import numpy as np
import pymc3 as pm
from sklearn.metrics import r2_score
import theano
import theano.tensor as T
from pymc3_models.exc import PyMC3ModelsError
from pymc3_models.models import BayesianModel
[docs]class LinearRegression(BayesianModel):
"""
Linear Regression built using PyMC3.
"""
def __init__(self):
super(LinearRegression, self).__init__()
[docs] def create_model(self):
"""
Creates and returns the PyMC3 model.
Note: The size of the shared variables must match the size of the training data.
Otherwise, setting the shared variables later will raise an error.
See http://docs.pymc.io/advanced_theano.html
Returns
-------
the PyMC3 model
"""
model_input = theano.shared(np.zeros([self.num_training_samples, self.num_pred]))
model_output = theano.shared(np.zeros(self.num_training_samples))
self.shared_vars = {
'model_input': model_input,
'model_output': model_output,
}
model = pm.Model()
with model:
alpha = pm.Normal('alpha', mu=0, sd=100, shape=(1))
betas = pm.Normal('betas', mu=0, sd=100, shape=(1, self.num_pred))
s = pm.HalfNormal('s', tau=1)
mean = alpha + T.sum(betas * model_input, 1)
y = pm.Normal('y', mu=mean, sd=s, observed=model_output)
return model
[docs] def fit(
self,
X,
y,
inference_type='advi',
num_advi_sample_draws=10000,
minibatch_size=None,
inference_args=None,
):
"""
Train the Linear Regression model
Parameters
----------
X : numpy array
shape [num_training_samples, num_pred]
y : numpy array
shape [num_training_samples, ]
inference_type : str (defaults to 'advi')
specifies which inference method to call
Currently, only 'advi' and 'nuts' are supported.
num_advi_sample_draws : int (defaults to 10000)
Number of samples to draw from ADVI approximation after it has been fit;
not used if inference_type != 'advi'
minibatch_size : int (defaults to None)
number of samples to include in each minibatch for ADVI
If None, minibatch is not run.
inference_args : dict (defaults to None)
arguments to be passed to the inference methods.
Check the PyMC3 docs for permissable values.
If None, default values will be set.
"""
self.num_training_samples, self.num_pred = X.shape
self.inference_type = inference_type
if y.ndim != 1:
y = np.squeeze(y)
if not inference_args:
inference_args = self._set_default_inference_args()
if self.cached_model is None:
self.cached_model = self.create_model()
if minibatch_size:
with self.cached_model:
minibatches = {
self.shared_vars['model_input']: pm.Minibatch(X, batch_size=minibatch_size),
self.shared_vars['model_output']: pm.Minibatch(y, batch_size=minibatch_size),
}
inference_args['more_replacements'] = minibatches
else:
self._set_shared_vars({'model_input': X, 'model_output': y})
self._inference(inference_type, inference_args, num_advi_sample_draws=num_advi_sample_draws)
return self
[docs] def predict(self, X, return_std=False, num_ppc_samples=2000):
"""
Predicts values of new data with a trained Linear Regression model
Parameters
----------
X : numpy array
shape [num_training_samples, num_pred]
return_std : bool (defaults to False)
flag of whether to return standard deviations with mean values
num_ppc_samples : int (defaults to 2000)
'samples' parameter passed to pm.sample_ppc
"""
if self.trace is None:
raise PyMC3ModelsError('Run fit on the model before predict.')
num_samples = X.shape[0]
if self.cached_model is None:
self.cached_model = self.create_model()
self._set_shared_vars({'model_input': X, 'model_output': np.zeros(num_samples)})
ppc = pm.sample_ppc(self.trace, model=self.cached_model, samples=num_ppc_samples)
if return_std:
return ppc['y'].mean(axis=0), ppc['y'].std(axis=0)
else:
return ppc['y'].mean(axis=0)
[docs] def score(self, X, y, num_ppc_samples=2000):
"""
Scores new data with a trained model with sklearn's r2_score.
Parameters
----------
X : numpy array
shape [num_training_samples, num_pred]
y : numpy array
shape [num_training_samples, ]
num_ppc_samples : int (defaults to 2000)
'samples' parameter passed to pm.sample_ppc
"""
return r2_score(y, self.predict(X, num_ppc_samples=num_ppc_samples))
[docs] def save(self, file_prefix):
params = {
'inference_type': self.inference_type,
'num_pred': self.num_pred,
'num_training_samples': self.num_training_samples
}
super(LinearRegression, self).save(file_prefix, params)
[docs] def load(self, file_prefix):
params = super(LinearRegression, self).load(file_prefix, load_custom_params=True)
self.inference_type = params['inference_type']
self.num_pred = params['num_pred']
self.num_training_samples = params['num_training_samples']