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import numpy as np |
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from scipy.optimize import fmin_l_bfgs_b |
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from Orange.classification import Learner, Model |
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__all__ = ["MLPLearner"] |
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def sigmoid(x): |
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return 1.0 / (1.0 + np.exp(-x)) |
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class MLPLearner(Learner): |
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"""Multilayer perceptron (feedforward neural network) |
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This model uses stochastic gradient descent and the |
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backpropagation algorithm to train the weights of a feedforward |
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neural network. The network uses the sigmoid activation |
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functions, except for the last layer which computes the softmax |
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activation function. The network can be used for binary and |
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multiclass classification. Stochastic gradient descent minimizes |
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the L2 regularize categorical crossentropy cost function. The |
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topology of the network can be customized by setting the layers |
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attribute. When using this model you should: |
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- Choose a suitable: |
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* topology (layers) |
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* regularization parameter (lambda\_) |
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* dropout (values of 0.2 for the input layer and 0.5 for the hidden |
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layers usually work well) |
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* The number of epochs of stochastic gradient descent (num_epochs) |
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* The learning rate of stochastic gradient descent (learning_rate) |
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- Continuize all discrete attributes |
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- Transform the data set so that the columns are on a similar scale |
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layers : list |
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The topology of the network. A network with |
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layer=[10, 100, 100, 3] has two hidden layers with 100 neurons each, |
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10 features and a class value with 3 distinct values. |
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lambda\_ : float, optional (default = 1.0) |
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The regularization parameter. Higher values of lambda\_ |
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force the coefficients to be small. |
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dropout : list, optional (default = None) |
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The dropout rate for each, but the last, |
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layer. The list should have one element less then the parameter layers. |
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Values of 0.2 for the input layer and 0.5 for the hidden layers usually |
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work well. |
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num_epochs : int, optional |
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The number of epochs of stochastic gradient descent |
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learning_rate : float, optional |
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The learning rate of stochastic gradient descent |
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batch_size : int, optional |
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The batch size of stochastic gradient descent |
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""" |
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name = 'mlp' |
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def __init__(self, layers, lambda_=1.0, dropout=None, preprocessors=None, |
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**opt_args): |
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super().__init__(preprocessors=preprocessors) |
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if dropout is None: |
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dropout = [0] * (len(layers) - 1) |
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assert len(dropout) == len(layers) - 1 |
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self.layers = layers |
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self.lambda_ = lambda_ |
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self.dropout = dropout |
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self.opt_args = opt_args |
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def unfold_params(self, params): |
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T, b = [], [] |
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acc = 0 |
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for l1, l2 in zip(self.layers, self.layers[1:]): |
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b.append(params[acc:acc + l2]) |
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acc += l2 |
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T.append(params[acc:acc + l1 * l2].reshape((l2, l1))) |
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acc += l1 * l2 |
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return T, b |
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def cost_grad(self, params, X, Y): |
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T, b = self.unfold_params(params) |
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# forward pass |
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a, z = [], [] |
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dropout_mask = [] |
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for i in range(len(T)): |
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if self.dropout is None or self.dropout[0] < 1e-7: |
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dropout_mask.append(1) |
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else: |
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dropout_mask.append( |
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np.random.binomial(1, 1 - self.dropout[0], |
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(X.shape[0], self.layers[i]))) |
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a.append(X * dropout_mask[0]) |
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for i in range(len(self.layers) - 2): |
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z.append(a[i].dot(T[i].T) + b[i]) |
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a.append(sigmoid(z[i]) * dropout_mask[i + 1]) |
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# softmax last layer |
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z.append(a[-1].dot(T[-1].T) + b[-1]) |
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P = np.exp(z[-1] - np.max(z[-1], axis=1)[:, None]) |
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P /= np.sum(P, axis=1)[:, None] |
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a.append(P) |
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# cost |
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cost = -np.sum(np.log(a[-1] + 1e-15) * Y) |
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for theta in T: |
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cost += self.lambda_ * np.dot(theta.flat, theta.flat) / 2.0 |
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cost /= X.shape[0] |
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# gradient |
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params = [] |
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for i in range(len(self.layers) - 1): |
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if i == 0: |
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d = a[-1] - Y |
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else: |
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d = d.dot(T[-i]) * a[-i - 1] * (1 - a[-i - 1]) |
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dT = (a[-i - 2] * dropout_mask[-i - 1]).T.dot(d).T + self.lambda_\ |
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* T[-i - 1] |
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db = np.sum(d, axis=0) |
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params.extend([dT.flat, db.flat]) |
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grad = np.concatenate(params[::-1]) / X.shape[0] |
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return cost, grad |
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def fit_bfgs(self, params, X, Y): |
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params, j, ret = fmin_l_bfgs_b(self.cost_grad, params, |
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args=(X, Y), **self.opt_args) |
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return params |
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def fit_sgd(self, params, X, Y, num_epochs=1000, batch_size=100, |
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learning_rate=0.1): |
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# shuffle examples |
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inds = np.random.permutation(X.shape[0]) |
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X = X[inds] |
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Y = Y[inds] |
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# split training and validation set |
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num_tr = int(X.shape[0] * 0.8) |
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X_tr, Y_tr = X[:num_tr], Y[:num_tr] |
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X_va, Y_va = X[num_tr:], Y[num_tr:] |
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early_stop = 100 |
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best_params = None |
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best_cost = np.inf |
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for epoch in range(num_epochs): |
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for i in range(0, num_tr, batch_size): |
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cost, grad = self.cost_grad(params, X_tr, Y_tr) |
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params -= learning_rate * grad |
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# test on validation set |
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T, b = self.unfold_params(params) |
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P_va = MLPModel(T, b, self.dropout).predict(X_va) |
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cost = -np.sum(np.log(P_va + 1e-15) * Y_va) |
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if cost < best_cost: |
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best_cost = cost |
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best_params = np.copy(params) |
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early_stop *= 2 |
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if epoch > early_stop: |
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break |
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return params |
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def fit(self, X, Y, W): |
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if np.isnan(np.sum(X)) or np.isnan(np.sum(Y)): |
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raise ValueError('MLP does not support unknown values') |
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if Y.shape[1] == 1: |
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num_classes = np.unique(Y).size |
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Y = np.eye(num_classes)[Y.ravel().astype(int)] |
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params = [] |
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num_params = 0 |
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for l1, l2 in zip(self.layers, self.layers[1:]): |
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num_params += l1 * l2 + l2 |
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i = 4.0 * np.sqrt(6.0 / (l1 + l2)) |
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params.append(np.random.uniform(-i, i, l1 * l2)) |
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params.append(np.zeros(l2)) |
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params = np.concatenate(params) |
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#params = self.fit_bfgs(params, X, Y) |
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params = self.fit_sgd(params, X, Y, **self.opt_args) |
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T, b = self.unfold_params(params) |
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return MLPModel(T, b, self.dropout) |
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class MLPModel(Model): |
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def __init__(self, T, b, dropout): |
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self.T = T |
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self.b = b |
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self.dropout = dropout |
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def predict(self, X): |
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a = X |
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for i in range(len(self.T) - 1): |
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d = 1 - self.dropout[i] |
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a = sigmoid(a.dot(self.T[i].T * d) + self.b[i]) |
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z = a.dot(self.T[-1].T) + self.b[-1] |
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P = np.exp(z - np.max(z, axis=1)[:, None]) |
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P /= np.sum(P, axis=1)[:, None] |
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return P |
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if __name__ == '__main__': |
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import Orange.data |
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import sklearn.cross_validation as skl_cross_validation |
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np.random.seed(42) |
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def numerical_grad(f, params, e=1e-4): |
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grad = np.zeros_like(params) |
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perturb = np.zeros_like(params) |
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for i in range(params.size): |
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perturb[i] = e |
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j1 = f(params - perturb) |
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j2 = f(params + perturb) |
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grad[i] = (j2 - j1) / (2.0 * e) |
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perturb[i] = 0 |
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return grad |
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d = Orange.data.Table('iris') |
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# # gradient check |
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# m = MLPLearner([4, 20, 20, 3], dropout=[0.0, 0.5, 0.0], lambda_=0.0) |
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# params = np.random.randn(5 * 20 + 21 * 20 + 21 * 3) * 0.1 |
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# Y = np.eye(3)[d.Y.ravel().astype(int)] |
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# |
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# ga = m.cost_grad(params, d.X, Y)[1] |
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# gm = numerical_grad(lambda t: m.cost_grad(t, d.X, Y)[0], params) |
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# |
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# print(np.sum((ga - gm)**2)) |
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# m = MLPLearner([4, 20, 3], dropout=[0.0, 0.0], lambda_=1.0) |
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# m(d) |
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for lambda_ in [0.03, 0.1, 0.3, 1, 3]: |
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m = MLPLearner([4, 20, 20, 3], lambda_=lambda_, num_epochs=1000, |
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learning_rate=0.1) |
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scores = [] |
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for tr_ind, te_ind in skl_cross_validation.StratifiedKFold(d.Y.ravel()): |
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s = np.mean(m(d[tr_ind])(d[te_ind]) == d[te_ind].Y.ravel()) |
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scores.append(s) |
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print(np.mean(scores), lambda_) |
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This can be caused by one of the following:
1. Missing Dependencies
This error could indicate a configuration issue of Pylint. Make sure that your libraries are available by adding the necessary commands.
2. Missing __init__.py files
This error could also result from missing
__init__.py
files in your module folders. Make sure that you place one file in each sub-folder.