import pandas as pd
import numpy as np
import seaborn as sns; sns.set()
import matplotlib.pyplot as plt
import matplotlib.dates as mdates
from sklearn.linear_model import LinearRegression
from scipy import stats
import statsmodels.api as sm
import pylab
# from google.colab import files
# from io import StringIO
# uploaded = files.upload()
url = 'https://raw.githubusercontent.com/assemzh/ProbProg-COVID-19/master/full_grouped.csv'
data = pd.read_csv(url)
data.Date = pd.to_datetime(data.Date)
# for fancy python printing
from IPython.display import Markdown, display
def printmd(string):
display(Markdown(string))
import warnings
warnings.filterwarnings('ignore')
import matplotlib as mpl
mpl.rcParams['figure.dpi'] = 250
/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead. import pandas.util.testing as tm
# function to make the time series of confirmed and daily confirmed cases for a specific country
def create_country (country, end_date, state = False) :
if state :
df = data.loc[data["Province/State"] == country, ["Province/State", "Date", "Confirmed", "Deaths", "Recovered"]]
else :
df = data.loc[data["Country/Region"] == country, ["Country/Region", "Date", "Confirmed", "Deaths", "Recovered"]]
df.columns = ["country", "date", "confirmed", "deaths", "recovered"]
# group by country and date, sum(confirmed, deaths, recovered). do this because countries have multiple cities
df = df.groupby(['country','date'])['confirmed', 'deaths', 'recovered'].sum().reset_index()
# convert date string to datetime
std_dateparser = lambda x: str(x)[5:10]
df.date = pd.to_datetime(df.date)
df['date_only'] = df.date.apply(std_dateparser)
df = df.sort_values(by = "date")
df = df[df.date <= end_date]
# make new confirmed cases every day:
cases_shifted = np.array([0] + list(df.confirmed[:-1]))
daily_confirmed = np.array(df.confirmed) - cases_shifted
df["daily_confirmed"] = daily_confirmed
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(7, 6))
ax = [ax]
sns.lineplot(x = df.date,
y = df.daily_confirmed,
ax = ax[0])
ax[0].set(ylabel='Daily Confirmed Cases')
ax[0].axvline(pd.to_datetime('2020-03-21'),
linestyle = '--', linewidth = 1.5,
label = "Policy start: Mar 21, 2020" ,
color = "red")
ax[0].xaxis.get_label().set_fontsize(16)
ax[0].yaxis.get_label().set_fontsize(16)
ax[0].title.set_fontsize(20)
ax[0].tick_params(labelsize=16)
myFmt = mdates.DateFormatter('%b %-d')
ax[0].xaxis.set_major_formatter(myFmt)
ax[0].set(ylabel='Daily Confirmed Cases', xlabel='');
ax[0].legend(loc = "bottom right", fontsize=12.8)
ax[0].xaxis.set_major_locator(mdates.MonthLocator(interval=1)) #to get a tick every month
sns.set_style("ticks")
plt.tight_layout()
sns.despine()
plt.savefig('/content/sample_data/aus_daily.pdf')
print(df.tail())
return df
def summary(samples):
site_stats = {}
for k, v in samples.items():
site_stats[k] = {
"mean": torch.mean(v, 0),
"std": torch.std(v, 0),
"5%": v.kthvalue(int(len(v) * 0.05), dim=0)[0],
"95%": v.kthvalue(int(len(v) * 0.95), dim=0)[0],
}
return site_stats
cad = create_country("Australia", end_date = "2020-05-31")
country date confirmed ... recovered date_only daily_confirmed 126 Australia 2020-05-27 7150 ... 6579 05-27 11 127 Australia 2020-05-28 7165 ... 6576 05-28 15 128 Australia 2020-05-29 7184 ... 6605 05-29 19 129 Australia 2020-05-30 7192 ... 6614 05-30 8 130 Australia 2020-05-31 7202 ... 6618 05-31 10 [5 rows x 7 columns]
cad_start = "2020-03-01" # 13 confirmed cases
cad = cad[cad.date >= cad_start].reset_index(drop = True)
cad["days_since_start"] = np.arange(cad.shape[0]) + 1
cad.shape
cad_tmp = cad[cad.date < "2020-05-01"]
cad_tmp.shape
(61, 8)
# variable for data to easily swap it out:
country_ = "Australia (Before May 1st)"
reg_data = cad_tmp.copy()
reg_data.head()
country | date | confirmed | deaths | recovered | date_only | daily_confirmed | days_since_start | |
---|---|---|---|---|---|---|---|---|
0 | Australia | 2020-03-01 | 27 | 1 | 11 | 03-01 | 2 | 1 |
1 | Australia | 2020-03-02 | 30 | 1 | 11 | 03-02 | 3 | 2 |
2 | Australia | 2020-03-03 | 39 | 1 | 11 | 03-03 | 9 | 3 |
3 | Australia | 2020-03-04 | 52 | 2 | 11 | 03-04 | 13 | 4 |
4 | Australia | 2020-03-05 | 55 | 2 | 21 | 03-05 | 3 | 5 |
!pip install pyro-ppl
!pip install numpyro
Collecting pyro-ppl Downloading https://files.pythonhosted.org/packages/aa/7a/fbab572fd385154a0c07b0fa138683aa52e14603bb83d37b198e5f9269b1/pyro_ppl-1.6.0-py3-none-any.whl (634kB) |████████████████████████████████| 634kB 16.8MB/s Requirement already satisfied: tqdm>=4.36 in /usr/local/lib/python3.7/dist-packages (from pyro-ppl) (4.41.1) Requirement already satisfied: numpy>=1.7 in /usr/local/lib/python3.7/dist-packages (from pyro-ppl) (1.19.5) Requirement already satisfied: opt-einsum>=2.3.2 in /usr/local/lib/python3.7/dist-packages (from pyro-ppl) (3.3.0) Requirement already satisfied: torch>=1.8.0 in /usr/local/lib/python3.7/dist-packages (from pyro-ppl) (1.8.1+cu101) Collecting pyro-api>=0.1.1 Downloading https://files.pythonhosted.org/packages/fc/81/957ae78e6398460a7230b0eb9b8f1cb954c5e913e868e48d89324c68cec7/pyro_api-0.1.2-py3-none-any.whl Requirement already satisfied: typing-extensions in /usr/local/lib/python3.7/dist-packages (from torch>=1.8.0->pyro-ppl) (3.7.4.3) Installing collected packages: pyro-api, pyro-ppl Successfully installed pyro-api-0.1.2 pyro-ppl-1.6.0 Collecting numpyro Downloading https://files.pythonhosted.org/packages/00/a6/064eedcec968207259acf06cf156c0ea9a6534328bdf7da0e768cfdb3239/numpyro-0.6.0-py3-none-any.whl (218kB) |████████████████████████████████| 225kB 20.0MB/s Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from numpyro) (4.41.1) Collecting jax==0.2.10 Downloading https://files.pythonhosted.org/packages/88/9d/2862825b5eddd0df64c78b22cc0b897f0128b1c6494bf39e4849e9e0fade/jax-0.2.10.tar.gz (589kB) |████████████████████████████████| 593kB 47.3MB/s Collecting jaxlib==0.1.62 Downloading https://files.pythonhosted.org/packages/7e/75/30f1c643b7edb1309b6d748809042241737fe43127cb41754266eca79250/jaxlib-0.1.62-cp37-none-manylinux2010_x86_64.whl (35.7MB) |████████████████████████████████| 35.7MB 78kB/s Requirement already satisfied: numpy>=1.12 in /usr/local/lib/python3.7/dist-packages (from jax==0.2.10->numpyro) (1.19.5) Requirement already satisfied: absl-py in /usr/local/lib/python3.7/dist-packages (from jax==0.2.10->numpyro) (0.12.0) Requirement already satisfied: opt_einsum in /usr/local/lib/python3.7/dist-packages (from jax==0.2.10->numpyro) (3.3.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from jaxlib==0.1.62->numpyro) (1.4.1) Requirement already satisfied: flatbuffers in /usr/local/lib/python3.7/dist-packages (from jaxlib==0.1.62->numpyro) (1.12) Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from absl-py->jax==0.2.10->numpyro) (1.15.0) Building wheels for collected packages: jax Building wheel for jax (setup.py) ... done Created wheel for jax: filename=jax-0.2.10-cp37-none-any.whl size=679776 sha256=7d0fef4762e0db39ed221ac892a147049a5b63230b808d9e1d7f4399db61851c Stored in directory: /root/.cache/pip/wheels/44/ea/ac/3be3bc19ee3b62f6fe1561eb6df1199284bb6bab819c1befa4 Successfully built jax Installing collected packages: jax, jaxlib, numpyro Found existing installation: jax 0.2.12 Uninstalling jax-0.2.12: Successfully uninstalled jax-0.2.12 Found existing installation: jaxlib 0.1.65+cuda110 Uninstalling jaxlib-0.1.65+cuda110: Successfully uninstalled jaxlib-0.1.65+cuda110 Successfully installed jax-0.2.10 jaxlib-0.1.62 numpyro-0.6.0
import torch
import pyro
import pyro.distributions as dist
from torch import nn
from pyro.nn import PyroModule, PyroSample
from pyro.infer import MCMC, NUTS, HMC
from pyro.infer.autoguide import AutoGuide, AutoDiagonalNormal
from pyro.infer import SVI, Trace_ELBO
from pyro.infer import Predictive
# we should be able to have an empirical estimate for the mean of the prior for the 2nd regression bias term
# this will be something like b = log(max(daily_confirmed))
# might be able to have 1 regression model but change the data so that we have new terms for (tau < t)
# like an interaction term
class COVID_change(PyroModule):
def __init__(self, in_features, out_features, b1_mu, b2_mu):
super().__init__()
self.linear1 = PyroModule[nn.Linear](in_features, out_features, bias = False)
self.linear1.weight = PyroSample(dist.Normal(0.5, 0.25).expand([1, 1]).to_event(1))
self.linear1.bias = PyroSample(dist.Normal(b1_mu, 1.))
# could possibly have stronger priors for the 2nd regression line, because we wont have as much data
self.linear2 = PyroModule[nn.Linear](in_features, out_features, bias = False)
self.linear2.weight = PyroSample(dist.Normal(0., 0.25).expand([1, 1])) #.to_event(1))
self.linear2.bias = PyroSample(dist.Normal(b2_mu, b2_mu/4))
def forward(self, x, y=None):
tau = pyro.sample("tau", dist.Beta(4, 3))
sigma = pyro.sample("sigma", dist.Uniform(0., 3.))
# fit lm's to data based on tau
sep = int(np.ceil(tau.detach().numpy() * len(x)))
mean1 = self.linear1(x[:sep]).squeeze(-1)
mean2 = self.linear2(x[sep:]).squeeze(-1)
mean = torch.cat((mean1, mean2))
obs = pyro.sample("obs", dist.StudentT(2, mean, sigma), obs=y)
return mean
tensor_data = torch.tensor(reg_data[["confirmed", "days_since_start", "daily_confirmed"]].values, dtype=torch.float)
x_data = tensor_data[:, 1].unsqueeze_(1)
y_data = np.log(tensor_data[:, 0])
y_data_daily = np.log(tensor_data[:, 2])
# prior hyper params
# take log of the average of the 1st quartile to get the prior mean for the bias of the 2nd regression line
q1 = np.quantile(y_data, q = 0.25)
bias_1_mean = np.mean(y_data.numpy()[y_data <= q1])
print("Prior mean for Bias 1: ", bias_1_mean)
# take log of the average of the 4th quartile to get the prior mean for the bias of the 2nd regression line
q4 = np.quantile(y_data, q = 0.75)
bias_2_mean = np.mean(y_data.numpy()[y_data >= q4])
print("Prior mean for Bias 2: ", bias_2_mean)
Prior mean for Bias 1: 4.5138054 Prior mean for Bias 2: 8.800875
model = COVID_change(1, 1,
b1_mu = bias_1_mean,
b2_mu = bias_2_mean)
# need more than 400 samples/chain if we want to use a flat prior on b_2 and w_2
num_samples = 400
# mcmc
nuts_kernel = NUTS(model)
mcmc = MCMC(nuts_kernel,
num_samples=num_samples,
warmup_steps = 200,
num_chains = 1)
mcmc.run(x_data, y_data)
samples = mcmc.get_samples()
Sample: 100%|██████████| 600/600 [24:27, 2.45s/it, step size=1.31e-04, acc. prob=0.936]
# Save the model:
import dill
# with open('aus.pkl', 'wb') as f:
# dill.dump(mcmc, f)
with open('aus.pkl', 'rb') as f:
mcmc = dill.load(f)
samples = mcmc.get_samples()
# extract individual posteriors
weight_1_post = samples["linear1.weight"].detach().numpy()
weight_2_post = samples["linear2.weight"].detach().numpy()
bias_1_post = samples["linear1.bias"].detach().numpy()
bias_2_post = samples["linear2.bias"].detach().numpy()
tau_post = samples["tau"].detach().numpy()
sigma_post = samples["sigma"].detach().numpy()
# build likelihood distribution:
tau_days = list(map(int, np.ceil(tau_post * len(x_data))))
mean_ = torch.zeros(len(tau_days), len(x_data))
obs_ = torch.zeros(len(tau_days), len(x_data))
for i in range(len(tau_days)) :
mean_[i, :] = torch.cat((x_data[:tau_days[i]] * weight_1_post[i] + bias_1_post[i],
x_data[tau_days[i]:] * weight_2_post[i] + bias_2_post[i])).reshape(len(x_data))
obs_[i, :] = dist.Normal(mean_[i, :], sigma_post[i]).sample()
samples["_RETURN"] = mean_
samples["obs"] = obs_
pred_summary = summary(samples)
mu = pred_summary["_RETURN"] # mean
y = pred_summary["obs"] # samples from likelihood: mu + sigma
y_shift = np.exp(y["mean"]) - np.exp(torch.cat((y["mean"][0:1], y["mean"][:-1])))
print(y_shift)
predictions = pd.DataFrame({
"days_since_start": x_data[:, 0],
"mu_mean": mu["mean"], # mean of likelihood
"mu_perc_5": mu["5%"],
"mu_perc_95": mu["95%"],
"y_mean": y["mean"], # mean of likelihood + noise
"y_perc_5": y["5%"],
"y_perc_95": y["95%"],
"true_confirmed": y_data,
"true_daily_confirmed": y_data_daily,
"y_daily_mean": y_shift
})
w1_ = pred_summary["linear1.weight"]
w2_ = pred_summary["linear2.weight"]
b1_ = pred_summary["linear1.bias"]
b2_ = pred_summary["linear2.bias"]
tau_ = pred_summary["tau"]
sigma_ = pred_summary["sigma"]
ind = int(np.ceil(tau_["mean"] * len(x_data)))
tensor([ 0.0000, 4.4640, 5.2986, 6.8328, 7.8025, 9.8307, 11.8612, 13.4422, 16.9518, 21.2977, 25.7285, 30.4241, 37.7013, 43.8305, 55.0542, 66.6997, 82.1629, 95.6561, 117.4060, 145.2230, 175.4886, 211.9290, 252.8590, 310.6555, 379.7236, 451.5439, 559.8037, 658.4072, 847.2842, 877.7178, 175.0576, -171.3018, 37.2290, 74.0874, 53.8413, 3.1011, 94.8687, 41.6509, 16.6680, 45.3633, 94.5469, -3.4326, 76.7153, 62.1982, 78.2866, 68.9971, 30.5205, 19.0586, 94.0020, 30.3032, 79.4014, 12.0522, 31.2920, 95.9932, 42.5098, 67.3188, 84.3203, 12.1406, 83.1426, 40.8364, 60.2397])
mcmc.summary()
diag = mcmc.diagnostics()
print(ind)
print(reg_data.date[ind])
sns.distplot(weight_1_post,
kde_kws = {"label": "Weight posterior before CP"},
# color = "blue",
norm_hist = True,
kde = True)
plt.axvline(x = w1_["mean"], linestyle = '--',label = "Mean weight before CP" ,)
# color = "blue")
sns.distplot(weight_2_post,
kde_kws = {"label": "Weight posterior after CP"},
color = "red",
norm_hist = True,
kde = True)
plt.axvline(x = w2_["mean"], linestyle = '--',label = "Mean weight after CP" ,
color = "red")
legend = plt.legend(loc='upper right')
legend.get_frame().set_alpha(1)
sns.set_style("ticks")
plt.tight_layout()
sns.despine()
plt.savefig('/content/sample_data/aus_weights.pdf')
30 2020-03-31 00:00:00
print(w1_["mean"])
print(w2_["mean"])
tensor([[0.1928]]) tensor([[0.0085]])
1- w2_['mean']/w1_['mean']
tensor([[0.9561]])
reg_data.date[40]
Timestamp('2020-04-10 00:00:00')
start_date_ = str(reg_data.date[0]).split(' ')[0]
change_date_ = str(reg_data.date[ind]).split(' ')[0]
print("Date of change for {}: {}".format(country_, change_date_))
import seaborn as sns
# plot data:
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(7, 5))
ax = [ax]
# log regression model
ax[0].scatter(y = np.exp(y_data[:ind]), x = x_data[:ind], s = 15);
ax[0].scatter(y = np.exp(y_data[ind:]), x = x_data[ind:], s = 15, color = "red");
ax[0].plot(predictions["days_since_start"],
np.exp(predictions["y_mean"]),
color = "green",
label = "Fitted line by MCMC-NUTS model")
ax[0].axvline(20,
linestyle = '--', linewidth = 1.5,
label = "Policy start: Mar 21, 2020" ,
color = "red")
ax[0].axvline(ind,
linestyle = '--', linewidth = 1.5,
label = "Date of Change: Mar 31, 2020",
color = "black")
ax[0].fill_between(predictions["days_since_start"],
np.exp(predictions["y_perc_5"]),
np.exp(predictions["y_perc_95"]),
alpha = 0.25,
label = "90% CI of predictions",
color = "teal");
ax[0].fill_betweenx([0, 1],
tau_["5%"] * len(x_data),
tau_["95%"] * len(x_data),
alpha = 0.25,
label = "90% CI of changing point",
color = "lightcoral",
transform=ax[0].get_xaxis_transform());
ax[0].set(ylabel = "Total Cases",)
ax[0].legend(loc = "lower right", fontsize=12.8)
ax[0].set_ylim([100,10000])
ax[0].set_xlim([5,60])
ax[0].xaxis.get_label().set_fontsize(16)
ax[0].yaxis.get_label().set_fontsize(16)
ax[0].title.set_fontsize(20)
ax[0].tick_params(labelsize=16)
plt.xticks(ticks=[10,20,30,50], labels=["Mar 10",
"Mar 21",
"Mar 31",
"Apr 20"], fontsize=15)
ax[0].set_yscale('log')
plt.setp(ax[0].get_xticklabels(), rotation=0, horizontalalignment='center')
print(reg_data.columns)
myFmt = mdates.DateFormatter('%m-%d')
sns.set_style("ticks")
sns.despine()
plt.savefig('/content/sample_data/aus_cp.pdf')
Date of change for Australia (Before May 1st): 2020-03-31 Index(['country', 'date', 'confirmed', 'deaths', 'recovered', 'date_only', 'daily_confirmed', 'days_since_start'], dtype='object')
fig, ax = plt.subplots(1,3, figsize=(15, 6))
#plt.figure(figsize=(11, 5))
sns.lineplot(x="date",
y="confirmed",
data= reg_data,
ax = ax[0]
).set_title("Confirmed COVID-19 Cases in %s" % country_)
ax[0].axvline(reg_data.date[ind], color="red", linestyle="--")
ax[1].scatter(y = reg_data.confirmed[:ind], x = x_data[:ind], s = 15);
ax[1].scatter(y = reg_data.confirmed[ind:], x = x_data[ind:], s = 15, color = "red");
ax[1].plot(predictions["days_since_start"],
np.exp(predictions["y_mean"]),
color = "green",
label = "Mean")
ax[1].axvline(ind, linestyle = '--',
linewidth = 1,
label = "Day of Change")
ax[1].legend(loc = "upper left")
ax[1].set(ylabel = "Confirmed Cases",
xlabel = "Days since %s" % start_date_,
title = "Confirmed Cases: %s" % country_);
ax[2].scatter(y = reg_data.daily_confirmed[:ind], x = x_data[:ind], s = 15);
ax[2].scatter(y = reg_data.daily_confirmed[ind:], x = x_data[ind:], s = 15, color = "red");
ax[2].plot(predictions["days_since_start"],
predictions["y_daily_mean"],
color = "green",
label = "Mean")
ax[2].axvline(ind, linestyle = '--',
linewidth = 1,
label = "Day of Change")
ax[2].legend(loc = "upper left")
ax[2].set(ylabel = "Daily Confirmed Cases",
xlabel = "Days since %s" % start_date_,
title = "Daily Confirmed Cases: %s" % country_);
printmd("**Date of change for {}: {}**".format(country_, change_date_));
import matplotlib.dates as mdates
myFmt = mdates.DateFormatter('%m-%d')
ax[0].xaxis.set_major_formatter(myFmt)
# ax[0].set_xticklabels(reg_data.date, rotation = 45, fontsize="10", va="center")
plt.setp(ax[0].get_xticklabels(), rotation=30, horizontalalignment='right')
ax[0].set(ylabel='Confirmed Cases', xlabel='Date');
plt.tight_layout()
plt.savefig('/content/sample_data/sing_mean.pdf')
Date of change for Australia (Before May 1st): 2020-03-31