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multilevel_regression.py
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/
multilevel_regression.py
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import numpy as np
import pandas as pd
from scipy.stats import boxcox, t
from scipy.special import inv_boxcox
import pymc3 as pm
import copy
from sklearn.model_selection import KFold
from sklearn.metrics import mean_squared_error
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_style('whitegrid')
pd.set_option('display.max_columns', 100, 'display.max_rows', 100)
class MultiLevelModel(object):
"""
Base class for a multi-level model
"""
def __init__(self):
self.trace_ = None
self.n_groups_ = None
self.n_features_ = None
self.model_ = None
def _build_model(self, X, y, **kwargs):
raise NotImplementedError()
def fit(self, X, y, draws=4000, tune=2000, chains=4, cores=4,
target_accept=.8, burn=500, **model_kwargs):
self.model_ = self._build_model(X=X, y=y, **model_kwargs)
with self.model_:
self.trace_ = pm.sample(
draws=draws, tune=tune, chains=chains,
cores=cores, target_accept=target_accept)[burn:]
return self
def predict(self, X, **kwargs):
raise NotImplementedError()
def cv(self, X, y, n_splits, random_state=None, **obj_func_kwargs):
folds = KFold(n_splits=n_splits, random_state=random_state)
cv_scores_train = np.empty(n_splits)
cv_scores_test = np.empty(n_splits)
for i, (train_idx, test_idx) in enumerate(folds.split(X)):
cv_scores_train[i], cv_scores_test[i] = \
self._objective_func(X, y, train_idx, test_idx, **obj_func_kwargs)
return cv_scores_train.mean(), cv_scores_train.std(), \
cv_scores_test.mean(), cv_scores_test.std()
def _objective_func(self, X_train, y_train, X_test, y_test, **kwargs):
raise NotImplementedError()
class PoolLinearModel(MultiLevelModel):
def _build_model(self, X, y, **kwargs):
with pm.Model() as model:
# priors
alpha = pm.Normal('alpha', mu=0, sigma=1e5)
beta = pm.Normal('beta', mu=0, sigma=1e5)
sigma = pm.HalfNormal('sigma', sigma=1e5)
# mean: linear regression
mu = alpha + beta * X # alpha + pm.math.dot(beta, X)
# degree of freedom
nu = pm.Exponential('nu', 1 / 30)
# observations
pm.StudentT('y', mu=mu, sigma=sigma, nu=nu, observed=y)
return model
def predict(self, X, **kwargs):
mu = self.trace_['alpha'] + self.trace_['beta'] * X[:, None]
dist = t(df=self.trace_['nu'], loc=mu, scale=self.trace_['sigma'])
if kwargs.get('q') is None:
return dist, dist.mean().mean(axis=1)
else:
return dist, [dist.ppf(q_).mean(axis=1) for q_ in kwargs['q']]
def _objective_func(self, X_train, y_train, X_test, y_test, **kwargs):
self.fit(X_train, y_train, **kwargs['fit'])
_, y_pred_train = self.predict(X_train)
_, y_pred_test = self.predict(X_test)
rmse_train = np.sqrt(mean_squared_error(y_train, y_pred_train))
rmse_test = np.sqrt(mean_squared_error(y_test, y_pred_test))
return rmse_train, rmse_test
class PartialPoolLinearModel(MultiLevelModel):
def _build_model(self, X, y, **kwargs):
group_idx = kwargs['group_idx']
n_groups = np.unique(group_idx).shape[0]
# n_features = X.shape[0]
with pm.Model() as model:
# intercept hyper-priors
alpha_mu = pm.Normal('alpha_mu', mu=0, sigma=1e5)
alpha_sigma = pm.HalfNormal('alpha_sigma', sigma=1e5)
# intercept prior
alpha_t = pm.Normal('alpha_t', mu=0, sigma=1, shape=n_groups)
alpha = pm.Deterministic('alpha', alpha_mu + alpha_sigma * alpha_t)
# slope hyper-priors
beta_mu = pm.Normal('beta_mu', mu=0, sigma=1e5)
beta_sigma = pm.HalfNormal('beta_sigma', sigma=1e5)
# slope prior
beta_t = pm.Normal('beta_t', mu=0, sigma=1, shape=n_groups)
beta = pm.Deterministic('beta', beta_mu + beta_sigma * beta_t)
# model error
sigma = pm.HalfNormal('sigma', sigma=1e5)
# degree of freedom
nu = pm.Exponential('nu', lam=1 / 30.)
# expected value
mu = alpha[group_idx] + beta[group_idx] * X
# data likelihood
pm.StudentT('y', mu=mu, sigma=sigma, nu=nu, observed=y)
return model
def predict(self, X, **kwargs):
group_idx = kwargs['group_idx']
mu = self.trace_['alpha'][:, group_idx] + self.trace_['beta'][:, group_idx] * X[:, None]
dist = t(df=self.trace_['nu'], loc=mu, scale=self.trace_['sigma'])
if kwargs.get('q') is None:
return dist, dist.mean().mean(axis=1)
else:
return dist, [dist.ppf(q_).mean(axis=1) for q_ in kwargs['q']]
def _objective_func(self, X, y, train_idx, test_idx, **kwargs):
# TODO: make sure group index are assigned properly
X_train, X_test = X[train_idx], X[test_idx]
y_train, y_test = y[train_idx], y[test_idx]
kwargs_ = copy.copy(kwargs)
kwargs_['fit']['group_idx'] = kwargs['fit']['group_idx'][train_idx]
self.fit(X_train, y_train, **kwargs_['fit'])
_, y_pred_train = self.predict(X_train, **kwargs['predict'])
_, y_pred_test = self.predict(X_test, **kwargs['predict'])
rmse_train = np.sqrt(mean_squared_error(y_train, y_pred_train))
rmse_test = np.sqrt(mean_squared_error(y_test, y_pred_test))
return rmse_train, rmse_test
class UnpoolLinearModel(PartialPoolLinearModel):
def _build_model(self, X, y, **kwargs):
group_idx = kwargs['group_idx']
n_groups = np.unique(group_idx).shape[0]
# n_features = X.shape[0]
with pm.Model() as model:
# priors
alpha = pm.Normal('alpha', mu=0, sigma=1e5, shape=n_groups) # shape=(n_groups, n_features)
beta = pm.Normal('beta', mu=0, sigma=1e5, shape=n_groups) # shape=(n_groups, n_features)
sigma = pm.HalfNormal('sigma', sigma=1e5)
# mean: linear regression
mu = alpha[group_idx] + beta[group_idx] * X # alpha[group_idx] + pm.math.dot(beta[group_idx], X)
# degree of freedom
nu = pm.Exponential('nu', 1 / 30.)
# observations
pm.StudentT('y', mu=mu, sigma=sigma, nu=nu, observed=y)
return model
def plot_prediction(x, y_mean, y_upper=None, y_lower=None, xlabel=None,
ylabel=None, ax=None, figsize=(18, 6), **kwargs):
if ax is None:
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111)
else:
fig = ax.get_figure()
ax.plot(x, y_mean, **kwargs)
if not (y_upper is None or y_lower is None):
ax.fill_between(x, y_upper, y_lower, alpha=kwargs.get('alpha', 0.5))
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
ax.legend()
return fig, ax