.14	-4.13	0.18	0.761	0.046	-6.092	0.079	
OGLE-LMC-CEP-1245	5.40	0.42	1.640	0.014	3.290	0.047	5810	110	-4.08	0.11	-3.38	0.14	0.698	0.033	-5.168	0.077	
OGLE-LMC-CEP-1249	6.32	0.38	1.746	0.012	3.492	0.046	5780	110	-4.60	0.10	-3.90	0.14	0.700	0.034	-5.689	0.069	
OGLE-LMC-CEP-1252	5.59	0.38	1.821	0.012	3.679	0.053	5850	130	-5.08	0.12	-4.41	0.16	0.671	0.040	-6.129	0.075	
OGLE-LMC-CEP-1256	5.20	0.40	1.621	0.014	3.218	0.047	5700	110	-3.92	0.11	-3.19	0.14	0.728	0.034	-5.048	0.077	
OGLE-LMC-CEP-1261	5.95	0.35	1.756	0.011	3.472	0.046	5640	110	-4.56	0.10	-3.82	0.14	0.744	0.035	-5.729	0.066	
OGLE-LMC-CEP-1266	5.26	0.40	1.593	0.014	3.186	0.048	5790	110	-3.83	0.11	-3.13	0.14	0.702	0.034	-4.922	0.078	
OGLE-LMC-CEP-1301	5.45	0.43	1.637	0.015	3.334	0.049	5970	110	-4.17	0.12	-3.52	0.14	0.646	0.034	-5.176	0.083	
OGLE-LMC-CEP-1304	4.91	0.41	1.539	0.014	3.059	0.048	5730	110	-3.52	0.11	-2.80	0.14	0.720	0.034	-4.641	0.078	
OGLE-LMC-CEP-1313	5.45	0.37	1.718	0.013	3.415	0.047	5700	110	-4.42	0.11	-3.69	0.14	0.724	0.034	-5.542	0.073	
OGLE-LMC-CEP-1321	5.13	0.39	1.563	0.014	3.194	0.047	6010	110	-3.81	0.11	-3.17	0.14	0.639	0.034	-4.809	0.076	
OGLE-LMC-CEP-1335	5.32	0.42	1.583	0.015	3.160	0.049	5760	110	-3.77	0.12	-3.06	0.14	0.712	0.034	-4.873	0.083	
OGLE-LMC-CEP-1344	5.96	0.36	1.748	0.012	3.513	0.046	5830	110	-4.64	0.11	-3.96	0.14	0.685	0.034	-5.716	0.068	
OGLE-LMC-CEP-1353	5.99	0.36	1.770	0.011	3.523	0.045	5710	110	-4.69	0.10	-3.97	0.13	0.722	0.034	-5.816	0.066	
OGLE-LMC-CEP-1370	5.44	0.40	1.576	0.014	3.162	0.048	5830	110	-3.76	0.11	-3.08	0.14	0.688	0.034	-4.839	0.077	
OGLE-LMC-CEP-1389	5.84	0.35	1.749	0.012	3.481	0.046	5720	110	-4.58	0.10	-3.87	0.14	0.719	0.034	-5.701	0.068	
OGLE-LMC-CEP-1396	5.45	0.43	1.602	0.015	3.266	0.049	5980	110	-4.00	0.11	-3.37	0.14	0.639	0.034	-5.002	0.083	
OGLE-LMC-CEP-1398	5.45	0.42	1.611	0.015	3.228	0.049	5800	110	-3.93	0.12	-3.24	0.15	0.698	0.034	-5.019	0.084	
OGLE-LMC-CEP-1404	5.08	0.40	1.694	0.014	3.366	0.049	5700	110	-4.30	0.11	-3.58	0.14	0.720	0.034	-5.421	0.076	
OGLE-LMC-CEP-1407	5.38	0.42	1.589	0.015	3.200	0.049	5850	110	-3.86	0.12	-3.18	0.14	0.680	0.034	-4.917	0.083	
OGLE-LMC-CEP-1416	5.46	0.42	1.629	0.015	3.281	0.048	5850	110	-4.06	0.11	-3.38	0.14	0.683	0.034	-5.122	0.082	
OGLE-LMC-CEP-1444	5.51	0.38	1.714	0.013	3.406	0.048	5700	110	-4.40	0.11	-3.68	0.14	0.719	0.034	-5.522	0.073	
OGLE-LMC-CEP-1463	5.79	0.37	1.756	0.013	3.520	0.046	5800	110	-4.67	0.11	-3.98	0.14	0.694	0.034	-5.758	0.071	
OGLE-LMC-CEP-1490	5.97	0.36	1.783	0.012	3.570	0.047	5780	110	-4.79	0.11	-4.09	0.14	0.703	0.035	-5.894	0.068	
OGLE-LMC-CEP-1494	5.77	0.39	1.668	0.014	3.360	0.047	5860	110	-4.25	0.11	-3.58	0.14	0.677	0.034	-5.308	0.076	
OGLE-LMC-CEP-1513	6.08	0.35	1.789	0.011	3.554	0.045	5700	110	-4.77	0.10	-4.05	0.13	0.726	0.034	-5.905	0.065	
OGLE-LMC-CEP-1526	5.54	0.39	1.722	0.013	3.460	0.046	5820	110	-4.51	0.11	-3.82	0.14	0.688	0.034	-5.584	0.073	
OGLE-LMC-CEP-1539	6.22	0.37	1.910	0.012	3.687	0.055	5340	130	-5.15	0.13	-4.29	0.16	0.848	0.042	-6.460	0.075	
OGLE-LMC-CEP-1553	6.03	0.39	1.719	0.013	3.432	0.046	5760	110	-4.45	0.10	-3.75	0.13	0.706	0.034	-5.552	0.071	
OGLE-LMC-CEP-1559	5.30	0.43	1.552	0.015	3.108	0.050	5810	110	-3.63	0.12	-2.95	0.15	0.694	0.034	-4.720	0.084	
OGLE-LMC-CEP-1560	5.41	0.43	1.593	0.015	3.202	0.050	5840	110	-3.86	0.12	-3.18	0.15	0.686	0.034	-4.933	0.084	
OGLE-LMC-CEP-1580	5.50	0.42	1.665	0.015	3.333	0.048	5780	110	-4.20	0.11	-3.50	0.14	0.701	0.034	-5.291	0.080	
OGLE-LMC-CEP-1590	5.34	0.41	1.638	0.014	3.291	0.048	5830	110	-4.09	0.11	-3.40	0.14	0.689	0.034	-5.159	0.079	
OGLE-LMC-CEP-1608	5.37	0.36	1.845	0.012	3.645	0.051	5600	120	-5.01	0.12	-4.24	0.15	0.760	0.039	-6.193	0.071	
OGLE-LMC-CEP-1614	5.43	0.42	1.623	0.015	3.221	0.049	5700	110	-3.93	0.12	-3.20	0.14	0.726	0.034	-5.054	0.082	
OGLE-LMC-CEP-1636	5.67	0.36	1.714	0.012	3.434	0.045	5780	110	-4.45	0.10	-3.75	0.13	0.701	0.034	-5.540	0.067	
OGLE-LMC-CEP-1647	5.22	0.37	1.779	0.012	3.569	0.045	5810	110	-4.81	0.10	-4.13	0.13	0.686	0.034	-5.881	0.067	
OGLE-LMC-CEP-1658	5.21	0.40	1.546	0.014	3.104	0.048	5830	110	-3.62	0.11	-2.94	0.14	0.688	0.034	-4.698	0.078	
OGLE-LMC-CEP-1667	5.41	0.42	1.703	0.014	3.433	0.047	5870	110	-4.44	0.11	-3.76	0.14	0.675	0.034	-5.494	0.077	
OGLE-LMC-CEP-1719	6.08	0.40	1.848	0.013	3.642	0.071	5590	170	-5.01	0.17	-4.25	0.22	0.758	0.056	-6.197	0.091	
OGLE-LMC-CEP-1737	5.17	0.42	1.561	0.015	3.109	0.050	5760	110	-3.64	0.12	-2.93	0.14	0.713	0.034	-4.752	0.082	
OGLE-LMC-CEP-1748	5.86	0.38	1.723	0.012	3.454	0.045	5810	110	-4.50	0.10	-3.80	0.13	0.693	0.034	-5.578	0.069	
OGLE-LMC-CEP-1757	5.39	0.39	1.571	0.014	3.146	0.048	5810	110	-3.72	0.11	-3.02	0.14	0.702	0.034	-4.815	0.077	
OGLE-LMC-CEP-1778	5.37	0.41	1.624	0.014	3.254	0.048	5790	110	-4.00	0.11	-3.30	0.14	0.700	0.034	-5.086	0.078	
OGLE-LMC-CEP-1785	5.56	0.40	1.665	0.014	3.330	0.047	5760	110	-4.19	0.11	-3.49	0.14	0.704	0.034	-5.291	0.076	
OGLE-LMC-CEP-1791	5.34	0.41	1.554	0.014	3.116	0.048	5820	110	-3.65	0.11	-2.97	0.14	0.690	0.034	-4.731	0.079	
OGLE-LMC-CEP-1794	5.20	0.41	1.598	0.015	3.267	0.049	6010	110	-3.99	0.11	-3.36	0.14	0.636	0.034	-4.991	0.081	
OGLE-LMC-CEP-1797	5.08	0.41	1.602	0.014	3.187	0.047	5720	110	-3.84	0.11	-3.12	0.14	0.721	0.034	-4.960	0.079	
OGLE-LMC-CEP-1799	5.42	0.42	1.635	0.014	3.288	0.048	5840	110	-4.08	0.11	-3.39	0.14	0.688	0.034	-5.149	0.080	
OGLE-LMC-CEP-1831	5.48	0.41	1.675	0.014	3.401	0.048	5930	110	-4.34	0.11	-3.68	0.14	0.658	0.034	-5.364	0.077	
OGLE-LMC-CEP-1846	5.15	0.40	1.545	0.014	3.116	0.048	5880	110	-3.64	0.11	-2.97	0.14	0.675	0.034	-4.697	0.077	
OGLE-LMC-CEP-1851	5.21	0.42	1.572	0.015	3.193	0.049	5940	110	-3.82	0.11	-3.17	0.14	0.654	0.034	-4.847	0.082	
OGLE-LMC-CEP-1866	5.85	0.36	1.744	0.012	3.473	0.046	5720	110	-4.56	0.10	-3.84	0.14	0.721	0.035	-5.679	0.068	
OGLE-LMC-CEP-1870	5.79	0.43	1.697	0.015	3.399	0.048	5790	110	-4.37	0.11	-3.67	0.14	0.697	0.034	-5.452	0.082	
OGLE-LMC-CEP-1887	5.45	0.42	1.671	0.014	3.361	0.048	5840	110	-4.26	0.11	-3.58	0.14	0.684	0.034	-5.329	0.079	
OGLE-LMC-CEP-1892	5.32	0.41	1.644	0.014	3.278	0.047	5740	110	-4.06	0.11	-3.35	0.14	0.715	0.034	-5.175	0.078	
OGLE-LMC-CEP-1899	5.36	0.40	1.579	0.014	3.200	0.048	5920	110	-3.84	0.11	-3.18	0.14	0.662	0.034	-4.880	0.078	
OGLE-LMC-CEP-1903	5.73	0.38	1.723	0.013	3.422	0.048	5690	110	-4.44	0.11	-3.72	0.14	0.724	0.034	-5.567	0.075	
OGLE-LMC-CEP-1904	5.17	0.41	1.583	0.015	3.237	0.049	6010	110	-3.92	0.11	-3.28	0.14	0.635	0.034	-4.913	0.081	
OGLE-LMC-CEP-1909	5.11	0.41	1.557	0.014	3.151	0.048	5900	110	-3.73	0.11	-3.07	0.14	0.665	0.034	-4.767	0.079	
OGLE-LMC-CEP-1910	5.51	0.37	1.805	0.012	3.666	0.053	5910	130	-5.04	0.12	-4.39	0.16	0.653	0.040	-6.060	0.075	
OGLE-LMC-CEP-1922	6.00	0.40	1.701	0.014	3.463	0.048	5960	110	-4.49	0.11	-3.84	0.14	0.645	0.034	-5.494	0.078	
OGLE-LMC-CEP-1926	5.74	0.48	1.695	0.017	3.416	0.051	5860	110	-4.39	0.12	-3.71	0.15	0.678	0.035	-5.449	0.091	
OGLE-LMC-CEP-1927	5.43	0.45	1.648	0.016	3.315	0.050	5830	110	-4.14	0.12	-3.46	0.15	0.687	0.034	-5.213	0.086	
OGLE-LMC-CEP-1933	5.79	0.38	1.800	0.012	3.599	0.048	5750	120	-4.88	0.11	-4.17	0.14	0.709	0.038	-5.986	0.067	
OGLE-LMC-CEP-1939	5.70	0.52	1.695	0.018	3.403	0.051	5820	110	-4.37	0.12	-3.68	0.15	0.689	0.035	-5.443	0.094	
OGLE-LMC-CEP-1942	5.98	0.36	1.750	0.012	3.469	0.045	5670	110	-4.55	0.10	-3.82	0.13	0.736	0.034	-5.699	0.067	
OGLE-LMC-CEP-1945	5.39	0.35	1.749	0.011	3.467	0.047	5670	120	-4.56	0.11	-3.83	0.14	0.731	0.036	-5.697	0.066	
OGLE-LMC-CEP-1954	5.43	0.38	1.876	0.012	3.599	0.057	5280	140	-4.92	0.13	-4.04	0.17	0.877	0.044	-6.283	0.076	
OGLE-LMC-CEP-1956	5.47	0.38	1.786	0.012	3.540	0.045	5660	110	-4.76	0.10	-4.02	0.13	0.732	0.034	-5.888	0.067	
OGLE-LMC-CEP-1957	6.63	0.35	1.767	0.011	3.509	0.046	5700	110	-4.66	0.10	-3.94	0.14	0.721	0.034	-5.775	0.067	
OGLE-LMC-CEP-1983	5.03	0.36	1.723	0.013	3.399	0.048	5610	110	-4.40	0.11	-3.65	0.14	0.748	0.035	-5.558	0.071	
OGLE-LMC-CEP-1984	5.47	0.45	1.665	0.016	3.341	0.050	5800	110	-4.21	0.12	-3.51	0.15	0.696	0.034	-5.290	0.086	
OGLE-LMC-CEP-1986	5.47	0.46	1.639	0.016	3.284	0.051	5790	110	-4.07	0.12	-3.37	0.15	0.699	0.034	-5.157	0.090	
OGLE-LMC-CEP-1990	5.30	0.45	1.576	0.016	3.157	0.050	5800	110	-3.76	0.12	-3.06	0.15	0.696	0.034	-4.842	0.086	
OGLE-LMC-CEP-1999	5.39	0.43	1.587	0.015	3.198	0.049	5860	110	-3.85	0.11	-3.18	0.14	0.678	0.034	-4.909	0.082	
OGLE-LMC-CEP-2013	5.35	0.43	1.574	0.015	3.172	0.050	5860	110	-3.79	0.12	-3.11	0.15	0.679	0.034	-4.845	0.085	
OGLE-LMC-CEP-2015	6.45	0.39	1.731	0.013	3.507	0.047	5910	110	-4.62	0.11	-3.95	0.14	0.659	0.034	-5.640	0.074	
OGLE-LMC-CEP-2017	5.33	0.42	1.629	0.015	3.299	0.049	5910	110	-4.09	0.12	-3.43	0.14	0.665	0.034	-5.126	0.083	
OGLE-LMC-CEP-2018	5.64	0.36	1.741	0.012	3.482	0.046	5770	110	-4.58	0.10	-3.87	0.13	0.704	0.034	-5.670	0.069	
OGLE-LMC-CEP-2022	5.49	0.43	1.681	0.014	3.394	0.048	5880	110	-4.34	0.11	-3.66	0.14	0.673	0.034	-5.386	0.079	
OGLE-LMC-CEP-2027	5.33	0.44	1.608	0.015	3.248	0.048	5880	110	-3.99	0.11	-3.33	0.14	0.660	0.034	-5.020	0.082	
OGLE-LMC-CEP-2028	6.04	0.35	1.784	0.012	3.543	0.047	5690	110	-4.74	0.11	-4.02	0.14	0.728	0.035	-5.876	0.068	
OGLE-LMC-CEP-2036	5.50	0.42	1.613	0.015	3.275	0.049	5950	110	-4.03	0.11	-3.38	0.14	0.652	0.034	-5.046	0.082	
OGLE-LMC-CEP-2042	5.89	0.36	1.747	0.012	3.493	0.046	5770	110	-4.60	0.11	-3.91	0.14	0.702	0.034	-5.703	0.071	
OGLE-LMC-CEP-2050	5.91	0.36	1.754	0.012	3.516	0.047	5800	110	-4.66	0.11	-3.96	0.14	0.696	0.035	-5.739	0.069	
OGLE-LMC-CEP-2051	5.39	0.37	1.739	0.012	3.484	0.046	5800	110	-4.57	0.11	-3.88	0.14	0.696	0.034	-5.663	0.070	
OGLE-LMC-CEP-2066	5.99	0.36	1.764	0.012	3.548	0.048	5840	110	-4.73	0.11	-4.05	0.14	0.683	0.035	-5.799	0.069	
OGLE-LMC-CEP-2090	5.62	0.36	1.742	0.012	3.480	0.045	5760	110	-4.57	0.10	-3.86	0.13	0.708	0.034	-5.674	0.068	
OGLE-LMC-CEP-2105	5.31	0.40	1.620	0.014	3.246	0.047	5800	110	-3.98	0.11	-3.28	0.14	0.699	0.034	-5.065	0.077	
OGLE-LMC-CEP-2109	6.27	0.37	1.729	0.012	3.475	0.046	5830	110	-4.55	0.10	-3.86	0.14	0.685	0.034	-5.615	0.069	
OGLE-LMC-CEP-2113	5.41	0.44	1.614	0.016	3.228	0.050	5790	110	-3.94	0.12	-3.24	0.15	0.703	0.034	-5.030	0.086	
OGLE-LMC-CEP-2121	5.39	0.44	1.583	0.017	3.188	0.052	5860	110	-3.82	0.12	-3.14	0.15	0.685	0.034	-4.888	0.091	
OGLE-LMC-CEP-2132	5.54	0.42	1.619	0.015	3.234	0.049	5770	110	-3.95	0.11	-3.25	0.14	0.704	0.034	-5.048	0.081	
OGLE-LMC-CEP-2152	5.35	0.42	1.674	0.014	3.334	0.048	5720	110	-4.21	0.11	-3.49	0.14	0.718	0.034	-5.329	0.080	
OGLE-LMC-CEP-2170	5.86	0.40	1.708	0.014	3.397	0.050	5700	110	-4.38	0.12	-3.65	0.15	0.722	0.034	-5.496	0.080	
OGLE-LMC-CEP-2171	5.50	0.46	1.621	0.017	3.237	0.053	5770	110	-3.96	0.13	-3.26	0.15	0.705	0.034	-5.056	0.093	
OGLE-LMC-CEP-2174	6.11	0.36	1.787	0.012	3.568	0.049	5760	120	-4.79	0.11	-4.09	0.15	0.708	0.037	-5.901	0.070	
OGLE-LMC-CEP-2177	5.26	0.41	1.558	0.014	3.136	0.048	5860	110	-3.70	0.11	-3.02	0.14	0.682	0.034	-4.761	0.080	
OGLE-LMC-CEP-2194	5.11	0.44	1.651	0.015	3.354	0.048	5940	110	-4.23	0.11	-3.57	0.14	0.657	0.034	-5.248	0.081	
OGLE-LMC-CEP-2204	5.95	0.36	1.764	0.012	3.548	0.047	5840	110	-4.73	0.11	-4.05	0.14	0.683	0.035	-5.801	0.069	
OGLE-LMC-CEP-2205	5.44	0.47	1.684	0.016	3.387	0.052	5830	110	-4.32	0.12	-3.63	0.15	0.688	0.036	-5.396	0.089	
OGLE-LMC-CEP-2225	6.05	0.35	1.748	0.011	3.467	0.045	5670	110	-4.55	0.10	-3.81	0.13	0.734	0.034	-5.693	0.066	
OGLE-LMC-CEP-2226	5.39	0.41	1.616	0.014	3.250	0.048	5840	110	-3.98	0.11	-3.29	0.14	0.688	0.034	-5.052	0.080	
OGLE-LMC-CEP-2234	5.22	0.40	1.611	0.014	3.237	0.047	5830	110	-3.95	0.11	-3.26	0.14	0.692	0.034	-5.028	0.077	
OGLE-LMC-CEP-2244	5.22	0.42	1.586	0.015	3.167	0.049	5770	110	-3.78	0.12	-3.08	0.14	0.710	0.034	-4.887	0.083	
OGLE-LMC-CEP-2249	5.79	0.45	1.700	0.016	3.463	0.052	5970	110	-4.49	0.12	-3.84	0.15	0.643	0.035	-5.495	0.089	
OGLE-LMC-CEP-2262	5.97	0.35	1.768	0.012	3.530	0.046	5750	110	-4.71	0.10	-3.99	0.14	0.709	0.034	-5.812	0.067	
OGLE-LMC-CEP-2265	5.53	0.41	1.623	0.014	3.274	0.048	5870	110	-4.04	0.11	-3.37	0.14	0.675	0.034	-5.091	0.079	
OGLE-LMC-CEP-2269	5.73	0.36	1.739	0.012	3.472	0.047	5760	110	-4.56	0.11	-3.86	0.14	0.704	0.034	-5.656	0.070	
OGLE-LMC-CEP-2281	5.38	0.42	1.569	0.015	3.179	0.049	5930	110	-3.79	0.11	-3.14	0.14	0.660	0.034	-4.828	0.081	
OGLE-LMC-CEP-2284	5.23	0.42	1.556	0.015	3.160	0.049	5950	110	-3.74	0.11	-3.09	0.14	0.653	0.034	-4.767	0.082	
OGLE-LMC-CEP-2298	5.32	0.41	1.563	0.014	3.165	0.048	5910	110	-3.76	0.11	-3.10	0.14	0.663	0.034	-4.797	0.079	
OGLE-LMC-CEP-2305	5.46	0.44	1.634	0.016	3.282	0.049	5820	110	-4.06	0.12	-3.37	0.14	0.692	0.034	-5.140	0.084	
OGLE-LMC-CEP-2308	5.63	0.40	1.677	0.014	3.356	0.047	5770	110	-4.26	0.11	-3.55	0.14	0.702	0.034	-5.353	0.077	
OGLE-LMC-CEP-2318	5.62	0.49	1.611	0.018	3.212	0.055	5760	110	-3.90	0.13	-3.19	0.16	0.711	0.034	-5.003	0.099	
OGLE-LMC-CEP-2329	6.17	0.44	1.697	0.015	3.461	0.051	5980	110	-4.49	0.12	-3.84	0.15	0.640	0.035	-5.483	0.085	
OGLE-LMC-CEP-2335	5.38	0.41	1.624	0.014	3.275	0.047	5850	110	-4.04	0.11	-3.36	0.14	0.681	0.034	-5.099	0.078	
OGLE-LMC-CEP-2337	5.55	0.41	1.885	0.013	3.635	0.071	5340	170	-5.01	0.16	-4.16	0.22	0.849	0.055	-6.331	0.091	
OGLE-LMC-CEP-2340	5.26	0.39	1.602	0.014	3.248	0.048	5920	110	-3.96	0.11	-3.29	0.14	0.664	0.034	-4.993	0.077	
OGLE-LMC-CEP-2349	5.61	0.48	1.639	0.017	3.285	0.052	5790	110	-4.08	0.12	-3.38	0.15	0.700	0.034	-5.165	0.093	
OGLE-LMC-CEP-2353	5.41	0.49	1.615	0.018	3.279	0.053	5940	110	-4.04	0.12	-3.39	0.15	0.652	0.034	-5.059	0.095	
OGLE-LMC-CEP-2354	5.38	0.45	1.595	0.016	3.193	0.052	5800	110	-3.85	0.12	-3.15	0.15	0.697	0.034	-4.934	0.090	
OGLE-LMC-CEP-2376	5.29	0.42	1.644	0.015	3.297	0.048	5790	110	-4.10	0.11	-3.40	0.14	0.698	0.034	-5.188	0.080	
OGLE-LMC-CEP-2401	5.49	0.37	1.644	0.012	3.170	0.046	5390	110	-3.83	0.10	-3.01	0.13	0.820	0.034	-5.108	0.069	
OGLE-LMC-CEP-2417	5.23	0.45	1.556	0.016	3.143	0.051	5890	110	-3.71	0.12	-3.04	0.15	0.671	0.034	-4.758	0.090	
OGLE-LMC-CEP-2418	5.40	0.43	1.586	0.015	3.177	0.050	5810	110	-3.81	0.12	-3.12	0.15	0.694	0.034	-4.889	0.084	
OGLE-LMC-CEP-2425	5.65	0.38	1.740	0.013	3.476	0.047	5750	110	-4.57	0.11	-3.85	0.14	0.709	0.035	-5.666	0.074	
OGLE-LMC-CEP-2454	5.29	0.42	1.613	0.015	3.253	0.049	5860	110	-3.98	0.11	-3.30	0.14	0.681	0.034	-5.045	0.082	
OGLE-LMC-CEP-2490	5.36	0.40	1.594	0.014	3.227	0.048	5910	110	-3.91	0.11	-3.25	0.14	0.667	0.034	-4.955	0.079	
OGLE-LMC-CEP-2519	5.23	0.39	1.570	0.014	3.181	0.048	5930	110	-3.79	0.11	-3.13	0.14	0.663	0.034	-4.830	0.077	
OGLE-LMC-CEP-2530	5.54	0.42	1.605	0.015	3.227	0.050	5840	110	-3.93	0.12	-3.25	0.15	0.684	0.034	-4.996	0.083	
OGLE-LMC-CEP-2543	5.49	0.40	1.591	0.014	3.211	0.048	5890	110	-3.88	0.11	-3.21	0.14	0.671	0.034	-4.930	0.078	
OGLE-LMC-CEP-2544	5.51	0.38	1.806	0.012	3.610	0.051	5750	120	-4.91	0.12	-4.20	0.15	0.710	0.039	-6.029	0.074	
OGLE-LMC-CEP-2551	5.17	0.41	1.600	0.014	3.269	0.048	5990	110	-4.00	0.11	-3.36	0.14	0.641	0.034	-4.996	0.080	
OGLE-LMC-CEP-2568	5.44	0.40	1.630	0.014	3.288	0.047	5860	110	-4.07	0.11	-3.40	0.14	0.676	0.034	-5.124	0.075	
OGLE-LMC-CEP-2571	5.37	0.40	1.604	0.014	3.217	0.048	5810	110	-3.90	0.11	-3.21	0.14	0.696	0.034	-4.985	0.077	
OGLE-LMC-CEP-2596	5.16	0.42	1.621	0.014	3.259	0.048	5830	110	-4.00	0.11	-3.31	0.14	0.691	0.034	-5.081	0.080	
OGLE-LMC-CEP-2598	5.35	0.41	1.648	0.014	3.291	0.048	5750	110	-4.10	0.11	-3.38	0.14	0.710	0.034	-5.203	0.078	
OGLE-LMC-CEP-2600	5.41	0.41	1.620	0.014	3.257	0.048	5840	110	-4.00	0.11	-3.31	0.14	0.688	0.034	-5.070	0.079	
OGLE-LMC-CEP-2604	5.43	0.41	1.650	0.014	3.290	0.048	5730	110	-4.10	0.11	-3.38	0.14	0.716	0.034	-5.209	0.080	
OGLE-LMC-CEP-2610	5.68	0.44	1.700	0.015	3.411	0.048	5820	110	-4.39	0.11	-3.70	0.14	0.692	0.034	-5.466	0.080	
OGLE-LMC-CEP-2612	5.50	0.44	1.666	0.016	3.323	0.050	5740	110	-4.18	0.12	-3.46	0.15	0.713	0.034	-5.286	0.086	
OGLE-LMC-CEP-2620	5.29	0.43	1.567	0.015	3.130	0.050	5780	110	-3.69	0.12	-2.99	0.15	0.704	0.034	-4.790	0.084	
OGLE-LMC-CEP-2637	5.23	0.44	1.563	0.016	3.194	0.051	6000	110	-3.81	0.12	-3.18	0.15	0.638	0.034	-4.815	0.088	
OGLE-LMC-CEP-2638	5.70	0.40	1.623	0.014	3.234	0.048	5750	110	-3.95	0.11	-3.24	0.14	0.715	0.034	-5.064	0.079	
OGLE-LMC-CEP-2663	5.42	0.42	1.594	0.015	3.195	0.049	5810	110	-3.85	0.12	-3.15	0.14	0.698	0.034	-4.935	0.082	
OGLE-LMC-CEP-2675	5.36	0.39	1.716	0.014	3.429	0.050	5750	110	-4.45	0.11	-3.74	0.15	0.710	0.035	-5.547	0.077	
OGLE-LMC-CEP-2676	6.16	0.40	1.708	0.014	3.450	0.047	5880	110	-4.48	0.11	-3.81	0.14	0.667	0.034	-5.516	0.077	
OGLE-LMC-CEP-2760	5.19	0.41	1.591	0.014	3.175	0.048	5760	110	-3.80	0.11	-3.09	0.14	0.713	0.034	-4.914	0.079	
OGLE-LMC-CEP-2765	5.83	0.37	1.814	0.012	3.566	0.045	5590	110	-4.83	0.10	-4.07	0.13	0.755	0.035	-6.002	0.066	
OGLE-LMC-CEP-2768	5.31	0.41	1.614	0.014	3.220	0.048	5750	110	-3.92	0.11	-3.21	0.14	0.712	0.034	-5.026	0.078	
OGLE-LMC-CEP-2775	5.61	0.36	1.770	0.012	3.580	0.046	5910	110	-4.83	0.10	-4.18	0.13	0.651	0.034	-5.846	0.067	
OGLE-LMC-CEP-2812	5.97	0.37	1.778	0.012	3.549	0.050	5740	120	-4.76	0.11	-4.04	0.15	0.711	0.039	-5.862	0.068	
OGLE-LMC-CEP-2813	5.54	0.37	1.738	0.012	3.496	0.047	5840	110	-4.60	0.11	-3.92	0.14	0.683	0.035	-5.669	0.070	
OGLE-LMC-CEP-2826	5.27	0.40	1.618	0.014	3.249	0.047	5820	110	-3.98	0.11	-3.28	0.14	0.697	0.034	-5.063	0.077	
OGLE-LMC-CEP-2871	5.35	0.46	1.698	0.016	3.418	0.049	5840	110	-4.41	0.12	-3.72	0.14	0.680	0.034	-5.466	0.087	
OGLE-LMC-CEP-2884	5.45	0.43	1.810	0.014	3.600	0.054	5700	140	-4.90	0.12	-4.17	0.16	0.723	0.046	-6.025	0.075	
OGLE-LMC-CEP-2903	5.24	0.38	1.596	0.013	3.234	0.047	5910	110	-3.92	0.11	-3.26	0.14	0.667	0.034	-4.964	0.073	
OGLE-LMC-CEP-2934	5.29	0.43	1.708	0.016	3.439	0.048	5840	110	-4.46	0.11	-3.77	0.14	0.682	0.035	-5.520	0.083	
OGLE-LMC-CEP-2941	5.35	0.46	1.552	0.016	3.085	0.052	5730	110	-3.59	0.12	-2.87	0.15	0.718	0.034	-4.703	0.090	
OGLE-LMC-CEP-2971	5.52	0.40	1.630	0.014	3.271	0.047	5820	110	-4.04	0.11	-3.35	0.14	0.693	0.034	-5.117	0.077	
OGLE-LMC-CEP-2999	5.05	0.37	1.648	0.013	3.208	0.046	5490	110	-3.94	0.11	-3.15	0.14	0.781	0.034	-5.150	0.072	
OGLE-LMC-CEP-3024	5.41	0.46	1.782	0.013	3.545	0.045	5710	110	-4.76	0.10	-4.04	0.13	0.717	0.035	-5.874	0.070	
OGLE-LMC-CEP-3028	5.36	0.47	1.631	0.017	3.324	0.051	5970	110	-4.15	0.12	-3.51	0.15	0.642	0.034	-5.147	0.091	
OGLE-LMC-CEP-3039	5.57	0.50	1.560	0.019	3.128	0.055	5820	110	-3.68	0.13	-2.99	0.16	0.693	0.034	-4.76	0.10	
OGLE-LMC-CEP-3064	5.32	0.40	1.602	0.014	3.196	0.048	5760	110	-3.86	0.11	-3.15	0.14	0.710	0.034	-4.963	0.077	
OGLE-LMC-CEP-3092	5.72	0.39	1.635	0.014	3.308	0.047	5900	110	-4.12	0.11	-3.45	0.14	0.667	0.034	-5.160	0.076	
OGLE-LMC-CEP-3150	5.46	0.40	1.610	0.014	3.231	0.047	5820	110	-3.94	0.11	-3.25	0.14	0.695	0.034	-5.020	0.077	
OGLE-LMC-CEP-3176	5.55	0.46	1.630	0.018	3.272	0.054	5830	110	-4.04	0.13	-3.35	0.16	0.691	0.034	-5.118	0.096	
OGLE-LMC-CEP-3185	5.41	0.45	1.610	0.017	3.273	0.051	5950	110	-4.02	0.12	-3.37	0.15	0.650	0.034	-5.039	0.090	
OGLE-LMC-CEP-3198	5.70	0.55	1.593	0.021	3.204	0.056	5840	110	-3.87	0.14	-3.19	0.16	0.684	0.034	-4.93	0.11	
OGLE-LMC-CEP-3202	5.65	0.64	1.649	0.025	3.334	0.065	5890	110	-4.18	0.16	-3.51	0.19	0.672	0.036	-5.22	0.13	
OGLE-LMC-CEP-3236	5.37	0.49	1.564	0.018	3.121	0.055	5770	110	-3.67	0.13	-2.96	0.16	0.711	0.034	-4.77	0.10	
OGLE-LMC-CEP-3260	5.73	0.42	1.685	0.015	3.358	0.048	5720	110	-4.27	0.11	-3.55	0.14	0.716	0.034	-5.383	0.080	
OGLE-LMC-CEP-3285	6.18	0.36	1.772	0.012	3.550	0.049	5800	120	-4.74	0.11	-4.06	0.15	0.694	0.037	-5.831	0.070	
OGLE-LMC-CEP-3317	6.05	0.36	1.769	0.011	3.512	0.046	5680	110	-4.66	0.10	-3.93	0.14	0.731	0.035	-5.805	0.066	
OGLE-LMC-CEP-3335	5.89	0.41	1.742	0.016	3.475	0.057	5740	120	-4.57	0.13	-3.85	0.17	0.712	0.038	-5.670	0.094	
OGLE-LMC-CEP-3423	5.11	0.42	1.599	0.014	3.179	0.048	5720	110	-3.82	0.11	-3.10	0.14	0.722	0.034	-4.941	0.079	
OGLE-LMC-CEP-3453	5.04	0.40	1.539	0.014	3.067	0.048	5760	110	-3.54	0.11	-2.83	0.14	0.712	0.034	-4.646	0.077	
OGLE-LMC-CEP-3484	5.82	0.36	1.743	0.012	3.470	0.047	5730	110	-4.55	0.11	-3.84	0.14	0.718	0.035	-5.671	0.071	
OGLE-LMC-CEP-3487	5.88	0.42	1.758	0.014	3.513	0.053	5770	130	-4.66	0.12	-3.95	0.16	0.705	0.040	-5.756	0.080	
OGLE-LMC-CEP-3518	5.75	0.36	1.752	0.012	3.479	0.047	5690	110	-4.58	0.11	-3.86	0.14	0.726	0.034	-5.715	0.070	
OGLE-LMC-CEP-3533	6.05	0.42	1.885	0.013	3.652	0.075	5390	180	-5.04	0.17	-4.20	0.23	0.838	0.057	-6.343	0.095	
OGLE-LMC-CEP-3565	6.17	0.38	1.789	0.013	3.570	0.053	5750	120	-4.81	0.12	-4.10	0.16	0.709	0.040	-5.917	0.076	
OGLE-LMC-CEP-3646	5.71	0.36	1.783	0.013	3.577	0.051	5800	120	-4.82	0.12	-4.13	0.15	0.690	0.037	-5.897	0.073	
OGLE-LMC-CEP-3677	5.94	0.37	1.756	0.013	3.490	0.048	5690	110	-4.61	0.11	-3.88	0.14	0.727	0.036	-5.743	0.073	
OGLE-LMC-CEP-3832	5.63	0.37	1.849	0.012	3.569	0.057	5360	140	-4.84	0.13	-4.00	0.17	0.839	0.044	-6.149	0.076	
OGLE-LMC-CEP-3960	5.44	0.35	1.793	0.012	3.565	0.048	5700	120	-4.80	0.11	-4.08	0.14	0.718	0.036	-5.920	0.068	
OGLE-LMC-CEP-3991	5.83	0.41	1.733	0.013	3.488	0.049	5850	110	-4.58	0.11	-3.90	0.14	0.680	0.036	-5.643	0.076	
OGLE-LMC-CEP-4033	6.06	0.36	1.818	0.012	3.603	0.050	5660	120	-4.89	0.11	-4.15	0.15	0.742	0.038	-6.045	0.070	
OGLE-LMC-CEP-4041	5.43	0.45	1.624	0.016	3.246	0.049	5770	110	-3.98	0.12	-3.27	0.14	0.709	0.034	-5.081	0.087	
OGLE-LMC-CEP-4042	5.29	0.42	1.587	0.015	3.166	0.049	5770	110	-3.78	0.12	-3.07	0.14	0.712	0.034	-4.890	0.083	
OGLE-LMC-CEP-4062	5.38	0.45	1.567	0.017	3.169	0.052	5910	110	-3.77	0.12	-3.11	0.15	0.667	0.034	-4.813	0.092	
OGLE-LMC-CEP-4094	5.40	0.45	1.567	0.016	3.149	0.052	5850	110	-3.73	0.12	-3.05	0.15	0.685	0.034	-4.799	0.090	
OGLE-LMC-CEP-4143	5.70	0.39	1.822	0.013	3.618	0.056	5680	140	-4.94	0.13	-4.21	0.17	0.731	0.044	-6.090	0.078	
OGLE-LMC-CEP-4153	5.84	0.35	1.794	0.012	3.557	0.048	5670	110	-4.78	0.11	-4.04	0.14	0.737	0.036	-5.928	0.069	
OGLE-LMC-CEP-4176	5.85	0.35	1.780	0.011	3.562	0.047	5770	110	-4.78	0.11	-4.08	0.14	0.702	0.035	-5.874	0.067	
OGLE-LMC-CEP-4194	5.86	0.37	1.774	0.012	3.558	0.049	5800	120	-4.77	0.11	-4.07	0.14	0.694	0.036	-5.853	0.071	
OGLE-LMC-CEP-4211	5.98	0.35	1.788	0.012	3.568	0.049	5750	120	-4.80	0.11	-4.09	0.14	0.712	0.036	-5.910	0.069	
OGLE-LMC-CEP-4249	5.43	0.46	1.578	0.017	3.188	0.052	5900	110	-3.82	0.12	-3.16	0.15	0.668	0.034	-4.865	0.092	
OGLE-LMC-CEP-4257	5.18	0.43	1.585	0.016	3.222	0.051	5950	110	-3.89	0.12	-3.24	0.15	0.655	0.034	-4.912	0.088	
OGLE-LMC-CEP-4274	5.46	0.45	1.653	0.015	3.316	0.048	5800	110	-4.15	0.11	-3.45	0.14	0.696	0.034	-5.235	0.083	
OGLE-LMC-CEP-4281	5.34	0.45	1.658	0.015	3.332	0.048	5830	110	-4.19	0.11	-3.50	0.14	0.690	0.034	-5.264	0.082	
OGLE-LMC-CEP-4287	5.79	0.45	1.714	0.016	3.429	0.052	5770	110	-4.44	0.12	-3.74	0.15	0.703	0.035	-5.531	0.088	
OGLE-LMC-CEP-4293	5.49	0.45	1.592	0.017	3.209	0.052	5870	110	-3.87	0.12	-3.20	0.15	0.678	0.034	-4.932	0.090	
OGLE-LMC-CEP-4316	5.31	0.36	1.742	0.012	3.453	0.049	5680	120	-4.52	0.11	-3.80	0.14	0.728	0.036	-5.654	0.071	
OGLE-LMC-CEP-4317	6.06	0.37	1.844	0.012	3.671	0.056	5700	140	-5.07	0.13	-4.35	0.17	0.723	0.043	-6.206	0.077	
OGLE-LMC-CEP-4319	5.80	0.40	1.706	0.014	3.416	0.048	5780	110	-4.40	0.11	-3.70	0.14	0.703	0.035	-5.500	0.079	
OGLE-LMC-CEP-4330	5.33	0.40	1.634	0.014	3.267	0.046	5770	110	-4.03	0.11	-3.32	0.14	0.708	0.033	-5.132	0.075	
OGLE-LMC-CEP-4396	5.48	0.44	1.613	0.016	3.232	0.050	5800	110	-3.94	0.12	-3.25	0.15	0.699	0.034	-5.031	0.086	
OGLE-LMC-CEP-4402	5.87	0.35	1.788	0.011	3.571	0.049	5740	120	-4.81	0.11	-4.10	0.14	0.706	0.038	-5.911	0.067	
OGLE-LMC-CEP-4409	5.63	0.37	1.702	0.013	3.360	0.047	5630	110	-4.29	0.11	-3.55	0.14	0.745	0.034	-5.445	0.072	
OGLE-LMC-CEP-4414	5.85	0.40	1.682	0.013	3.362	0.046	5760	110	-4.27	0.11	-3.57	0.14	0.706	0.034	-5.371	0.074	
OGLE-LMC-CEP-4440	5.42	0.40	1.629	0.014	3.256	0.046	5760	110	-4.00	0.11	-3.29	0.14	0.710	0.033	-5.105	0.075	
OGLE-LMC-CEP-4465	5.33	0.43	1.567	0.016	3.135	0.050	5800	110	-3.70	0.12	-3.00	0.15	0.705	0.034	-4.795	0.086	
OGLE-LMC-CEP-4470	5.35	0.44	1.577	0.016	3.181	0.051	5890	110	-3.80	0.12	-3.14	0.15	0.672	0.034	-4.856	0.090	
OGLE-LMC-CEP-4474	5.45	0.46	1.662	0.016	3.333	0.049	5810	110	-4.20	0.11	-3.50	0.14	0.694	0.034	-5.278	0.085	
OGLE-LMC-CEP-4475	5.31	0.40	1.584	0.014	3.170	0.049	5800	110	-3.79	0.11	-3.09	0.14	0.702	0.034	-4.880	0.080	
OGLE-LMC-CEP-4476	5.39	0.46	1.654	0.015	3.340	0.048	5870	110	-4.20	0.11	-3.52	0.14	0.677	0.034	-5.254	0.083	
OGLE-LMC-CEP-4484	5.21	0.43	1.647	0.015	3.274	0.050	5710	110	-4.06	0.12	-3.34	0.15	0.723	0.034	-5.184	0.084	
OGLE-LMC-CEP-4504	5.31	0.41	1.594	0.015	3.208	0.049	5850	110	-3.87	0.11	-3.19	0.14	0.687	0.034	-4.944	0.081	
OGLE-LMC-CEP-4512	6.10	0.36	1.793	0.013	3.569	0.058	5710	130	-4.80	0.13	-4.09	0.17	0.722	0.042	-5.929	0.081	
OGLE-LMC-CEP-4524	5.37	0.42	1.603	0.015	3.203	0.050	5770	110	-3.87	0.12	-3.17	0.15	0.708	0.034	-4.972	0.083	
OGLE-LMC-CEP-4544	4.86	0.36	1.752	0.012	3.439	0.046	5570	110	-4.50	0.10	-3.74	0.14	0.761	0.035	-5.689	0.066	
OGLE-LMC-CEP-4600	6.01	0.49	1.887	0.017	3.646	0.088	5360	200	-5.03	0.20	-4.17	0.27	0.852	0.065	-6.35	0.11

In [48]:

ests_DF = pd.read_table('ML-OGLE_LMC_CEP.dat', sep='\s+')

In [ ]:

In [49]:

var = 'logL'
mew = 1.8
ms = 20
plt.plot(DF['logP'], -2.5*DF[var].values + 4.77, '.', 
         mfc='white', mec='white', mew=mew, alpha=1, ms=ms)
plt.plot(DF['logP'], -2.5*DF[var].values + 4.77, '.', label='Models', 
         mfc='darkblue', mec='white', mew=mew, alpha=0.5, ms=ms)
plt.plot(logPs, -2.5*ests[:,X_columns.index(var)] + 4.77, '.', 
         mfc='white', mec='white', mew=mew, alpha=1, ms=ms)
plt.plot(logPs, -2.5*ests[:,X_columns.index(var)] + 4.77, '.', label='Predicted', 
         mfc='#F97100', mec='white', mew=mew, alpha=0.6, ms=ms)
plt.xlabel('$\log\;P/$days')
plt.ylabel('Absolute Magnitude')
#plt.ylabel('$\log\;L/$L$_\odot$')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-PM-predicted.pdf')#, bbox_inches='tight')
plt.show()

In [50]:

var = 'W'
mew = 1.4
ms = 18
for idx, star in DF.sample(frac=1, random_state=0).iterrows():
    plt.plot(DF['logP'].iloc[idx], DF[var].iloc[idx], '.', 
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms, label='')
    plt.plot(DF['logP'].iloc[idx], DF[var].iloc[idx], '.', label='Models' if idx == 1 else '', 
             mfc='#F97100', mec='None', mew=mew, alpha=0.5, ms=ms-2)
for ii in range(len(logPs)):
    plt.plot(logPs[ii], ests[:,X_columns.index(var)][ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(logPs[ii], ests[:,X_columns.index(var)][ii], '.', label='Predicted' if ii == 1 else '', 
             mfc='darkblue', mec='None', mew=mew, alpha=0.75, ms=ms-2)
plt.xlabel('$\log\;P/$days')
plt.ylabel('Wesenheit Index')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-W.pdf')#, bbox_inches='tight')
plt.show()

In [51]:

var = 'I_M0'
mew = 1.4
ms = 18
for idx, star in DF.sample(frac=1, random_state=0).iterrows():
    plt.plot(DF['logP'].iloc[idx], DF[var].iloc[idx], '.', 
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms, label='')
    plt.plot(DF['logP'].iloc[idx], DF[var].iloc[idx], '.', label='Models' if idx == 1 else '', 
             mfc='#F97100', mec='None', mew=mew, alpha=0.5, ms=ms-2)
for ii in range(len(logPs)):
    plt.plot(logPs[ii], ests[:,X_columns.index(var)][ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(logPs[ii], ests[:,X_columns.index(var)][ii], '.', label='Predicted' if ii == 1 else '', 
             mfc='darkblue', mec='None', mew=mew, alpha=0.75, ms=ms-2)
plt.xlabel('$\log\;P/$days')
plt.ylabel('$M_I$')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-I.pdf')#, bbox_inches='tight')
plt.show()

In [52]:

var = 'V_M0'
mew = 1.4
ms = 18
for idx, star in DF.sample(frac=1, random_state=0).iterrows():
    plt.plot(DF['logP'].iloc[idx], DF[var].iloc[idx], '.', 
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms, label='')
    plt.plot(DF['logP'].iloc[idx], DF[var].iloc[idx], '.', label='Models' if idx == 1 else '', 
             mfc='#F97100', mec='None', mew=mew, alpha=0.5, ms=ms-2)
for ii in range(len(logPs)):
    plt.plot(logPs[ii], ests[:,X_columns.index(var)][ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(logPs[ii], ests[:,X_columns.index(var)][ii], '.', label='Predicted' if ii == 1 else '', 
             mfc='darkblue', mec='None', mew=mew, alpha=0.75, ms=ms-2)
plt.xlabel('$\log\;P/$days')
plt.ylabel('$M_V$')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-V.pdf')#, bbox_inches='tight')
plt.show()

In [53]:

var = 'VI'
mew = 1.4
ms = 18
for idx, star in DF.sample(frac=1, random_state=0).iterrows():
    plt.plot(DF['logP'].iloc[idx], DF[var].iloc[idx], '.', 
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms, label='')
    plt.plot(DF['logP'].iloc[idx], DF[var].iloc[idx], '.', label='Models' if idx == 1 else '', 
             mfc='#F97100', mec='None', mew=mew, alpha=0.5, ms=ms-2)
for ii in range(len(logPs)):
    plt.plot(logPs[ii], ests[:,X_columns.index(var)][ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(logPs[ii], ests[:,X_columns.index(var)][ii], '.', label='Predicted' if ii == 1 else '', 
             mfc='darkblue', mec='None', mew=mew, alpha=0.75, ms=ms-2)
plt.xlabel('$\log\;P/$days')
plt.ylabel('$V - I$')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-VI.pdf')#, bbox_inches='tight')
plt.show()

In [54]:

var = 'logL'
mew = 1.4
ms = 18
for idx, star in DF.sample(frac=1, random_state=0).iterrows():
    plt.plot(DF['M'].iloc[idx], DF[var].iloc[idx], '.', 
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms, label='')
    plt.plot(DF['M'].iloc[idx], DF[var].iloc[idx], '.', label='Models' if idx == 1 else '', 
             mfc='#F97100', mec='None', mew=mew, alpha=0.5, ms=ms-2)
for ii in range(len(logPs)):
    plt.plot(ests[:,X_columns.index('M')][ii], ests[:,X_columns.index(var)][ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(ests[:,X_columns.index('M')][ii], ests[:,X_columns.index(var)][ii], '.', label='Predicted' if ii == 1 else '', 
             mfc='darkblue', mec='None', mew=mew, alpha=0.75, ms=ms-2)
plt.ylabel('$\log\;L/$L$_\odot$')
plt.xlabel('$M/$M$_\odot$')
plt.legend(loc='best')
#plt.xlim([0.4, 1.5])
#plt.savefig('CEP-LMC-VI.pdf')#, bbox_inches='tight')
plt.show()

In [ ]:

Compare with observations

In [55]:

V_data = pd.read_table('/scratch/seismo/bellinger/asteroseismology/regression/classical/data/cep_lmc_v.dat', sep='\s+')
I_data = pd.read_table('/scratch/seismo/bellinger/asteroseismology/regression/classical/data/cep_lmc_i.dat', sep='\s+')
evi_data = pd.read_table('evi_lmc_ceph.dat', sep='\s+')

In [56]:

ev_mean_val = evi_data['ev_i'].mean()

In [57]:

from uncertainties import ufloat

actual_Ws = []
e_actual_Ws = []
actual_Is = []
actual_Vs = []
actual_VIs = []
for star_name in tqdm(star_names):
    V = ufloat(V_data[V_data['ID'] == star_name]['A0'].iloc[0], V_data[V_data['ID'] == star_name]['eA0'].iloc[0])
    I = ufloat(I_data[I_data['ID'] == star_name]['A0'].iloc[0], I_data[I_data['ID'] == star_name]['eA0'].iloc[0])
    W = I - 1.55 * (V-I)
    actual_Ws += [W.nominal_value]
    e_actual_Ws += [W.std_dev]
    
    ev = evi_data[evi_data['id'] == star_name]
    if ev.shape[0] == 0:
        ev = ev_mean_val
    else:
        ev = ev.iloc[0]['ev_i']
    #A_V = 2.4*E(V-I)
    #A_I = 1.41*E(V-I)
    actual_Is += [I.nominal_value - 1.41*ev]
    actual_Vs += [V.nominal_value - 2.4*ev]
    actual_VIs += [(V-I).nominal_value]

actual_Ws = np.array(actual_Ws)
e_actual_Ws = np.array(e_actual_Ws)
actual_Is = np.array(actual_Is)
actual_Vs = np.array(actual_Vs)
actual_VIs = np.array(actual_VIs)

HBox(children=(IntProgress(value=0, max=325), HTML(value='')))

In [58]:

mew = 1.4 # marker edge width
ms = 18 # marker size 

In [59]:

for ii in range(len(logPs)):
    plt.plot(logPs[ii], actual_Is[ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(logPs[ii], actual_Is[ii], '.', label='Observed' if ii == 1 else '', 
             mfc='#000000', mec='None', mew=mew, alpha=0.75, ms=ms-2)

plt.xlabel('$\log\;P/$days')
plt.ylabel('$M_I$')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-I-obs.pdf')#, bbox_inches='tight')
plt.show()

In [60]:

for ii in range(len(logPs)):
    plt.plot(logPs[ii], actual_Vs[ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(logPs[ii], actual_Vs[ii], '.', label='Observed' if ii == 1 else '', 
             mfc='#000000', mec='None', mew=mew, alpha=0.75, ms=ms-2)
plt.xlabel('$\log\;P/$days')
plt.ylabel('$M_V$')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-V-obs.pdf')
plt.show()

In [61]:

for ii in range(len(logPs)):
    plt.plot(logPs[ii], actual_VIs[ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(logPs[ii], actual_VIs[ii], '.', label='Observed' if ii == 1 else '', 
             mfc='#000000', mec='None', mew=mew, alpha=0.75, ms=ms-2)
plt.xlabel('$\log\;P/$days')
plt.ylabel('$V-I$')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-VI-obs.pdf')#, bbox_inches='tight')
plt.show()

In [62]:

for ii in range(len(logPs)):
    plt.plot(logPs[ii], actual_Ws[ii], '.', label='',
             mfc='None', mec='white', mew=mew, alpha=1, ms=ms)
    plt.plot(logPs[ii], actual_Ws[ii], '.', label='Observed' if ii == 1 else '', 
             mfc='#000000', mec='None', mew=mew, alpha=0.75, ms=ms-2)
plt.xlabel('$\log\;P/$days')
plt.ylabel('Wesenheit Index')
plt.legend(loc='best')
plt.xlim([0.4, 1.5])
plt.savefig('CEP-LMC-W-obs.pdf')#, bbox_inches='tight')
plt.show()

In [ ]:

Estimate distances

In [63]:

plt.plot(DF['logP'], DF['W'], '.', c='gray', label='Models')
plt.plot(logPs, ests[:,X_columns.index('W')], '.', label='Predicted', c='red')
plt.plot(logPs, actual_Ws, '.', label='Actual', c='blue')
plt.xlabel('$\log\;P/$days')
plt.ylabel('Wesenheit Index')
plt.legend(loc='best')
plt.savefig('CEP-LMC-W-comp.pdf')
plt.show()

In [64]:

from uncertainties import unumpy
# 49.59 +/- 0.09_statistical +/- 0.054_systematic Kpc
pietrzynski = 5 * unumpy.log10(1000*ufloat(49.59, np.sqrt((0.09)**2 + (0.054)**2))) - 5
pietrzynski

Out[64]:

18.47697054145555+/-0.0045959169367960516

In [65]:

Ws = ests[:,X_columns.index('W')]
e_Ws = e_ests[:,X_columns.index('W')]

print((actual_Ws - Ws).mean(), '+/-', (actual_Ws -Ws).std())

values = actual_Ws - Ws
weights = 1. / np.sqrt( np.array(e_Ws)**2 + np.array(e_actual_Ws)**2 + 0.89**2 ) 

average = np.average(values, weights=weights)
variance = np.average((values-average)**2, weights=weights)
print(average, '+/-', np.sqrt(variance))

18.683185206153095 +/- 0.1479352628858759
18.68317993439398 +/- 0.14797463537056807

In [66]:

inliers = [True for ii in range(len(actual_Ws))]
while True:
    values = np.array(actual_Ws - ests[:,X_columns.index('W')])
    weights = 1. / np.sqrt( e_ests[:,X_columns.index('W')]**2 + e_actual_Ws**2 + 0.047**2 )**2
    
    average = np.average(values[inliers], weights=weights[inliers])
    variance = np.average((values-average)[inliers]**2, weights=weights[inliers])
    
    new_outliers = np.abs(values[inliers] - average)/np.sqrt(variance) > 5
    if not np.any(new_outliers):
        break
    inliers = np.logical_not(np.abs(values - average)/np.sqrt(variance) > 5)

print(average, '+/-', np.sqrt(variance))

plt.scatter(logPs, actual_Ws - ests[:,X_columns.index('W')], c=np.logical_not(inliers))
#plt.plot(np.array(logPs)[inlier_mask], np.array(actual_Ws - Ws)[inlier_mask], '.')
#plt.plot(np.array(logPs)[outlier_mask], np.array(actual_Ws - Ws)[outlier_mask], '.')

plt.xlabel('$\log\;P/$days')
plt.ylabel('$W_{\\rm{actual}} - W_{\\rm{predicted}}$')
plt.show()

18.688798148600128 +/- 0.09343736583259395

In [67]:

plt.suptitle('         LMC: Cepheids', y=0.99)
plt.hist(np.array(actual_Ws - ests[:,X_columns.index('W')])[inliers])
plt.xlabel('Distance modulus: $W_{\\rm{actual}} - W_{\\rm{predicted}}$ [mag]')
plt.ylabel('Counts')
plt.xlim([17.8, 19.2])
plt.text(17.83, 78, 'Weighted mean:\n$18.688 \pm 0.093$ mag')

plt.savefig('distance_modulus_hist.pdf')
plt.show()

In [ ]:

Use random forests to obtain feature importances

In [68]:

y_col_names = ['$\log\;P$', 
               '$I$ Amplitude', '$I$ Skewness', '$I$ Acuteness',
               '$V$ Amplitude', '$V$ Skewness', '$V$ Acuteness',
               '$I$ $A_1$', '$I$ $A_2$', '$I$ $A_3$',
               '$V$ $A_1$', '$V$ $A_2$', '$V$ $A_3$']

rf = RandomForestRegressor(n_estimators=1024, random_state=1)
X = DF[y_columns]
rf.fit(X, DF['logL'])

importances = rf.feature_importances_
std = np.std([tree.feature_importances_ for tree in rf.estimators_], axis=0)
indices = np.argsort(importances)

In [69]:

plt.figure(figsize=(6,8))
plt.suptitle('                     Cepheids: Luminosity', y=0.99)
rects1 = plt.barh(range(X.shape[1])[:-1], importances[indices][:-1],
       color="r", #yerr=std[indices][1:], 
                  align="center")
plt.yticks(range(X.shape[1])[:-1], [y_col_names[idx] for idx in indices][:-1])#, rotation='vertical')
plt.ylim([-1, X.shape[1]-1])
plt.xlabel('Feature importance')

plt.xlim([0, 0.16])
ax = plt.gca()
ax.set_xticks([0, 0.08, 0.16])
ax.set_xticklabels(['0%', '8%', '16%'])

plt.text(0.0972, -0.1, 'period: %.1f%%' % (importances[0]*100))
plt.text(0.04,   -0.7, 'light curve structure: %.1f%%' % (sum(importances[1:])*100))

def autolabel(rects):
    for rect in rects:
        height = rect.get_height()
        ax.annotate('%.1f' % (height*100) + '%',
                    xy=(rect.get_x() + rect.get_width() / 2, height),
                    xytext=(0, 3), 
                    textcoords="offset points",
                    ha='center', va='bottom')

plt.savefig('CEP-L-importances.pdf')
plt.show()

In [70]:

y_col_names = ['$\log\;P$', 
               '$I$ Amplitude', '$I$ Skewness', '$I$ Acuteness',
               '$V$ Amplitude', '$V$ Skewness', '$V$ Acuteness',
               '$I$ $A_1$', '$I$ $A_2$', '$I$ $A_3$',
               '$V$ $A_1$', '$V$ $A_2$', '$V$ $A_3$']

rf = RandomForestRegressor(n_estimators=1024, random_state=1)
X = DF[y_columns]
rf.fit(X, DF['M'])

importances = rf.feature_importances_
std = np.std([tree.feature_importances_ for tree in rf.estimators_], axis=0)
indices = np.argsort(importances)

plt.figure(figsize=(6,8))
plt.suptitle('                   Cepheids: Mass', y=0.99)
rects1 = plt.barh(range(X.shape[1])[:-1], importances[indices][:-1],
       color="r", #yerr=std[indices][1:], 
                  align="center")
plt.yticks(range(X.shape[1])[:-1], [y_col_names[idx] for idx in indices][:-1])#, rotation='vertical')
plt.ylim([-1, X.shape[1]-1])
plt.xlabel('Feature importance')

plt.xlim([0, 0.16])
ax = plt.gca()
ax.set_xticks([0, 0.08, 0.16])
ax.set_xticklabels(['0%', '8%', '16%'])

plt.text(0.0972, -0.1, 'period: %.1f%%' % (importances[0]*100))
plt.text(0.04,   -0.7, 'light curve structure: %.1f%%' % (sum(importances[1:])*100))

def autolabel(rects):
    for rect in rects:
        height = rect.get_height()
        ax.annotate('%.1f' % (height*100) + '%',
                    xy=(rect.get_x() + rect.get_width() / 2, height),
                    xytext=(0, 3), 
                    textcoords="offset points",
                    ha='center', va='bottom')

plt.savefig('CEP-M-importances.pdf')
plt.show()

In [71]:

y_col_names = ['$\log\;P$', 
               '$I$ Amplitude', '$I$ Skewness', '$I$ Acuteness',
               '$V$ Amplitude', '$V$ Skewness', '$V$ Acuteness',
               '$I$ $A_1$', '$I$ $A_2$', '$I$ $A_3$',
               '$V$ $A_1$', '$V$ $A_2$', '$V$ $A_3$']

rf = RandomForestRegressor(n_estimators=1024, random_state=1)
X = DF[y_columns]
rf.fit(X, DF['Teff'])

importances = rf.feature_importances_
std = np.std([tree.feature_importances_ for tree in rf.estimators_], axis=0)
indices = np.argsort(importances)

plt.figure(figsize=(6,8))
plt.suptitle('                  Cepheids: Effective Temperature', y=0.99)
rects1 = plt.barh(range(X.shape[1])[:-1], importances[indices][:-1],
       color="r", #yerr=std[indices][1:], 
                  align="center")
plt.yticks(range(X.shape[1])[:-1], [y_col_names[idx] for idx in indices][:-1])#, rotation='vertical')
plt.ylim([-1, X.shape[1]-1])
plt.xlabel('Feature importance')

plt.xlim([0, 0.16])
ax = plt.gca()
ax.set_xticks([0, 0.08, 0.16])
ax.set_xticklabels(['0%', '8%', '16%'])

plt.text(0.0972, -0.1, 'period: %.1f%%' % (importances[0]*100))
plt.text(0.04,   -0.7, 'light curve structure: %.1f%%' % (sum(importances[1:])*100))

def autolabel(rects):
    for rect in rects:
        height = rect.get_height()
        ax.annotate('%.1f' % (height*100) + '%',
                    xy=(rect.get_x() + rect.get_width() / 2, height),
                    xytext=(0, 3), 
                    textcoords="offset points",
                    ha='center', va='bottom')

plt.savefig('CEP-Teff-importances.pdf')
plt.show()

In [72]:

y_col_names = ['$\log\;P$', 
               '$I$ Amplitude', '$I$ Skewness', '$I$ Acuteness',
               '$V$ Amplitude', '$V$ Skewness', '$V$ Acuteness',
               '$I$ $A_1$', '$I$ $A_2$', '$I$ $A_3$',
               '$V$ $A_1$', '$V$ $A_2$', '$V$ $A_3$']

rf = RandomForestRegressor(n_estimators=1024, random_state=1)
X = DF[y_columns]
rf.fit(X, DF['W'])

importances = rf.feature_importances_
std = np.std([tree.feature_importances_ for tree in rf.estimators_], axis=0)
indices = np.argsort(importances)

plt.figure(figsize=(6,8))
plt.suptitle('                    Cepheids: Wesenehit', y=0.99)
rects1 = plt.barh(range(X.shape[1])[:-1], importances[indices][:-1],
       color="r", #yerr=std[indices][1:], 
                  align="center")
plt.yticks(range(X.shape[1])[:-1], [y_col_names[idx] for idx in indices][:-1])#, rotation='vertical')
plt.ylim([-1, X.shape[1]-1])
plt.xlabel('Feature importance')

plt.xlim([0, 0.16])
ax = plt.gca()
ax.set_xticks([0, 0.08, 0.16])
ax.set_xticklabels(['0%', '8%', '16%'])

plt.text(0.0972, -0.1, 'period: %.1f%%' % (importances[0]*100))
plt.text(0.045,   -0.7, 'light curve structure: %.1f%%' % (sum(importances[1:])*100))

def autolabel(rects):
    for rect in rects:
        height = rect.get_height()
        ax.annotate('%.1f' % (height*100) + '%',
                    xy=(rect.get_x() + rect.get_width() / 2, height),
                    xytext=(0, 3), 
                    textcoords="offset points",
                    ha='center', va='bottom')

plt.savefig('CEP-W-importances.pdf')
plt.show()

In [73]:

y_col_names = ['$\log\;P$', 
               '$I$ Amplitude', '$I$ Skewness', '$I$ Acuteness',
               '$V$ Amplitude', '$V$ Skewness', '$V$ Acuteness',
               '$I$ $A_1$', '$I$ $A_2$', '$I$ $A_3$',
               '$V$ $A_1$', '$V$ $A_2$', '$V$ $A_3$']

rf = RandomForestRegressor(n_estimators=1024, random_state=1)
X = DF[y_columns]
rf.fit(X, DF['logR'])

importances = rf.feature_importances_
std = np.std([tree.feature_importances_ for tree in rf.estimators_], axis=0)
indices = np.argsort(importances)

plt.figure(figsize=(6,8))
plt.suptitle('                    Cepheids: Radius', y=0.99)
rects1 = plt.barh(range(X.shape[1])[:-1], importances[indices][:-1],
       color="r", #yerr=std[indices][1:], 
                  align="center")
plt.yticks(range(X.shape[1])[:-1], [y_col_names[idx] for idx in indices][:-1])#, rotation='vertical')
plt.ylim([-1, X.shape[1]-1])
plt.xlabel('Feature importance')

plt.xlim([0, 0.16])
ax = plt.gca()
ax.set_xticks([0, 0.08, 0.16])
ax.set_xticklabels(['0%', '8%', '16%'])

plt.text(0.0972, -0.1, 'period: %.1f%%' % (importances[0]*100))
plt.text(0.045,   -0.7, 'light curve structure: %.1f%%' % (sum(importances[1:])*100))

def autolabel(rects):
    for rect in rects:
        height = rect.get_height()
        ax.annotate('%.1f' % (height*100) + '%',
                    xy=(rect.get_x() + rect.get_width() / 2, height),
                    xytext=(0, 3), 
                    textcoords="offset points",
                    ha='center', va='bottom')

plt.savefig('CEP-logR-importances.pdf')
plt.show()

In [ ]:

Compare performance of neural network with a random forest

In [74]:

ml = TransformedTargetRegressor(regressor=Pipeline(
            [('scaler', RobustScaler()), 
             ('mlp', MLPRegressor(hidden_layer_sizes=(100, 100), 
                                  max_iter=2000, activation='relu', solver='lbfgs', tol=1e-7))]),
         transformer=RobustScaler())

lm = LinearRegression()

rf = RandomForestRegressor(n_estimators=1024, random_state=1)

In [75]:

np.random.seed(0) 
cross_val_score(rf, DF[y_columns], DF['M'], cv=ShuffleSplit(n_splits=5, random_state=0), scoring='neg_mean_squared_error').mean()

Out[75]:

-0.1271930454254147

In [76]:

np.random.seed(0) 
cross_val_score(ml, DF[y_columns], DF['M'], cv=ShuffleSplit(n_splits=5, random_state=0), scoring='neg_mean_squared_error').mean()

Out[76]:

-0.101913586103855

In [77]:

np.random.seed(0) 
cross_val_score(lm, DF[y_columns], DF['M'], cv=ShuffleSplit(n_splits=5, random_state=0), scoring='neg_mean_squared_error').mean()

Out[77]:

-0.2947592361576207