Mercurial > ift6266
annotate deep/rbm/rbm.py @ 422:e7790db265b1
Basic text for section 3, add a bit more detail to section 4.2.2
| author | Arnaud Bergeron <abergeron@gmail.com> |
|---|---|
| date | Fri, 30 Apr 2010 16:24:30 -0400 |
| parents | e36ccffb3870 |
| children |
| rev | line source |
|---|---|
| 347 | 1 """This tutorial introduces restricted boltzmann machines (RBM) using Theano. |
| 2 | |
| 3 Boltzmann Machines (BMs) are a particular form of energy-based model which | |
| 4 contain hidden variables. Restricted Boltzmann Machines further restrict BMs | |
| 5 to those without visible-visible and hidden-hidden connections. | |
| 6 """ | |
| 7 | |
| 8 import numpy, time, cPickle, gzip, PIL.Image | |
| 9 | |
| 10 import theano | |
| 11 import theano.tensor as T | |
| 12 import os | |
| 369 | 13 import pdb |
| 14 import numpy | |
| 15 import pylab | |
| 16 import time | |
| 17 import theano.tensor.nnet | |
| 18 import pylearn | |
| 372 | 19 #import ift6266 |
| 20 import theano,pylearn.version #,ift6266 | |
| 369 | 21 from pylearn.io import filetensor as ft |
| 372 | 22 #from ift6266 import datasets |
| 23 | |
| 24 from jobman.tools import DD, flatten | |
| 25 from jobman import sql | |
| 347 | 26 |
| 27 from theano.tensor.shared_randomstreams import RandomStreams | |
| 28 | |
| 29 from utils import tile_raster_images | |
| 30 from logistic_sgd import load_data | |
| 31 | |
| 32 class RBM(object): | |
| 33 """Restricted Boltzmann Machine (RBM) """ | |
| 369 | 34 def __init__(self, input=None, n_visible=32*32, n_hidden=500, \ |
| 347 | 35 W = None, hbias = None, vbias = None, numpy_rng = None, |
| 36 theano_rng = None): | |
| 37 """ | |
| 38 RBM constructor. Defines the parameters of the model along with | |
| 39 basic operations for inferring hidden from visible (and vice-versa), | |
| 40 as well as for performing CD updates. | |
| 41 | |
| 42 :param input: None for standalone RBMs or symbolic variable if RBM is | |
| 43 part of a larger graph. | |
| 44 | |
| 45 :param n_visible: number of visible units | |
| 46 | |
| 47 :param n_hidden: number of hidden units | |
| 48 | |
| 49 :param W: None for standalone RBMs or symbolic variable pointing to a | |
| 50 shared weight matrix in case RBM is part of a DBN network; in a DBN, | |
| 51 the weights are shared between RBMs and layers of a MLP | |
| 52 | |
| 53 :param hbias: None for standalone RBMs or symbolic variable pointing | |
| 54 to a shared hidden units bias vector in case RBM is part of a | |
| 55 different network | |
| 56 | |
| 57 :param vbias: None for standalone RBMs or a symbolic variable | |
| 58 pointing to a shared visible units bias | |
| 59 """ | |
| 60 | |
| 61 self.n_visible = n_visible | |
| 62 self.n_hidden = n_hidden | |
| 63 | |
| 64 | |
| 65 if W is None : | |
| 66 # W is initialized with `initial_W` which is uniformely sampled | |
| 67 # from -6./sqrt(n_visible+n_hidden) and 6./sqrt(n_hidden+n_visible) | |
| 68 # the output of uniform if converted using asarray to dtype | |
| 69 # theano.config.floatX so that the code is runable on GPU | |
| 70 initial_W = numpy.asarray( numpy.random.uniform( | |
| 71 low = -numpy.sqrt(6./(n_hidden+n_visible)), | |
| 72 high = numpy.sqrt(6./(n_hidden+n_visible)), | |
| 73 size = (n_visible, n_hidden)), | |
| 74 dtype = theano.config.floatX) | |
| 75 # theano shared variables for weights and biases | |
| 76 W = theano.shared(value = initial_W, name = 'W') | |
| 77 | |
| 78 if hbias is None : | |
| 79 # create shared variable for hidden units bias | |
| 80 hbias = theano.shared(value = numpy.zeros(n_hidden, | |
| 81 dtype = theano.config.floatX), name='hbias') | |
| 82 | |
| 83 if vbias is None : | |
| 84 # create shared variable for visible units bias | |
| 85 vbias = theano.shared(value =numpy.zeros(n_visible, | |
| 86 dtype = theano.config.floatX),name='vbias') | |
| 87 | |
| 88 if numpy_rng is None: | |
| 89 # create a number generator | |
| 90 numpy_rng = numpy.random.RandomState(1234) | |
| 91 | |
| 92 if theano_rng is None : | |
| 93 theano_rng = RandomStreams(numpy_rng.randint(2**30)) | |
| 94 | |
| 95 | |
| 96 # initialize input layer for standalone RBM or layer0 of DBN | |
| 97 self.input = input if input else T.dmatrix('input') | |
| 98 | |
| 99 self.W = W | |
| 100 self.hbias = hbias | |
| 101 self.vbias = vbias | |
| 102 self.theano_rng = theano_rng | |
| 369 | 103 |
| 347 | 104 # **** WARNING: It is not a good idea to put things in this list |
| 105 # other than shared variables created in this function. | |
| 106 self.params = [self.W, self.hbias, self.vbias] | |
| 107 self.batch_size = self.input.shape[0] | |
| 108 | |
| 109 def free_energy(self, v_sample): | |
| 110 ''' Function to compute the free energy ''' | |
| 111 wx_b = T.dot(v_sample, self.W) + self.hbias | |
| 112 vbias_term = T.sum(T.dot(v_sample, self.vbias)) | |
| 113 hidden_term = T.sum(T.log(1+T.exp(wx_b))) | |
| 114 return -hidden_term - vbias_term | |
| 115 | |
| 116 def sample_h_given_v(self, v0_sample): | |
| 117 ''' This function infers state of hidden units given visible units ''' | |
| 118 # compute the activation of the hidden units given a sample of the visibles | |
| 119 h1_mean = T.nnet.sigmoid(T.dot(v0_sample, self.W) + self.hbias) | |
| 120 # get a sample of the hiddens given their activation | |
| 121 h1_sample = self.theano_rng.binomial(size = h1_mean.shape, n = 1, prob = h1_mean) | |
| 122 return [h1_mean, h1_sample] | |
| 123 | |
| 124 def sample_v_given_h(self, h0_sample): | |
| 125 ''' This function infers state of visible units given hidden units ''' | |
| 126 # compute the activation of the visible given the hidden sample | |
| 127 v1_mean = T.nnet.sigmoid(T.dot(h0_sample, self.W.T) + self.vbias) | |
| 128 # get a sample of the visible given their activation | |
| 129 v1_sample = self.theano_rng.binomial(size = v1_mean.shape,n = 1,prob = v1_mean) | |
| 130 return [v1_mean, v1_sample] | |
| 131 | |
| 132 def gibbs_hvh(self, h0_sample): | |
| 133 ''' This function implements one step of Gibbs sampling, | |
| 134 starting from the hidden state''' | |
| 135 v1_mean, v1_sample = self.sample_v_given_h(h0_sample) | |
| 136 h1_mean, h1_sample = self.sample_h_given_v(v1_sample) | |
| 137 return [v1_mean, v1_sample, h1_mean, h1_sample] | |
| 138 | |
| 139 def gibbs_vhv(self, v0_sample): | |
| 140 ''' This function implements one step of Gibbs sampling, | |
| 141 starting from the visible state''' | |
| 142 h1_mean, h1_sample = self.sample_h_given_v(v0_sample) | |
| 143 v1_mean, v1_sample = self.sample_v_given_h(h1_sample) | |
| 144 return [h1_mean, h1_sample, v1_mean, v1_sample] | |
| 145 | |
| 369 | 146 def cd(self, lr = 0.1, persistent=None, k=1): |
| 347 | 147 """ |
| 148 This functions implements one step of CD-1 or PCD-1 | |
| 149 | |
| 150 :param lr: learning rate used to train the RBM | |
| 151 :param persistent: None for CD. For PCD, shared variable containing old state | |
| 152 of Gibbs chain. This must be a shared variable of size (batch size, number of | |
| 153 hidden units). | |
| 154 | |
| 155 Returns the updates dictionary. The dictionary contains the update rules for weights | |
| 156 and biases but also an update of the shared variable used to store the persistent | |
| 157 chain, if one is used. | |
| 158 """ | |
| 159 | |
| 160 # compute positive phase | |
| 161 ph_mean, ph_sample = self.sample_h_given_v(self.input) | |
| 162 | |
| 163 # decide how to initialize persistent chain: | |
| 164 # for CD, we use the newly generate hidden sample | |
| 165 # for PCD, we initialize from the old state of the chain | |
| 166 if persistent is None: | |
| 167 chain_start = ph_sample | |
| 168 else: | |
| 169 chain_start = persistent | |
| 170 | |
| 369 | 171 # perform actual negative phase (the CD-1) |
| 347 | 172 [nv_mean, nv_sample, nh_mean, nh_sample] = self.gibbs_hvh(chain_start) |
| 173 | |
| 369 | 174 #perform CD-k |
| 175 if k-1>0: | |
| 176 for i in range(k-1): | |
| 177 [nv_mean, nv_sample, nh_mean, nh_sample] = self.gibbs_hvh(nh_sample) | |
| 178 | |
| 179 | |
| 180 | |
| 347 | 181 # determine gradients on RBM parameters |
| 182 g_vbias = T.sum( self.input - nv_mean, axis = 0)/self.batch_size | |
| 183 g_hbias = T.sum( ph_mean - nh_mean, axis = 0)/self.batch_size | |
| 184 g_W = T.dot(ph_mean.T, self.input )/ self.batch_size - \ | |
| 185 T.dot(nh_mean.T, nv_mean )/ self.batch_size | |
| 186 | |
| 187 gparams = [g_W.T, g_hbias, g_vbias] | |
| 188 | |
| 189 # constructs the update dictionary | |
| 190 updates = {} | |
| 191 for gparam, param in zip(gparams, self.params): | |
| 192 updates[param] = param + gparam * lr | |
| 193 | |
| 194 if persistent: | |
| 195 # Note that this works only if persistent is a shared variable | |
| 196 updates[persistent] = T.cast(nh_sample, dtype=theano.config.floatX) | |
| 197 # pseudo-likelihood is a better proxy for PCD | |
| 198 cost = self.get_pseudo_likelihood_cost(updates) | |
| 199 else: | |
| 200 # reconstruction cross-entropy is a better proxy for CD | |
| 201 cost = self.get_reconstruction_cost(updates, nv_mean) | |
| 202 | |
| 203 return cost, updates | |
| 204 | |
| 205 def get_pseudo_likelihood_cost(self, updates): | |
| 206 """Stochastic approximation to the pseudo-likelihood""" | |
| 207 | |
| 208 # index of bit i in expression p(x_i | x_{\i}) | |
| 209 bit_i_idx = theano.shared(value=0, name = 'bit_i_idx') | |
| 210 | |
| 211 # binarize the input image by rounding to nearest integer | |
| 212 xi = T.iround(self.input) | |
| 213 | |
| 214 # calculate free energy for the given bit configuration | |
| 215 fe_xi = self.free_energy(xi) | |
| 216 | |
| 217 # flip bit x_i of matrix xi and preserve all other bits x_{\i} | |
| 218 # Equivalent to xi[:,bit_i_idx] = 1-xi[:, bit_i_idx] | |
| 219 # NB: slice(start,stop,step) is the python object used for | |
| 220 # slicing, e.g. to index matrix x as follows: x[start:stop:step] | |
| 221 xi_flip = T.setsubtensor(xi, 1-xi[:, bit_i_idx], | |
| 222 idx_list=(slice(None,None,None),bit_i_idx)) | |
| 223 | |
| 224 # calculate free energy with bit flipped | |
| 225 fe_xi_flip = self.free_energy(xi_flip) | |
| 226 | |
| 227 # equivalent to e^(-FE(x_i)) / (e^(-FE(x_i)) + e^(-FE(x_{\i}))) | |
| 228 cost = self.n_visible * T.log(T.nnet.sigmoid(fe_xi_flip - fe_xi)) | |
| 229 | |
| 230 # increment bit_i_idx % number as part of updates | |
| 231 updates[bit_i_idx] = (bit_i_idx + 1) % self.n_visible | |
| 232 | |
| 233 return cost | |
| 234 | |
| 235 def get_reconstruction_cost(self, updates, nv_mean): | |
| 236 """Approximation to the reconstruction error""" | |
| 237 | |
| 238 cross_entropy = T.mean( | |
| 239 T.sum(self.input*T.log(nv_mean) + | |
| 240 (1 - self.input)*T.log(1-nv_mean), axis = 1)) | |
| 241 | |
| 242 return cross_entropy | |
| 243 | |
| 244 | |
| 245 | |
| 372 | 246 def test_rbm(b_size = 20, nhidden = 1000, kk = 1, persistance = 0): |
| 369 | 247 """ |
| 248 Demonstrate *** | |
| 249 | |
| 250 This is demonstrated on MNIST. | |
| 251 | |
| 252 :param learning_rate: learning rate used for training the RBM | |
| 253 | |
| 254 :param training_epochs: number of epochs used for training | |
| 255 | |
| 256 :param dataset: path the the pickled dataset | |
| 257 | |
| 258 """ | |
| 259 | |
| 260 learning_rate=0.1 | |
| 261 | |
| 372 | 262 # if data_set==0: |
| 263 # datasets=datasets.nist_all() | |
| 264 # elif data_set==1: | |
| 265 # datasets=datasets.nist_P07() | |
| 266 # elif data_set==2: | |
| 267 # datasets=datasets.PNIST07() | |
| 369 | 268 |
| 269 | |
| 372 | 270 data_path = '/data/lisa/data/nist/by_class/' |
| 271 f = open(data_path+'all/all_train_data.ft') | |
| 272 g = open(data_path+'all/all_train_labels.ft') | |
| 273 h = open(data_path+'all/all_test_data.ft') | |
| 274 i = open(data_path+'all/all_test_labels.ft') | |
| 275 | |
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276 train_set_x_uint8 = theano.shared(ft.read(f)) |
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277 test_set_x_uint8 = theano.shared(ft.read(h)) |
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278 |
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279 |
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280 train_set_x = T.cast(train_set_x_uint8/255.,theano.config.floatX) |
| 372 | 281 train_set_y = ft.read(g) |
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282 test_set_x = T.cast(test_set_x_uint8/255.,theano.config.floatX) |
| 372 | 283 test_set_y = ft.read(i) |
| 284 | |
| 285 f.close() | |
| 286 g.close() | |
| 287 i.close() | |
| 288 h.close() | |
| 289 | |
| 290 #t = len(train_set_x) | |
| 291 | |
| 369 | 292 # revoir la recuperation des donnees |
| 293 ## dataset = load_data(dataset) | |
| 294 ## | |
| 295 ## train_set_x, train_set_y = datasets[0] | |
| 296 ## test_set_x , test_set_y = datasets[2] | |
| 372 | 297 training_epochs = 1 # a determiner |
| 369 | 298 |
| 299 batch_size = b_size # size of the minibatch | |
| 300 | |
| 301 # compute number of minibatches for training, validation and testing | |
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302 n_train_batches = train_set_x_uint8.value.shape[0] / batch_size |
| 369 | 303 |
| 304 # allocate symbolic variables for the data | |
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305 index = T.lscalar() # index to a [mini]batch |
| 369 | 306 x = T.matrix('x') # the data is presented as rasterized images |
| 307 | |
| 308 rng = numpy.random.RandomState(123) | |
| 309 theano_rng = RandomStreams( rng.randint(2**30)) | |
| 310 | |
| 311 | |
| 312 # construct the RBM class | |
| 313 rbm = RBM( input = x, n_visible=32*32, \ | |
| 314 n_hidden = nhidden, numpy_rng = rng, theano_rng = theano_rng) | |
| 315 | |
| 316 | |
| 317 # initialize storage fot the persistent chain (state = hidden layer of chain) | |
| 318 if persistance == 1: | |
| 319 persistent_chain = theano.shared(numpy.zeros((batch_size, 500))) | |
| 320 # get the cost and the gradient corresponding to one step of CD | |
| 321 cost, updates = rbm.cd(lr=learning_rate, persistent=persistent_chain, k= kk) | |
| 322 | |
| 323 else: | |
| 324 # get the cost and the gradient corresponding to one step of CD | |
| 325 #persistance_chain = None | |
| 326 cost, updates = rbm.cd(lr=learning_rate, persistent=None, k= kk) | |
| 327 | |
| 328 ################################# | |
| 329 # Training the RBM # | |
| 330 ################################# | |
| 372 | 331 #os.chdir('~') |
| 332 dirname = str(persistance) + '_' + str(nhidden) + '_' + str(b_size) + '_'+ str(kk) | |
| 369 | 333 os.makedirs(dirname) |
| 334 os.chdir(dirname) | |
| 372 | 335 print 'yes' |
| 369 | 336 # it is ok for a theano function to have no output |
| 337 # the purpose of train_rbm is solely to update the RBM parameters | |
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338 print type(batch_size) |
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339 print index.dtype |
| 372 | 340 train_rbm = theano.function([index], cost, |
| 369 | 341 updates = updates, |
| 372 | 342 givens = { x: train_set_x[index*batch_size:(index+1)*batch_size]}) |
| 369 | 343 |
| 372 | 344 print 'yep' |
| 369 | 345 plotting_time = 0.0 |
| 346 start_time = time.clock() | |
| 347 bufsize = 1000 | |
| 348 | |
| 349 # go through training epochs | |
| 350 costs = [] | |
| 351 for epoch in xrange(training_epochs): | |
| 352 | |
| 353 # go through the training set | |
| 354 mean_cost = [] | |
| 372 | 355 for batch_index in xrange(n_train_batches): |
| 356 mean_cost += [train_rbm(batch_index)] | |
| 357 # for mini_x, mini_y in datasets.train(b_size): | |
| 358 # mean_cost += [train_rbm(mini_x)] | |
| 369 | 359 ## learning_rate = learning_rate - 0.0001 |
| 360 ## learning_rate = learning_rate/(tau+( epoch*batch_index*batch_size)) | |
| 361 | |
| 362 #learning_rate = learning_rate/10 | |
| 363 | |
| 364 costs.append(numpy.mean(mean_cost)) | |
| 365 | |
| 366 # Plot filters after each training epoch | |
| 367 plotting_start = time.clock() | |
| 368 # Construct image from the weight matrix | |
| 369 image = PIL.Image.fromarray(tile_raster_images( X = rbm.W.value.T, | |
| 370 img_shape = (32,32),tile_shape = (10,10), | |
| 371 tile_spacing=(1,1))) | |
| 372 image.save('filters_at_epoch_%i.png'%epoch) | |
| 373 plotting_stop = time.clock() | |
| 374 plotting_time += (plotting_stop - plotting_start) | |
| 375 | |
| 376 end_time = time.clock() | |
| 377 | |
| 378 pretraining_time = (end_time - start_time) - plotting_time | |
| 379 | |
| 380 | |
| 381 | |
| 382 ################################# | |
| 383 # Sampling from the RBM # | |
| 384 ################################# | |
| 385 | |
| 386 # find out the number of test samples | |
| 372 | 387 #number_of_test_samples = 100 |
| 388 number_of_test_samples = test_set_x.value.shape[0] | |
| 369 | 389 |
| 372 | 390 #test_set_x, test_y = datasets.test(100*b_size) |
| 369 | 391 # pick random test examples, with which to initialize the persistent chain |
| 392 test_idx = rng.randint(number_of_test_samples - b_size) | |
| 393 persistent_vis_chain = theano.shared(test_set_x.value[test_idx:test_idx+b_size]) | |
| 394 | |
| 395 # define one step of Gibbs sampling (mf = mean-field) | |
| 396 [hid_mf, hid_sample, vis_mf, vis_sample] = rbm.gibbs_vhv(persistent_vis_chain) | |
| 397 | |
| 398 # the sample at the end of the channel is returned by ``gibbs_1`` as | |
| 399 # its second output; note that this is computed as a binomial draw, | |
| 400 # therefore it is formed of ints (0 and 1) and therefore needs to | |
| 401 # be converted to the same dtype as ``persistent_vis_chain`` | |
| 402 vis_sample = T.cast(vis_sample, dtype=theano.config.floatX) | |
| 403 | |
| 404 # construct the function that implements our persistent chain | |
| 405 # we generate the "mean field" activations for plotting and the actual samples for | |
| 406 # reinitializing the state of our persistent chain | |
| 407 sample_fn = theano.function([], [vis_mf, vis_sample], | |
| 408 updates = { persistent_vis_chain:vis_sample}) | |
| 409 | |
| 410 # sample the RBM, plotting every `plot_every`-th sample; do this | |
| 411 # until you plot at least `n_samples` | |
| 412 n_samples = 10 | |
| 413 # run minibatch size chains for gibbs samples (number of negative particles) | |
| 414 plot_every = b_size | |
| 415 | |
| 416 for idx in xrange(n_samples): | |
| 417 | |
| 418 # do `plot_every` intermediate samplings of which we do not care | |
| 419 for jdx in xrange(plot_every): | |
| 420 vis_mf, vis_sample = sample_fn() | |
| 421 | |
| 422 # construct image | |
| 423 image = PIL.Image.fromarray(tile_raster_images( | |
| 424 X = vis_mf, | |
| 425 img_shape = (32,32), | |
| 426 tile_shape = (10,10), | |
| 427 tile_spacing = (1,1) ) ) | |
| 428 #print ' ... plotting sample ', idx | |
| 429 image.save('sample_%i_step_%i.png'%(idx,idx*jdx)) | |
| 430 | |
| 431 #save the model | |
| 432 model = [rbm.W, rbm.vbias, rbm.hbias] | |
| 433 f = fopen('params.txt', 'w') | |
| 372 | 434 cPickle.dump(model, f, protocol = -1) |
| 369 | 435 f.close() |
| 436 #os.chdir('./..') | |
| 372 | 437 return numpy.mean(costs), pretraining_time*36 |
| 369 | 438 |
| 439 | |
| 440 def experiment(state, channel): | |
| 441 | |
| 442 (mean_cost, time_execution) = test_rbm(b_size = state.b_size,\ | |
| 443 nhidden = state.ndidden,\ | |
| 444 kk = state.kk,\ | |
| 445 persistance = state.persistance,\ | |
| 372 | 446 ) |
| 369 | 447 |
| 448 state.mean_costs = mean_costs | |
| 449 state.time_execution = time_execution | |
| 450 pylearn.version.record_versions(state,[theano,ift6266,pylearn]) | |
| 451 return channel.COMPLETE | |
| 452 | |
| 453 if __name__ == '__main__': | |
| 372 | 454 |
| 455 TABLE_NAME='RBM_tapha' | |
| 369 | 456 |
| 372 | 457 # DB path... |
| 458 test_rbm() | |
| 459 #db = sql.db('postgres://ift6266h10:f0572cd63b@gershwin/ift6266h10_db/'+ TABLE_NAME) | |
| 460 | |
| 461 #state = DD() | |
| 462 #for b_size in 50, 75, 100: | |
| 463 # state.b_size = b_size | |
| 464 # for nhidden in 1000,1250,1500: | |
| 465 # state.nhidden = nhidden | |
| 466 # for kk in 1,2,3,4: | |
| 467 # state.kk = kk | |
| 468 # for persistance in 0,1: | |
| 469 # state.persistance = persistance | |
| 470 # sql.insert_job(rbm.experiment, flatten(state), db) | |
| 471 | |
| 472 | |
| 473 #db.createView(TABLE_NAME + 'view') |