def negative_log_likelihood(self, y): """Return the mean of the negative log-likelihood of the prediction of this model under a given target distribution. .. math:: \frac{1}{|\mathcal{D}|} \mathcal{L} (\theta=\{W,b\}, \mathcal{D}) = \frac{1}{|\mathcal{D}|} \sum_{i=0}^{|\mathcal{D}|} \log(P(Y=y^{(i)}|x^{(i)}, W,b)) \\ \ell (\theta=\{W,b\}, \mathcal{D}) :type y: my_theano.tensor.TensorType :param y: corresponds to a vector that gives for each example the correct label Note: we use the mean instead of the sum so that the learning rate is less dependent on the batch size """ # start-snippet-2 # y.shape[0] is (symbolically) the number of rows in y, i.e., # number of examples (call it n) in the minibatch # T.arange(y.shape[0]) is a symbolic vector which will contain # [0,1,2,... n-1] 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 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]]] and T.mean(LP[T.arange(y.shape[0]),y]) is # the mean (across minibatch examples) of the elements in v, # i.e., the mean log-likelihood across the minibatch. return -T.mean(T.log(self.p_y_given_x)[T.arange(y.shape[0]), y])
def negative_log_likelihood(p_y, y): """Return the mean of the negative log-likelihood of the prediction of this model under a given target distribution. .. math:: \frac{1}{|\mathcal{D}|} \mathcal{L} (\theta=\{W,b\}, \mathcal{D}) = \frac{1}{|\mathcal{D}|} \sum_{i=0}^{|\mathcal{D}|} \log(P(Y=y^{(i)}|x^{(i)}, W,b)) \\ \ell (\theta=\{W,b\}, \mathcal{D}) :param p_y: the probability distribution of y given x :type y: my_theano.tensor.TensorType :param y: corresponds to a vector that gives for each example the correct label Note: we use the mean instead of the sum so that the learning rate is less dependent on the batch size """ # start-snippet-2 # y.shape[0] is (symbolically) the number of rows in y, i.e., # number of examples (call it n) in the minibatch # T.arange(y.shape[0]) is a symbolic vector which will contain # [0,1,2,... n-1] 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 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]]] and T.mean(LP[T.arange(y.shape[0]),y]) is # the mean (across minibatch examples) of the elements in v, # i.e., the mean log-likelihood across the minibatch. return -T.mean(T.log(p_y)[T.arange(y.shape[0]), y])
def zero_one(p_y, y): """ :param p_y: the probability distribution of y given x :type y: my_theano.tensor.TensorType :param y: corresponds to a vector that gives for each example the correct label :param p_y: :param y: :return: """ return T.mean(T.neq(T.argmax(p_y, axis=1), y))
def errors(self, y): """Return a float representing the number of errors in the minibatch over the total number of examples of the minibatch ; zero one loss over the size of the minibatch :type y: my_theano.tensor.TensorType :param y: corresponds to a vector that gives for each example the correct label """ # check if y has same dimension of y_pred if y.ndim != self.y_pred.ndim: raise TypeError( 'y should have the same shape as self.y_pred', ('y', y.type, 'y_pred', self.y_pred.type) ) # check if y is of the correct datatype if y.dtype.startswith('int'): # the T.neq operator returns a vector of 0s and 1s, where 1 # represents a mistake in prediction return T.mean(T.neq(self.y_pred, y)) else: raise NotImplementedError()