157 lines
5.4 KiB
Python
157 lines
5.4 KiB
Python
# %% 1
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# Package imports
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import matplotlib.pyplot as plt
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import numpy as np
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import sklearn
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import sklearn.datasets
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import sklearn.linear_model
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import matplotlib
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# Display plots inline and change default figure size
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%matplotlib inline
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matplotlib.rcParams['figure.figsize'] = (10.0, 8.0)
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# %% 2
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np.random.seed(3)
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X, y = sklearn.datasets.make_moons(200, noise=0.20)
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plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)
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# %% 3
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# Train the logistic rgeression classifier
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clf = sklearn.linear_model.LogisticRegressionCV()
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clf.fit(X, y)
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# %% 4
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# Helper function to plot a decision boundary.
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# If you don't fully understand this function don't worry, it just generates the contour plot below.
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def plot_decision_boundary(pred_func):
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# Set min and max values and give it some padding
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x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
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y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
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h = 0.01
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# Generate a grid of points with distance h between them
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xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
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# Predict the function value for the whole gid
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Z = pred_func(np.c_[xx.ravel(), yy.ravel()])
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Z = Z.reshape(xx.shape)
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# Plot the contour and training examples
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plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
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plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)
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# %% 12
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# Plot the decision boundary
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plot_decision_boundary(lambda x: clf.predict(x))
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plt.title("Logistic Regression")
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# %% 15
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num_examples = len(X) # training set size
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nn_input_dim = 2 # input layer dimensionality
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nn_output_dim = 2 # output layer dimensionality
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# Gradient descent parameters (I picked these by hand)
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epsilon = 0.01 # learning rate for gradient descent
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reg_lambda = 0.01 # regularization strength
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# %% 7
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# Helper function to evaluate the total loss on the dataset
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def calculate_loss(model):
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W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
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# Forward propagation to calculate our predictions
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z1 = X.dot(W1) + b1
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a1 = np.tanh(z1)
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z2 = a1.dot(W2) + b2
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exp_scores = np.exp(z2)
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probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
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# Calculating the loss
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corect_logprobs = -np.log(probs[range(num_examples), y])
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data_loss = np.sum(corect_logprobs)
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# Add regulatization term to loss (optional)
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data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
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return 1./num_examples * data_loss
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# %% 8
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# Helper function to predict an output (0 or 1)
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def predict(model, x):
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W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
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# Forward propagation
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z1 = x.dot(W1) + b1
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a1 = np.tanh(z1)
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z2 = a1.dot(W2) + b2
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exp_scores = np.exp(z2)
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probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
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return np.argmax(probs, axis=1)
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# %% 16
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# This function learns parameters for the neural network and returns the model.
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# - nn_hdim: Number of nodes in the hidden layer
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# - num_passes: Number of passes through the training data for gradient descent
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# - print_loss: If True, print the loss every 1000 iterations
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def build_model(nn_hdim, num_passes=20000, print_loss=False):
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# Initialize the parameters to random values. We need to learn these.
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np.random.seed(0)
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W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim)
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b1 = np.zeros((1, nn_hdim))
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W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim)
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b2 = np.zeros((1, nn_output_dim))
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# This is what we return at the end
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model = {}
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# Gradient descent. For each batch...
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for i in range(0, num_passes):
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# Forward propagation
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z1 = X.dot(W1) + b1
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a1 = np.tanh(z1)
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z2 = a1.dot(W2) + b2
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exp_scores = np.exp(z2)
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probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
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# Backpropagation
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delta3 = probs
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delta3[range(num_examples), y] -= 1
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dW2 = (a1.T).dot(delta3)
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db2 = np.sum(delta3, axis=0, keepdims=True)
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delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
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dW1 = np.dot(X.T, delta2)
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db1 = np.sum(delta2, axis=0)
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# Add regularization terms (b1 and b2 don't have regularization terms)
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dW2 += reg_lambda * W2
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dW1 += reg_lambda * W1
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# Gradient descent parameter update
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W1 += -epsilon * dW1
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b1 += -epsilon * db1
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W2 += -epsilon * dW2
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b2 += -epsilon * db2
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# Assign new parameters to the model
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model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}
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# Optionally print the loss.
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# This is expensive because it uses the whole dataset, so we don't want to do it too often.
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if print_loss and i % 1000 == 0:
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print("Loss after iteration %i: %f" %(i, calculate_loss(model)))
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return model
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# %% 17
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# Build a model with a 3-dimensional hidden layer
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model = build_model(3, print_loss=True)
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# Plot the decision boundary
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plot_decision_boundary(lambda x: predict(model, x))
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plt.title("Decision Boundary for hidden layer size 3")
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# %% 14
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plt.figure(figsize=(16, 32))
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hidden_layer_dimensions = [1, 2, 3, 4, 5, 20, 50]
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for i, nn_hdim in enumerate(hidden_layer_dimensions):
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plt.subplot(5, 2, i+1)
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plt.title('Hidden Layer size %d' % nn_hdim)
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model = build_model(nn_hdim)
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plot_decision_boundary(lambda x: predict(model, x))
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plt.show()
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