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('2020-03-25'),
linestyle = '--', linewidth = 1.5,
label = "Date of Lockdown: Mar 25, 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 = "upper right", fontsize=12.8)
sns.set_style("ticks")
ax[0].xaxis.set_major_locator(mdates.MonthLocator(interval=1)) #to get a tick every month
plt.tight_layout()
sns.despine()
plt.savefig('/content/sample_data/nz_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("New Zealand", end_date = "2020-05-31")
country date confirmed ... recovered date_only daily_confirmed 126 New Zealand 2020-05-27 1504 ... 1474 05-27 0 127 New Zealand 2020-05-28 1504 ... 1481 05-28 0 128 New Zealand 2020-05-29 1504 ... 1481 05-29 0 129 New Zealand 2020-05-30 1504 ... 1481 05-30 0 130 New Zealand 2020-05-31 1504 ... 1481 05-31 0 [5 rows x 7 columns]
cad_start = "2020-03-20" # 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
(42, 8)
# variable for data to easily swap it out:
country_ = "New Zealand (Before May 1st)"
reg_data = cad_tmp.copy()
reg_data.head()
country | date | confirmed | deaths | recovered | date_only | daily_confirmed | days_since_start | |
---|---|---|---|---|---|---|---|---|
0 | New Zealand | 2020-03-20 | 39 | 0 | 0 | 03-20 | 11 | 1 |
1 | New Zealand | 2020-03-21 | 52 | 0 | 0 | 03-21 | 13 | 2 |
2 | New Zealand | 2020-03-22 | 102 | 0 | 0 | 03-22 | 50 | 3 |
3 | New Zealand | 2020-03-23 | 102 | 0 | 0 | 03-23 | 0 | 4 |
4 | New Zealand | 2020-03-24 | 155 | 0 | 12 | 03-24 | 53 | 5 |
!pip install pyro-ppl
!pip install numpyro
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: 5.228802 Prior mean for Bias 2: 7.2882066
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 [35:20, 3.53s/it, step size=1.95e-03, acc. prob=0.787]
# Save the model:
import dill
# with open('newz.pkl', 'wb') as f:
# dill.dump(mcmc, f)
with open('newz.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, 15.8725, 20.2801, 26.8865, 32.5610, 42.9602, 52.2524, 67.1801, 87.8423, 108.9554, 138.8970, 182.3773, 180.1835, 83.8043, 26.4193, 28.7574, 6.4791, 17.1486, 15.2979, 9.4363, 24.9604, 9.7537, 8.2566, 28.7927, 7.6711, 17.5988, 3.3445, 42.3142, 11.2130, 18.5885, 12.2999, 17.2067, 25.4421, 18.3486, 8.3947, 9.0435, 15.9739, 25.5782, 20.5530, 26.4995, 20.7136, 15.9384])
mcmc.summary()
diag = mcmc.diagnostics()
mean std median 5.0% 95.0% n_eff r_hat tau 0.30 0.03 0.30 0.26 0.35 23.21 1.10 sigma 0.08 0.01 0.08 0.05 0.09 58.71 1.00 linear1.weight[0,0] 0.24 0.03 0.24 0.19 0.30 20.29 1.23 linear1.bias 3.84 0.22 3.88 3.41 4.10 19.70 1.24 linear2.weight[0,0] 0.01 0.00 0.01 0.01 0.02 38.89 1.00 linear2.bias 6.85 0.07 6.85 6.74 6.95 38.67 1.00 Number of divergences: 0
print(ind)
print(reg_data.date[ind])
sns.distplot(weight_1_post,
kde_kws = {"label": "Weight posterior before CP"},
color = "red",
norm_hist = True,
kde = True)
plt.axvline(x = w1_["mean"], linestyle = '--',label = "Mean weight before CP" ,
color = "red")
sns.distplot(weight_2_post,
kde_kws = {"label": "Weight posterior after CP"},
color = "teal",
norm_hist = True,
kde = True)
plt.axvline(x = w2_["mean"], linestyle = '--',label = "Mean weight after CP" ,
color = "teal")
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/nz_weights.pdf')
13 2020-04-02 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(5,
linestyle = '--', linewidth = 1.5,
label = "Date of Lockdown: Mar 25, 2020" ,
color = "red")
ax[0].axvline(ind,
linestyle = '--', linewidth = 1.5,
label = "Date of Change: Apr 2, 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([11,10000])
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=[5, 13, 21, 31], labels=["Mar 25",
"Apr 2",
"Apr 10",
"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/nz_cp.pdf')
Date of change for New Zealand (Before May 1st): 2020-04-02 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/nz_mean.pdf')
Date of change for New Zealand (Before May 1st): 2020-04-02