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RBM from Edwin Chen
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""" | |
This code is taken from Edwin Chen's RBM repo: | |
https://github.com/echen/restricted-boltzmann-machines | |
Overview: http://blog.echen.me/2011/07/18/introduction-to-restricted-boltzmann-machines/ | |
Change Log (11/24/14): | |
- PEP8 (Ben Gelb) | |
""" | |
from __future__ import print_function | |
import numpy as np | |
class RBM(object): | |
def __init__(self, num_visible, num_hidden, learning_rate=0.1): | |
self.num_hidden = num_hidden | |
self.num_visible = num_visible | |
self.learning_rate = learning_rate | |
# Initialize a weight matrix, of dimensions (num_visible x num_hidden), | |
# using a Gaussian distribution with mean 0 and standard deviation 0.1. | |
self.weights = 0.1 * np.random.randn(self.num_visible, self.num_hidden) | |
# Insert weights for the bias units into the first row and first column. | |
self.weights = np.insert(self.weights, 0, 0, axis=0) | |
self.weights = np.insert(self.weights, 0, 0, axis=1) | |
def train(self, data, max_epochs=1000): | |
""" | |
Train the machine. | |
Parameters | |
---------- | |
data: A matrix where each row is a training example consisting of | |
the states of visible units. | |
""" | |
num_examples = data.shape[0] | |
# Insert bias units of 1 into the first column. | |
data = np.insert(data, 0, 1, axis=1) | |
for epoch in range(max_epochs): | |
# Clamp to the data and sample from the hidden units. | |
# (This is the "positive CD phase", aka the reality phase.) | |
pos_hidden_activations = np.dot(data, self.weights) | |
pos_hidden_probs = self._logistic(pos_hidden_activations) | |
pos_hidden_states = pos_hidden_probs > np.random.rand( | |
num_examples, self.num_hidden + 1) | |
# Note that we're using the activation *probabilities* of the | |
# hidden states, not the hidden states themselves, when computing | |
# associations. We could also use the states; see section 3 of | |
# Hinton's "A Practical Guide to Training Restricted Boltzmann | |
# Machines" for more. | |
pos_associations = np.dot(data.T, pos_hidden_probs) | |
# Reconstruct the visible units and sample again from the | |
# hidden units. | |
# (This is the "negative CD phase", aka the daydreaming phase.) | |
neg_visible_activations = np.dot(pos_hidden_states, self.weights.T) | |
neg_visible_probs = self._logistic(neg_visible_activations) | |
# Fix the bias unit. | |
neg_visible_probs[:, 0] = 1 | |
neg_hidden_activations = np.dot(neg_visible_probs, self.weights) | |
neg_hidden_probs = self._logistic(neg_hidden_activations) | |
# Note, again, that we're using the activation *probabilities* when | |
# computing associations, not the states | |
# themselves. | |
neg_associations = np.dot(neg_visible_probs.T, neg_hidden_probs) | |
# Update weights. | |
self.weights += self.learning_rate * ( | |
(pos_associations - neg_associations) / num_examples) | |
error = np.sum((data - neg_visible_probs) ** 2) | |
print("Epoch %s: error is %s" % (epoch, error)) | |
def run_visible(self, data): | |
""" | |
Assuming the RBM has been trained | |
(so that weights for the network have been learned), | |
run the network on a set of visible units, to get a sample of | |
the hidden units. | |
Parameters | |
---------- | |
data: A matrix where each row consists of the states of the | |
visible units. | |
Returns | |
------- | |
hidden_states: A matrix where each row consists of the hidden units | |
activated from the visible | |
units in the data matrix passed in. | |
""" | |
num_examples = data.shape[0] | |
# Create a matrix, where each row is to be the hidden units | |
# (plus a bias unit) | |
# sampled from a training example. | |
hidden_states = np.ones((num_examples, self.num_hidden + 1)) | |
# Insert bias units of 1 into the first column of data. | |
data = np.insert(data, 0, 1, axis=1) | |
# Calculate the activations of the hidden units. | |
hidden_activations = np.dot(data, self.weights) | |
# Calculate the probabilities of turning the hidden units on. | |
hidden_probs = self._logistic(hidden_activations) | |
# Turn the hidden units on with their specified probabilities. | |
hidden_states[:, :] = hidden_probs > np.random.rand( | |
num_examples, | |
self.num_hidden + 1 | |
) | |
# Always fix the bias unit to 1. | |
# hidden_states[:,0] = 1 | |
# Ignore the bias units. | |
hidden_states = hidden_states[:, 1:] | |
return hidden_states | |
# TODO: Remove the code duplication between this method and `run_visible`? | |
def run_hidden(self, data): | |
""" | |
Assuming the RBM has been trained (so that weights for the network | |
have been learned), run the network on a set of hidden units, to get | |
a sample of the visible units. | |
Parameters | |
---------- | |
data: A matrix where each row consists of the states of the hidden | |
units. | |
Returns | |
------- | |
visible_states: A matrix where each row consists of the visible units | |
activated from the hidden units in the data matrix | |
passed in. | |
""" | |
num_examples = data.shape[0] | |
# Create a matrix, where each row is to be the visible units | |
# (plus a bias unit) | |
# sampled from a training example. | |
visible_states = np.ones((num_examples, self.num_visible + 1)) | |
# Insert bias units of 1 into the first column of data. | |
data = np.insert(data, 0, 1, axis=1) | |
# Calculate the activations of the visible units. | |
visible_activations = np.dot(data, self.weights.T) | |
# Calculate the probabilities of turning the visible units on. | |
visible_probs = self._logistic(visible_activations) | |
# Turn the visible units on with their specified probabilities. | |
visible_states[:, :] = visible_probs > np.random.rand( | |
num_examples, | |
self.num_visible + 1 | |
) | |
# Always fix the bias unit to 1. | |
# visible_states[:,0] = 1 | |
# Ignore the bias units. | |
visible_states = visible_states[:, 1:] | |
return visible_states | |
def daydream(self, num_samples): | |
""" | |
Randomly initialize the visible units once, and start running | |
alternating Gibbs sampling steps (where each step consists of updating | |
all the hidden units, and then updating all of the visible units), | |
taking a sample of the visible units at each step. | |
Note that we only initialize the network *once*, so these samples | |
are correlated. | |
Returns | |
------- | |
samples: A matrix, where each row is a sample of the visible units | |
produced while the network was | |
daydreaming. | |
""" | |
# Create a matrix, where each row is to be a sample of of the | |
# visible units | |
# (with an extra bias unit), initialized to all ones. | |
samples = np.ones((num_samples, self.num_visible + 1)) | |
# Take the first sample from a uniform distribution. | |
samples[0, 1:] = np.random.rand(self.num_visible) | |
# Start the alternating Gibbs sampling. | |
# Note that we keep the hidden units binary states, but leave the | |
# visible units as real probabilities. See section 3 of Hinton's | |
# "A Practical Guide to Training Restricted Boltzmann Machines" | |
# for more on why. | |
for i in range(1, num_samples): | |
visible = samples[i - 1, :] | |
# Calculate the activations of the hidden units. | |
hidden_activations = np.dot(visible, self.weights) | |
# Calculate the probabilities of turning the hidden units on. | |
hidden_probs = self._logistic(hidden_activations) | |
# Turn the hidden units on with their specified probabilities. | |
hidden_states = hidden_probs > np.random.rand(self.num_hidden + 1) | |
# Always fix the bias unit to 1. | |
hidden_states[0] = 1 | |
# Recalculate the probabilities that the visible units are on. | |
visible_activations = np.dot(hidden_states, self.weights.T) | |
visible_probs = self._logistic(visible_activations) | |
visible_states = visible_probs > np.random.rand( | |
self.num_visible + 1 | |
) | |
samples[i, :] = visible_states | |
# Ignore the bias units (the first column) | |
# since they're always set to 1. | |
return samples[:, 1:] | |
def _logistic(self, x): | |
return 1.0 / (1 + np.exp(-x)) | |
if __name__ == '__main__': | |
r = RBM(num_visible=6, num_hidden=2) | |
training_data = np.array([ | |
[1, 1, 1, 0, 0, 0], | |
[1, 0, 1, 0, 0, 0], | |
[1, 1, 1, 0, 0, 0], | |
[0, 0, 1, 1, 1, 0], | |
[0, 0, 1, 1, 0, 0], | |
[0, 0, 1, 1, 1, 0]] | |
) | |
r.train(training_data, max_epochs=5000) | |
print(r.weights) | |
user = np.array([[0, 0, 0, 1, 1, 0]]) | |
print(r.run_visible(user)) |
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