In [1]:
%matplotlib inline
%env THEANO_FLAGS=device=cpu, floatX=float32, warn_float64=ignore
import theano
import matplotlib.pyplot as plt
import numpy as np
import pymc3 as pm
import pandas as pd
data = pd.read_csv(pm.get_data('radon.csv'))
county_names = data.county.unique()
county_idx = data['county_code'].values
n_counties = len(data.county.unique())
total_size = len(data)
Here, 'log_radon_t' is a dependent variable, while 'floor_t' and 'county_idx_t' determine independent variable.
In [2]:
import theano.tensor as tt
log_radon_t = pm.Minibatch(data.log_radon.values, 100)
floor_t = pm.Minibatch(data.floor.values, 100)
county_idx_t = pm.Minibatch(data.county_code.values, 100)
In [3]:
with pm.Model() as hierarchical_model:
# Hyperpriors for group nodes
mu_a = pm.Normal('mu_alpha', mu=0., sd=100**2)
sigma_a = pm.Uniform('sigma_alpha', lower=0, upper=100)
mu_b = pm.Normal('mu_beta', mu=0., sd=100**2)
sigma_b = pm.Uniform('sigma_beta', lower=0, upper=100)
Intercept for each county, distributed around group mean mu_a. Above we just set mu and sd to a fixed value while here we plug in a common group distribution for all a and b (which are vectors of length n_counties).
In [4]:
with hierarchical_model:
a = pm.Normal('alpha', mu=mu_a, sd=sigma_a, shape=n_counties)
# Intercept for each county, distributed around group mean mu_a
b = pm.Normal('beta', mu=mu_b, sd=sigma_b, shape=n_counties)
Model prediction of radon level a[county_idx] translates to a[0, 0, 0, 1, 1, ...], we thus link multiple household measures of a county to its coefficients.
In [5]:
with hierarchical_model:
radon_est = a[county_idx_t] + b[county_idx_t] * floor_t
Finally, we specify the likelihood:
In [6]:
with hierarchical_model:
# Model error
eps = pm.Uniform('eps', lower=0, upper=100)
# Data likelihood
radon_like = pm.Normal('radon_like', mu=radon_est, sd=eps, observed=log_radon_t, total_size=len(data))
Random variable 'radon_like', associated with 'log_radon_t', should be given to the function for ADVI to denote that as observations in the likelihood term.
On the other hand, 'minibatches' should include the three variables above.
Then, run ADVI with mini-batch.
In [7]:
with hierarchical_model:
approx = pm.fit(100000, callbacks=[pm.callbacks.CheckParametersConvergence(tolerance=1e-4)])
Check the trace of ELBO and compare the result with MCMC.
In [8]:
import matplotlib.pyplot as plt
import seaborn as sns
plt.plot(approx.hist)
Out[8]:
In [9]:
# Inference button (TM)!
with pm.Model():
mu_a = pm.Normal('mu_alpha', mu=0., sd=100**2)
sigma_a = pm.Uniform('sigma_alpha', lower=0, upper=100)
mu_b = pm.Normal('mu_beta', mu=0., sd=100**2)
sigma_b = pm.Uniform('sigma_beta', lower=0, upper=100)
a = pm.Normal('alpha', mu=mu_a, sd=sigma_a, shape=n_counties)
b = pm.Normal('beta', mu=mu_b, sd=sigma_b, shape=n_counties)
# Model error
eps = pm.Uniform('eps', lower=0, upper=100)
radon_est = a[county_idx] + b[county_idx] * data.floor.values
radon_like = pm.Normal(
'radon_like', mu=radon_est, sd=eps, observed=data.log_radon.values)
step = pm.NUTS(scaling=approx.cov.eval(), is_cov=True)
hierarchical_trace = pm.sample(2000, step, start=approx.sample()[0], progressbar=True)
In [10]:
means = approx.bij.rmap(approx.mean.eval())
sds = approx.bij.rmap(approx.std.eval())
In [11]:
from scipy import stats
import seaborn as sns
varnames = means.keys()
fig, axs = plt.subplots(nrows=len(varnames), figsize=(12, 18))
for var, ax in zip(varnames, axs):
mu_arr = means[var]
sigma_arr = sds[var]
ax.set_title(var)
for i, (mu, sigma) in enumerate(zip(mu_arr.flatten(), sigma_arr.flatten())):
sd3 = (-4*sigma + mu, 4*sigma + mu)
x = np.linspace(sd3[0], sd3[1], 300)
y = stats.norm(mu, sigma).pdf(x)
ax.plot(x, y)
if hierarchical_trace[var].ndim > 1:
t = hierarchical_trace[var][i]
else:
t = hierarchical_trace[var]
sns.distplot(t, kde=False, norm_hist=True, ax=ax)
fig.tight_layout()