"""Restricted Boltzmann Machine
"""
# Authors: Yann N. Dauphin <dauphiya@iro.umontreal.ca>
# Vlad Niculae
# Gabriel Synnaeve
# Lars Buitinck
# License: BSD 3 clause
import time
import numpy as np
import scipy.sparse as sp
from scipy.special import expit # logistic function
from ..base import BaseEstimator
from ..base import TransformerMixin
from ..externals.six.moves import xrange
from ..utils import check_array
from ..utils import check_random_state
from ..utils import gen_even_slices
from ..utils import issparse
from ..utils.extmath import safe_sparse_dot
from ..utils.extmath import log_logistic
from ..utils.validation import check_is_fitted
class BernoulliRBM(BaseEstimator, TransformerMixin):
"""Bernoulli Restricted Boltzmann Machine (RBM).
A Restricted Boltzmann Machine with binary visible units and
binary hidden units. Parameters are estimated using Stochastic Maximum
Likelihood (SML), also known as Persistent Contrastive Divergence (PCD)
[2].
The time complexity of this implementation is ``O(d ** 2)`` assuming
d ~ n_features ~ n_components.
Read more in the :ref:`User Guide <rbm>`.
Parameters
----------
n_components : int, optional
Number of binary hidden units.
learning_rate : float, optional
The learning rate for weight updates. It is *highly* recommended
to tune this hyper-parameter. Reasonable values are in the
10**[0., -3.] range.
batch_size : int, optional
Number of examples per minibatch.
n_iter : int, optional
Number of iterations/sweeps over the training dataset to perform
during training.
verbose : int, optional
The verbosity level. The default, zero, means silent mode.
random_state : integer or numpy.RandomState, optional
A random number generator instance to define the state of the
random permutations generator. If an integer is given, it fixes the
seed. Defaults to the global numpy random number generator.
Attributes
----------
intercept_hidden_ : array-like, shape (n_components,)
Biases of the hidden units.
intercept_visible_ : array-like, shape (n_features,)
Biases of the visible units.
components_ : array-like, shape (n_components, n_features)
Weight matrix, where n_features in the number of
visible units and n_components is the number of hidden units.
Examples
--------
>>> import numpy as np
>>> from sklearn.neural_network import BernoulliRBM
>>> X = np.array([[0, 0, 0], [0, 1, 1], [1, 0, 1], [1, 1, 1]])
>>> model = BernoulliRBM(n_components=2)
>>> model.fit(X)
BernoulliRBM(batch_size=10, learning_rate=0.1, n_components=2, n_iter=10,
random_state=None, verbose=0)
References
----------
[1] Hinton, G. E., Osindero, S. and Teh, Y. A fast learning algorithm for
deep belief nets. Neural Computation 18, pp 1527-1554.
http://www.cs.toronto.edu/~hinton/absps/fastnc.pdf
[2] Tieleman, T. Training Restricted Boltzmann Machines using
Approximations to the Likelihood Gradient. International Conference
on Machine Learning (ICML) 2008
"""
def __init__(self, n_components=256, learning_rate=0.1, batch_size=10,
n_iter=10, verbose=0, random_state=None):
self.n_components = n_components
self.learning_rate = learning_rate
self.batch_size = batch_size
self.n_iter = n_iter
self.verbose = verbose
self.random_state = random_state
def _mean_hiddens(self, v):
"""Computes the probabilities P(h=1|v).
Parameters
----------
v : array-like, shape (n_samples, n_features)
Values of the visible layer.
Returns
-------
h : array-like, shape (n_samples, n_components)
Corresponding mean field values for the hidden layer.
"""
p = safe_sparse_dot(v, self.components_.T)
p += self.intercept_hidden_
return expit(p, out=p)
def _sample_hiddens(self, v, rng):
"""Sample from the distribution P(h|v).
Parameters
----------
v : array-like, shape (n_samples, n_features)
Values of the visible layer to sample from.
rng : RandomState
Random number generator to use.
Returns
-------
h : array-like, shape (n_samples, n_components)
Values of the hidden layer.
"""
p = self._mean_hiddens(v)
return (rng.random_sample(size=p.shape) < p)
def _sample_visibles(self, h, rng):
"""Sample from the distribution P(v|h).
Parameters
----------
h : array-like, shape (n_samples, n_components)
Values of the hidden layer to sample from.
rng : RandomState
Random number generator to use.
Returns
-------
v : array-like, shape (n_samples, n_features)
Values of the visible layer.
"""
p = np.dot(h, self.components_)
p += self.intercept_visible_
expit(p, out=p)
return (rng.random_sample(size=p.shape) < p)
def _free_energy(self, v):
"""Computes the free energy F(v) = - log sum_h exp(-E(v,h)).
Parameters
----------
v : array-like, shape (n_samples, n_features)
Values of the visible layer.
Returns
-------
free_energy : array-like, shape (n_samples,)
The value of the free energy.
"""
return (- safe_sparse_dot(v, self.intercept_visible_)
- np.logaddexp(0, safe_sparse_dot(v, self.components_.T)
+ self.intercept_hidden_).sum(axis=1))
def gibbs(self, v):
"""Perform one Gibbs sampling step.
Parameters
----------
v : array-like, shape (n_samples, n_features)
Values of the visible layer to start from.
Returns
-------
v_new : array-like, shape (n_samples, n_features)
Values of the visible layer after one Gibbs step.
"""
check_is_fitted(self, "components_")
if not hasattr(self, "random_state_"):
self.random_state_ = check_random_state(self.random_state)
h_ = self._sample_hiddens(v, self.random_state_)
v_ = self._sample_visibles(h_, self.random_state_)
return v_
[docs] def partial_fit(self, X, y=None):
"""Fit the model to the data X which should contain a partial
segment of the data.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Training data.
Returns
-------
self : BernoulliRBM
The fitted model.
"""
X = check_array(X, accept_sparse='csr', dtype=np.float64)
if not hasattr(self, 'random_state_'):
self.random_state_ = check_random_state(self.random_state)
if not hasattr(self, 'components_'):
self.components_ = np.asarray(
self.random_state_.normal(
0,
0.01,
(self.n_components, X.shape[1])
),
order='F')
if not hasattr(self, 'intercept_hidden_'):
self.intercept_hidden_ = np.zeros(self.n_components, )
if not hasattr(self, 'intercept_visible_'):
self.intercept_visible_ = np.zeros(X.shape[1], )
if not hasattr(self, 'h_samples_'):
self.h_samples_ = np.zeros((self.batch_size, self.n_components))
self._fit(X, self.random_state_)
def _fit(self, v_pos, rng):
"""Inner fit for one mini-batch.
Adjust the parameters to maximize the likelihood of v using
Stochastic Maximum Likelihood (SML).
Parameters
----------
v_pos : array-like, shape (n_samples, n_features)
The data to use for training.
rng : RandomState
Random number generator to use for sampling.
"""
h_pos = self._mean_hiddens(v_pos)
v_neg = self._sample_visibles(self.h_samples_, rng)
h_neg = self._mean_hiddens(v_neg)
lr = float(self.learning_rate) / v_pos.shape[0]
update = safe_sparse_dot(v_pos.T, h_pos, dense_output=True).T
update -= np.dot(h_neg.T, v_neg)
self.components_ += lr * update
self.intercept_hidden_ += lr * (h_pos.sum(axis=0) - h_neg.sum(axis=0))
self.intercept_visible_ += lr * (np.asarray(
v_pos.sum(axis=0)).squeeze() -
v_neg.sum(axis=0))
h_neg[rng.uniform(size=h_neg.shape) < h_neg] = 1.0 # sample binomial
self.h_samples_ = np.floor(h_neg, h_neg)
[docs] def score_samples(self, X):
"""Compute the pseudo-likelihood of X.
Parameters
----------
X : {array-like, sparse matrix} shape (n_samples, n_features)
Values of the visible layer. Must be all-boolean (not checked).
Returns
-------
pseudo_likelihood : array-like, shape (n_samples,)
Value of the pseudo-likelihood (proxy for likelihood).
Notes
-----
This method is not deterministic: it computes a quantity called the
free energy on X, then on a randomly corrupted version of X, and
returns the log of the logistic function of the difference.
"""
check_is_fitted(self, "components_")
v = check_array(X, accept_sparse='csr')
rng = check_random_state(self.random_state)
# Randomly corrupt one feature in each sample in v.
ind = (np.arange(v.shape[0]),
rng.randint(0, v.shape[1], v.shape[0]))
if issparse(v):
data = -2 * v[ind] + 1
v_ = v + sp.csr_matrix((data.A.ravel(), ind), shape=v.shape)
else:
v_ = v.copy()
v_[ind] = 1 - v_[ind]
fe = self._free_energy(v)
fe_ = self._free_energy(v_)
return v.shape[1] * log_logistic(fe_ - fe)
[docs] def fit(self, X, y=None):
"""Fit the model to the data X.
Parameters
----------
X : {array-like, sparse matrix} shape (n_samples, n_features)
Training data.
Returns
-------
self : BernoulliRBM
The fitted model.
"""
X = check_array(X, accept_sparse='csr', dtype=np.float64)
n_samples = X.shape[0]
rng = check_random_state(self.random_state)
self.components_ = np.asarray(
rng.normal(0, 0.01, (self.n_components, X.shape[1])),
order='F')
self.intercept_hidden_ = np.zeros(self.n_components, )
self.intercept_visible_ = np.zeros(X.shape[1], )
self.h_samples_ = np.zeros((self.batch_size, self.n_components))
n_batches = int(np.ceil(float(n_samples) / self.batch_size))
batch_slices = list(gen_even_slices(n_batches * self.batch_size,
n_batches, n_samples))
verbose = self.verbose
begin = time.time()
for iteration in xrange(1, self.n_iter + 1):
for batch_slice in batch_slices:
self._fit(X[batch_slice], rng)
if verbose:
end = time.time()
print("[%s] Iteration %d, pseudo-likelihood = %.2f,"
" time = %.2fs"
% (type(self).__name__, iteration,
self.score_samples(X).mean(), end - begin))
begin = end
return self
