Mercurial > ift6266
annotate code_tutoriel/logistic_sgd.py @ 402:83413ac10913
Added more stats printing. Now you dont need to parameters which dataset you are testing, it will detect it automatically
| author | humel |
|---|---|
| date | Wed, 28 Apr 2010 11:28:28 -0400 |
| parents | 4bc5eeec6394 |
| children |
| rev | line source |
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| 0 | 1 """ |
| 2 This tutorial introduces logistic regression using Theano and stochastic | |
| 3 gradient descent. | |
| 4 | |
| 5 Logistic regression is a probabilistic, linear classifier. It is parametrized | |
| 6 by a weight matrix :math:`W` and a bias vector :math:`b`. Classification is | |
| 7 done by projecting data points onto a set of hyperplanes, the distance to | |
| 8 which is used to determine a class membership probability. | |
| 9 | |
| 10 Mathematically, this can be written as: | |
| 11 | |
| 12 .. math:: | |
| 13 P(Y=i|x, W,b) &= softmax_i(W x + b) \\ | |
| 14 &= \frac {e^{W_i x + b_i}} {\sum_j e^{W_j x + b_j}} | |
| 15 | |
| 16 | |
| 17 The output of the model or prediction is then done by taking the argmax of | |
| 18 the vector whose i'th element is P(Y=i|x). | |
| 19 | |
| 20 .. math:: | |
| 21 | |
| 22 y_{pred} = argmax_i P(Y=i|x,W,b) | |
| 23 | |
| 24 | |
| 25 This tutorial presents a stochastic gradient descent optimization method | |
| 26 suitable for large datasets, and a conjugate gradient optimization method | |
| 27 that is suitable for smaller datasets. | |
| 28 | |
| 29 | |
| 30 References: | |
| 31 | |
| 32 - textbooks: "Pattern Recognition and Machine Learning" - | |
| 33 Christopher M. Bishop, section 4.3.2 | |
| 34 | |
| 35 """ | |
| 36 __docformat__ = 'restructedtext en' | |
| 37 | |
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38 import numpy, time, cPickle, gzip |
| 0 | 39 |
| 40 import theano | |
| 41 import theano.tensor as T | |
| 42 | |
| 43 | |
| 44 class LogisticRegression(object): | |
| 45 """Multi-class Logistic Regression Class | |
| 46 | |
| 47 The logistic regression is fully described by a weight matrix :math:`W` | |
| 48 and bias vector :math:`b`. Classification is done by projecting data | |
| 49 points onto a set of hyperplanes, the distance to which is used to | |
| 50 determine a class membership probability. | |
| 51 """ | |
| 52 | |
| 53 | |
| 54 | |
| 55 | |
| 56 def __init__(self, input, n_in, n_out): | |
| 57 """ Initialize the parameters of the logistic regression | |
| 58 | |
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59 :type input: theano.tensor.TensorType |
| 0 | 60 :param input: symbolic variable that describes the input of the |
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61 architecture (one minibatch) |
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62 |
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63 :type n_in: int |
| 0 | 64 :param n_in: number of input units, the dimension of the space in |
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65 which the datapoints lie |
| 0 | 66 |
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67 :type n_out: int |
| 0 | 68 :param n_out: number of output units, the dimension of the space in |
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69 which the labels lie |
| 0 | 70 |
| 71 """ | |
| 72 | |
| 73 # initialize with 0 the weights W as a matrix of shape (n_in, n_out) | |
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74 self.W = theano.shared(value=numpy.zeros((n_in,n_out), dtype = theano.config.floatX), |
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75 name='W') |
| 0 | 76 # initialize the baises b as a vector of n_out 0s |
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77 self.b = theano.shared(value=numpy.zeros((n_out,), dtype = theano.config.floatX), |
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78 name='b') |
| 0 | 79 |
| 80 | |
| 81 # compute vector of class-membership probabilities in symbolic form | |
| 82 self.p_y_given_x = T.nnet.softmax(T.dot(input, self.W)+self.b) | |
| 83 | |
| 84 # compute prediction as class whose probability is maximal in | |
| 85 # symbolic form | |
| 86 self.y_pred=T.argmax(self.p_y_given_x, axis=1) | |
| 87 | |
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88 # parameters of the model |
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89 self.params = [self.W, self.b] |
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90 |
| 0 | 91 |
| 92 | |
| 93 | |
| 94 | |
| 95 def negative_log_likelihood(self, y): | |
| 96 """Return the mean of the negative log-likelihood of the prediction | |
| 97 of this model under a given target distribution. | |
| 98 | |
| 99 .. math:: | |
| 100 | |
| 101 \frac{1}{|\mathcal{D}|} \mathcal{L} (\theta=\{W,b\}, \mathcal{D}) = | |
| 102 \frac{1}{|\mathcal{D}|} \sum_{i=0}^{|\mathcal{D}|} \log(P(Y=y^{(i)}|x^{(i)}, W,b)) \\ | |
| 103 \ell (\theta=\{W,b\}, \mathcal{D}) | |
| 104 | |
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105 :type y: theano.tensor.TensorType |
| 0 | 106 :param y: corresponds to a vector that gives for each example the |
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107 correct label |
| 0 | 108 |
| 109 Note: we use the mean instead of the sum so that | |
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110 the learning rate is less dependent on the batch size |
| 0 | 111 """ |
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112 # y.shape[0] is (symbolically) the number of rows in y, i.e., number of examples (call it n) in the minibatch |
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113 # T.arange(y.shape[0]) is a symbolic vector which will contain [0,1,2,... n-1] |
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114 # T.log(self.p_y_given_x) is a matrix of Log-Probabilities (call it LP) with one row per example and one column per class |
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115 # LP[T.arange(y.shape[0]),y] is a vector v containing [LP[0,y[0]], LP[1,y[1]], LP[2,y[2]], ..., LP[n-1,y[n-1]]] |
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116 # and T.mean(LP[T.arange(y.shape[0]),y]) is the mean (across minibatch examples) of the elements in v, |
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117 # i.e., the mean log-likelihood across the minibatch. |
| 0 | 118 return -T.mean(T.log(self.p_y_given_x)[T.arange(y.shape[0]),y]) |
| 119 | |
| 120 | |
| 121 def errors(self, y): | |
| 122 """Return a float representing the number of errors in the minibatch | |
| 123 over the total number of examples of the minibatch ; zero one | |
| 124 loss over the size of the minibatch | |
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125 |
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126 :type y: theano.tensor.TensorType |
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127 :param y: corresponds to a vector that gives for each example the |
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128 correct label |
| 0 | 129 """ |
| 130 | |
| 131 # check if y has same dimension of y_pred | |
| 132 if y.ndim != self.y_pred.ndim: | |
| 133 raise TypeError('y should have the same shape as self.y_pred', | |
| 134 ('y', target.type, 'y_pred', self.y_pred.type)) | |
| 135 # check if y is of the correct datatype | |
| 136 if y.dtype.startswith('int'): | |
| 137 # the T.neq operator returns a vector of 0s and 1s, where 1 | |
| 138 # represents a mistake in prediction | |
| 139 return T.mean(T.neq(self.y_pred, y)) | |
| 140 else: | |
| 141 raise NotImplementedError() | |
| 142 | |
| 143 | |
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144 def load_data(dataset): |
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145 ''' Loads the dataset |
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146 |
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147 :type dataset: string |
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148 :param dataset: the path to the dataset (here MNIST) |
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149 ''' |
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150 |
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151 ############# |
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152 # LOAD DATA # |
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153 ############# |
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154 print '... loading data' |
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155 |
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156 # Load the dataset |
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157 f = gzip.open(dataset,'rb') |
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158 train_set, valid_set, test_set = cPickle.load(f) |
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159 f.close() |
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160 |
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161 |
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162 def shared_dataset(data_xy): |
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163 """ Function that loads the dataset into shared variables |
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164 |
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165 The reason we store our dataset in shared variables is to allow |
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166 Theano to copy it into the GPU memory (when code is run on GPU). |
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167 Since copying data into the GPU is slow, copying a minibatch everytime |
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168 is needed (the default behaviour if the data is not in a shared |
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169 variable) would lead to a large decrease in performance. |
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170 """ |
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171 data_x, data_y = data_xy |
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172 shared_x = theano.shared(numpy.asarray(data_x, dtype=theano.config.floatX)) |
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173 shared_y = theano.shared(numpy.asarray(data_y, dtype=theano.config.floatX)) |
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174 # When storing data on the GPU it has to be stored as floats |
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175 # therefore we will store the labels as ``floatX`` as well |
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176 # (``shared_y`` does exactly that). But during our computations |
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177 # we need them as ints (we use labels as index, and if they are |
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178 # floats it doesn't make sense) therefore instead of returning |
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179 # ``shared_y`` we will have to cast it to int. This little hack |
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180 # lets ous get around this issue |
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181 return shared_x, T.cast(shared_y, 'int32') |
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182 |
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183 test_set_x, test_set_y = shared_dataset(test_set) |
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184 valid_set_x, valid_set_y = shared_dataset(valid_set) |
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185 train_set_x, train_set_y = shared_dataset(train_set) |
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186 |
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187 rval = [(train_set_x, train_set_y), (valid_set_x,valid_set_y), (test_set_x, test_set_y)] |
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188 return rval |
| 0 | 189 |
| 190 | |
| 191 | |
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192 |
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193 def sgd_optimization_mnist(learning_rate=0.13, n_epochs=1000, dataset='mnist.pkl.gz'): |
| 0 | 194 """ |
| 195 Demonstrate stochastic gradient descent optimization of a log-linear | |
| 196 model | |
| 197 | |
| 198 This is demonstrated on MNIST. | |
| 199 | |
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200 :type learning_rate: float |
| 0 | 201 :param learning_rate: learning rate used (factor for the stochastic |
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202 gradient) |
| 0 | 203 |
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204 :type n_epochs: int |
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205 :param n_epochs: maximal number of epochs to run the optimizer |
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206 |
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207 :type dataset: string |
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208 :param dataset: the path of the MNIST dataset file from |
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209 http://www.iro.umontreal.ca/~lisa/deep/data/mnist/mnist.pkl.gz |
| 0 | 210 |
| 211 """ | |
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212 datasets = load_data(dataset) |
| 0 | 213 |
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214 train_set_x, train_set_y = datasets[0] |
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215 valid_set_x, valid_set_y = datasets[1] |
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216 test_set_x , test_set_y = datasets[2] |
| 0 | 217 |
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218 batch_size = 600 # size of the minibatch |
| 0 | 219 |
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220 # compute number of minibatches for training, validation and testing |
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221 n_train_batches = train_set_x.value.shape[0] / batch_size |
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222 n_valid_batches = valid_set_x.value.shape[0] / batch_size |
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223 n_test_batches = test_set_x.value.shape[0] / batch_size |
| 0 | 224 |
| 225 | |
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226 ###################### |
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227 # BUILD ACTUAL MODEL # |
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228 ###################### |
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229 print '... building the model' |
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230 |
| 0 | 231 |
| 232 # allocate symbolic variables for the data | |
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233 index = T.lscalar() # index to a [mini]batch |
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234 x = T.matrix('x') # the data is presented as rasterized images |
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235 y = T.ivector('y') # the labels are presented as 1D vector of |
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236 # [int] labels |
| 0 | 237 |
| 238 # construct the logistic regression class | |
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239 # Each MNIST image has size 28*28 |
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240 classifier = LogisticRegression( input=x, n_in=28*28, n_out=10) |
| 0 | 241 |
| 242 # the cost we minimize during training is the negative log likelihood of | |
| 243 # the model in symbolic format | |
| 244 cost = classifier.negative_log_likelihood(y) | |
| 245 | |
| 246 # compiling a Theano function that computes the mistakes that are made by | |
| 247 # the model on a minibatch | |
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248 test_model = theano.function(inputs = [index], |
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249 outputs = classifier.errors(y), |
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250 givens={ |
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251 x:test_set_x[index*batch_size:(index+1)*batch_size], |
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252 y:test_set_y[index*batch_size:(index+1)*batch_size]}) |
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253 |
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254 validate_model = theano.function( inputs = [index], |
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255 outputs = classifier.errors(y), |
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256 givens={ |
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257 x:valid_set_x[index*batch_size:(index+1)*batch_size], |
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258 y:valid_set_y[index*batch_size:(index+1)*batch_size]}) |
| 0 | 259 |
| 260 # compute the gradient of cost with respect to theta = (W,b) | |
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261 g_W = T.grad(cost = cost, wrt = classifier.W) |
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262 g_b = T.grad(cost = cost, wrt = classifier.b) |
| 0 | 263 |
| 264 # specify how to update the parameters of the model as a dictionary | |
| 265 updates ={classifier.W: classifier.W - learning_rate*g_W,\ | |
| 266 classifier.b: classifier.b - learning_rate*g_b} | |
| 267 | |
| 268 # compiling a Theano function `train_model` that returns the cost, but in | |
| 269 # the same time updates the parameter of the model based on the rules | |
| 270 # defined in `updates` | |
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271 train_model = theano.function(inputs = [index], |
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272 outputs = cost, |
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273 updates = updates, |
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274 givens={ |
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275 x:train_set_x[index*batch_size:(index+1)*batch_size], |
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276 y:train_set_y[index*batch_size:(index+1)*batch_size]}) |
| 0 | 277 |
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278 ############### |
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279 # TRAIN MODEL # |
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280 ############### |
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281 print '... training the model' |
| 0 | 282 # early-stopping parameters |
| 283 patience = 5000 # look as this many examples regardless | |
| 284 patience_increase = 2 # wait this much longer when a new best is | |
| 285 # found | |
| 286 improvement_threshold = 0.995 # a relative improvement of this much is | |
| 287 # considered significant | |
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288 validation_frequency = min(n_train_batches, patience/2) |
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289 # go through this many |
| 0 | 290 # minibatche before checking the network |
| 291 # on the validation set; in this case we | |
| 292 # check every epoch | |
| 293 | |
| 294 best_params = None | |
| 295 best_validation_loss = float('inf') | |
| 296 test_score = 0. | |
| 297 start_time = time.clock() | |
| 298 | |
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299 done_looping = False |
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300 epoch = 0 |
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301 while (epoch < n_epochs) and (not done_looping): |
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302 epoch = epoch + 1 |
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303 for minibatch_index in xrange(n_train_batches): |
| 0 | 304 |
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305 minibatch_avg_cost = train_model(minibatch_index) |
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306 # iteration number |
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307 iter = epoch * n_train_batches + minibatch_index |
| 0 | 308 |
| 309 if (iter+1) % validation_frequency == 0: | |
| 310 # compute zero-one loss on validation set | |
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311 validation_losses = [validate_model(i) for i in xrange(n_valid_batches)] |
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312 this_validation_loss = numpy.mean(validation_losses) |
| 0 | 313 |
| 314 print('epoch %i, minibatch %i/%i, validation error %f %%' % \ | |
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315 (epoch, minibatch_index+1,n_train_batches, \ |
| 0 | 316 this_validation_loss*100.)) |
| 317 | |
| 318 | |
| 319 # if we got the best validation score until now | |
| 320 if this_validation_loss < best_validation_loss: | |
| 321 #improve patience if loss improvement is good enough | |
| 322 if this_validation_loss < best_validation_loss * \ | |
| 323 improvement_threshold : | |
| 324 patience = max(patience, iter * patience_increase) | |
| 325 | |
| 326 best_validation_loss = this_validation_loss | |
| 327 # test it on the test set | |
| 328 | |
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329 test_losses = [test_model(i) for i in xrange(n_test_batches)] |
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330 test_score = numpy.mean(test_losses) |
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331 |
| 0 | 332 print((' epoch %i, minibatch %i/%i, test error of best ' |
| 333 'model %f %%') % \ | |
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334 (epoch, minibatch_index+1, n_train_batches,test_score*100.)) |
| 0 | 335 |
| 336 if patience <= iter : | |
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337 done_looping = True |
| 0 | 338 break |
| 339 | |
| 340 end_time = time.clock() | |
| 341 print(('Optimization complete with best validation score of %f %%,' | |
| 342 'with test performance %f %%') % | |
| 343 (best_validation_loss * 100., test_score*100.)) | |
| 344 print ('The code ran for %f minutes' % ((end_time-start_time)/60.)) | |
| 345 | |
| 346 if __name__ == '__main__': | |
| 347 sgd_optimization_mnist() | |
| 348 |