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KSegmentsModel.py
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KSegmentsModel.py
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import pymc3 as pm
from numpy.random import normal
from datetime import timedelta
import warnings
warnings.filterwarnings('ignore')
plt.style.use('seaborn-darkgrid')
class KSegmentsModel:
"""Instantiates a model object for COVID-19 data on a country"""
def __init__(self, data, country_name):
self.country_name = country_name
self.df = self.create_extra_fields(data)
self.k = 2
self.start = 0
self.end = -1
self.trace = None
def create_extra_fields(self, data):
"""Creates extra fields required for data parsing"""
df = data.loc[data['Country/Region'] == self.country_name,
["Country/Region", "Date", "Confirmed", "Deaths", "Recovered"]]
df.columns = ['country', 'date', 'confirmed', 'deaths', 'recovered']
df.groupby(['country', 'date'])['confirmed', 'deaths', 'recovered'].sum().reset_index()
df.date = pd.to_datetime(df.date)
df = df.sort_values(by='date')
# create daily cases
day_before = np.array([0]+list(df['confirmed'][:-1]))
daily_confirmed = np.array(df['confirmed']) - day_before
df['daily_confirmed'] = daily_confirmed
# create rolling mean
df['rolling_mean'] = df['daily_confirmed'].rolling(window=4).mean()
# create log of daily cases
start_date = df['date'].min()
df['days_since_start'] = df['date'] - start_date
df['days_since_start'] = df['days_since_start'].dt.days.astype(int)
df['log_daily_confirmed'] = np.log1p(df['daily_confirmed'])
# view confirmed cases
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(15, 6))
sns.lineplot(x=df.date, y=df.daily_confirmed, ax=ax1)
ax1.set(ylabel='Daily Confirmed Cases', xlabel='Date',
title=f'Daily New Confirmed Cases in {self.country_name}')
sns.lineplot(x=df.date, y=df.confirmed, ax=ax2)
ax2.set(ylabel='Cumulative Confirmed Cases', xlabel='Date',
title=f'Cumulative Total Confirmed Cases in {self.country_name}')
return df
def plot_log(self, start=0, end=-1):
"""Plots the log scatter graph for the given data"""
plt.figure(figsize=(12, 7))
ax = sns.scatterplot(
x=self.df['days_since_start'].iloc[start:end],
y=self.df['log_daily_confirmed'].iloc[start:end])
min_date = self.df['date'].iloc[0].date()
start_date = self.df['date'].iloc[start].date()
end_date = self.df['date'].iloc[end].date()
ax.set(ylabel='Log of daily new cases', xlabel=f'Days since {min_date}',
title=f'Log Daily confirmed cases: {self.country_name} from {start_date} to {end_date}')
return ax
def fit(self, k, start=0, end=-1,, sample=20000, tune=1000, chains=2, cores=2):
"""Fits a segmented linear regression model on the data"""
# Update instance parameters
self.k = k
self.start = start
self.end = end
x = self.df['days_since_start'][start:end]
y = self.df['log_daily_confirmed'].iloc[start:end]
with pm.Model() as model:
sigma = pm.HalfCauchy('sigma', beta=10, testval=1.)
# switchpoint array
s_arr = []
s_testvals = x.quantile(q=[i/k for i in range(1, k)]).values
for i in range(k-1):
s_arr.append(
pm.DiscreteUniform(
f's{i+1}',
lower = x.iloc[0] if not s_arr else s_arr[-1],
upper = x.iloc[-1], testval = s_testvals[i]))
# priors for the pre and post switch intercepts and gradients
w_arr = []
b_arr = []
for i in range(k):
w_arr.append(pm.Uniform(f'w{i+1}', lower=-10, upper=10))
b_arr.append(pm.Normal(f'b{i+1}', 0, sd=20))
w_switch_arr = []
b_switch_arr = []
for i in range(k-1):
w_switch_arr.append(
pm.math.switch(
s_arr[-(i+1)] < x,
w_arr[-1] if not w_switch_arr else w_switch_arr[-1],
w_arr[-(i+2)]))
b_switch_arr.append(
pm.math.switch(
s_arr[-(i+1)] < x,
b_arr[-1] if not b_switch_arr else b_switch_arr[-1],
b_arr[-(i+2)]))
likelihood = pm.Normal(
'y', mu = w_switch_arr[-1] * x + b_switch_arr[-1], sd=sigma, observed=y)
start = pm.find_MAP()
nuts_arr = [sigma]
for i in range(k):
nuts_arr.append(b_arr[i])
nuts_arr.append(w_arr[i])
step1 = pm.NUTS(nuts_arr)
step2 = pm.Metropolis(s_arr)
trace = pm.sample(
sample, tune=tune, step=[step1, step2],
start=start, chains=chains, progressbar=True, cores=cores)
# Update trace
self.trace = trace
return trace
def plot_posterior(self, burn_in=5000):
"""Plots the posterior distribution of samples parameters"""
# define parameters
t = self.trace
k = self.k
num_plots = 2 * k + (k-1) + 1
fig, axs = plt.subplots(nrows=num_plots, ncols=1, figsize=(15, 3 * num_plots))
ax_idx = 0
for i in range(k):
axs[ax_idx].hist(t[f'w{i+1}'][burn_in:], histtype='stepfilled',
bins=25, alpha=0.85, label=f"posterior of $w{i+1}$",
color="red", density=True)
axs[ax_idx].legend(loc='upper right')
ax_idx += 1
axs[ax_idx].hist(t[f'b{i+1}'][burn_in:], histtype='stepfilled',
bins=25, alpha=0.85, label=f"posterior of $b{i+1}$",
color="blue", density=True)
axs[ax_idx].legend(loc='upper right')
ax_idx += 1
for i in range(k-1):
axs[ax_idx].hist(t[f's{i+1}'][burn_in:], histtype='stepfilled',
bins=25, alpha=0.85, label=f"posterior of $s{i+1}$",
color="green", density=True)
axs[ax_idx].legend(loc='upper right')
ax_idx += 1
axs[ax_idx].hist(t['sigma'][burn_in:], histtype='stepfilled',
bins=25, alpha=0.85, label="posterior of $sigma$",
color="yellow", density=True)
axs[ax_idx].legend(loc='upper right')
def plot_extrapolation(self, days_after=30, burn_in=5000):
"""Plots the extrapolation `days_after` with the fitted model and data"""
# define parameters
df = self.df
start = self.start
end = self.end
x = df['days_since_start'][start:end]
y = df['log_daily_confirmed'].iloc[start:end]
t = self.trace
k = self.k
# get expected values
w_preds = [get_pred(w, burn_in) for w in [t[f'w{i+1}'] for i in range(k)]]
b_preds = [get_pred(b, burn_in) for b in [t[f'b{i+1}'] for i in range(k)]]
s_preds = [int(round(get_pred(s, burn_in))) for s in [t[f's{i+1}'] for i in range(k-1)]]
sigma_samples = t['sigma'][burn_in:]
# define y_fit
y_fit = get_y(x, s_preds, b_preds, w_preds, std=0)
# define 90% credible intervals for data
lower_bounds, upper_bounds = get_confidence_intervals(sigma_samples, y_fit)
# define 90% credible intervals for extrapolation
last_day = df['date'].iloc[end-1]
x_after = np.linspace(x.iloc[-1], x.iloc[-1]+days_after, days_after+1)
dates_after = np.array([last_day + timedelta(days=x) for x in range(days_after+1)])
y_fit_pred = b_preds[-1] + w_preds[-1] * x_after
pred_lower_bounds, pred_upper_bounds = get_confidence_intervals(sigma_samples, y_fit_pred)
# Plot the original and extrapolation
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(18, 7))
sns.lineplot(x, y_fit, color='orange', label='y fit from posterior means',
ax=ax1)
sns.scatterplot(df['days_since_start'], df['log_daily_confirmed'], label='Actual y', ax=ax1)
sns.lineplot(x_after, y_fit_pred, color='r', label='Extrapolated y fit', ax=ax1)
ax1.fill_between(x, lower_bounds, upper_bounds, alpha=0.5,
label='90% credible simulated y')
ax1.fill_between(x_after, pred_lower_bounds, pred_upper_bounds, alpha=0.5,
color='r', label='Extrapolated 90% credible simulated y')
ymin, ymax = ax1.get_ylim()
for i in range(k-1):
ax1.vlines(s_preds[i], ymin, ymax, linestyle='--', label=f'Switchpoint at x = {s_preds[i]}')
ax1.set(xlabel='Days since 2020-01-22', ylabel='Log of Daily Confirmed',
title=f'Log of daily confirmed with {k} segments for {self.country_name}')
ax1.legend(loc='best')
sns.lineplot(df['date'], df['daily_confirmed'],
label='Daily confirmed', ax=ax2)
sns.lineplot(df['date'], df['rolling_mean'], label='Rolling mean', ax=ax2)
ax2.fill_between(df['date'][start:end], np.exp(lower_bounds), np.exp(upper_bounds),
alpha=0.5, label='90% credible simulated y')
ax2.fill_between(dates_after, np.exp(pred_lower_bounds), np.exp(pred_upper_bounds),
alpha=0.5, color='r', label='Extrapolated 90% credible simulated y')
ymin, ymax = ax2.get_ylim()
switch_dates = []
for i in range(k-1):
switch_date = df['date'].iloc[0]+timedelta(days=s_preds[i])
ax2.vlines(switch_date, ymin, ymax, linestyle='--',
label=f'Switchpoint at {switch_date.date()}')
ax2.set(xlim=[df['date'].iloc[0], dates_after[-1]], xlabel='Date',
ylabel='Daily Confirmed',
title=f'Daily confirmed graph with {k} segments for {self.country_name}')
ax2.legend(loc='best')
@staticmethod
def get_y(x, s, b, w, std=0.1):
x = np.array(x)
y = np.zeros(shape=x.shape)
switch_idx = 0
for i in range(len(y)):
if switch_idx < len(s) and x[i] >= s[switch_idx]:
switch_idx += 1
y[i] = x[i] * w[switch_idx] + b[switch_idx] + normal(0, std, 1)
return y
@staticmethod
def get_pred(samples, burn_in=5000):
return samples[burn_in:].mean()
@staticmethod
def get_confidence_intervals(sigma_samples, y_fit, alpha=0.9):
y_fit = np.array(y_fit)
sigma_mean = sigma_samples[5000:].mean()
y_samples = np.zeros(shape=(len(y_fit), 100))
for i in range(len(y_fit)):
y_samples[i, :] = np.random.normal(y_fit[i], sigma_mean, 100)
y_samples[i, :] = sorted(y_samples[i, :])
low = int((1-alpha) * 100/2)
high = 100-low
credible_intervals = [(y_samples[i, low], y_samples[i, high]) for i in range(len(y_fit))]
lower_bounds = [low for low, _ in credible_intervals]
upper_bounds = [high for _, high in credible_intervals]
return lower_bounds, upper_bounds