different types of initialization and their effects

Author: Saurabh Tandale

Initialization/.ipynb_checkpoints/Initialization-checkpoint.ipynb

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+import numpy as np
+import matplotlib.pyplot as plt
+import h5py
+import sklearn
+import sklearn.datasets
+
+def sigmoid(x):
+    """
+    Compute the sigmoid of x
+
+    Arguments:
+    x -- A scalar or numpy array of any size.
+
+    Return:
+    s -- sigmoid(x)
+    """
+    s = 1/(1+np.exp(-x))
+    return s
+
+def relu(x):
+    """
+    Compute the relu of x
+
+    Arguments:
+    x -- A scalar or numpy array of any size.
+
+    Return:
+    s -- relu(x)
+    """
+    s = np.maximum(0,x)
+    
+    return s
+
+def forward_propagation(X, parameters):
+    """
+    Implements the forward propagation (and computes the loss) presented in Figure 2.
+    
+    Arguments:
+    X -- input dataset, of shape (input size, number of examples)
+    Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
+    parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3":
+                    W1 -- weight matrix of shape ()
+                    b1 -- bias vector of shape ()
+                    W2 -- weight matrix of shape ()
+                    b2 -- bias vector of shape ()
+                    W3 -- weight matrix of shape ()
+                    b3 -- bias vector of shape ()
+    
+    Returns:
+    loss -- the loss function (vanilla logistic loss)
+    """
+        
+    # retrieve parameters
+    W1 = parameters["W1"]
+    b1 = parameters["b1"]
+    W2 = parameters["W2"]
+    b2 = parameters["b2"]
+    W3 = parameters["W3"]
+    b3 = parameters["b3"]
+    
+    # LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID
+    z1 = np.dot(W1, X) + b1
+    a1 = relu(z1)
+    z2 = np.dot(W2, a1) + b2
+    a2 = relu(z2)
+    z3 = np.dot(W3, a2) + b3
+    a3 = sigmoid(z3)
+    
+    cache = (z1, a1, W1, b1, z2, a2, W2, b2, z3, a3, W3, b3)
+    
+    return a3, cache
+
+def backward_propagation(X, Y, cache):
+    """
+    Implement the backward propagation presented in figure 2.
+    
+    Arguments:
+    X -- input dataset, of shape (input size, number of examples)
+    Y -- true "label" vector (containing 0 if cat, 1 if non-cat)
+    cache -- cache output from forward_propagation()
+    
+    Returns:
+    gradients -- A dictionary with the gradients with respect to each parameter, activation and pre-activation variables
+    """
+    m = X.shape[1]
+    (z1, a1, W1, b1, z2, a2, W2, b2, z3, a3, W3, b3) = cache
+    
+    dz3 = 1./m * (a3 - Y)
+    dW3 = np.dot(dz3, a2.T)
+    db3 = np.sum(dz3, axis=1, keepdims = True)
+    
+    da2 = np.dot(W3.T, dz3)
+    dz2 = np.multiply(da2, np.int64(a2 > 0))
+    dW2 = np.dot(dz2, a1.T)
+    db2 = np.sum(dz2, axis=1, keepdims = True)
+    
+    da1 = np.dot(W2.T, dz2)
+    dz1 = np.multiply(da1, np.int64(a1 > 0))
+    dW1 = np.dot(dz1, X.T)
+    db1 = np.sum(dz1, axis=1, keepdims = True)
+    
+    gradients = {"dz3": dz3, "dW3": dW3, "db3": db3,
+                 "da2": da2, "dz2": dz2, "dW2": dW2, "db2": db2,
+                 "da1": da1, "dz1": dz1, "dW1": dW1, "db1": db1}
+    
+    return gradients
+
+def update_parameters(parameters, grads, learning_rate):
+    """
+    Update parameters using gradient descent
+    
+    Arguments:
+    parameters -- python dictionary containing your parameters 
+    grads -- python dictionary containing your gradients, output of n_model_backward
+    
+    Returns:
+    parameters -- python dictionary containing your updated parameters 
+                  parameters['W' + str(i)] = ... 
+                  parameters['b' + str(i)] = ...
+    """
+    
+    L = len(parameters) // 2 # number of layers in the neural networks
+
+    # Update rule for each parameter
+    for k in range(L):
+        parameters["W" + str(k+1)] = parameters["W" + str(k+1)] - learning_rate * grads["dW" + str(k+1)]
+        parameters["b" + str(k+1)] = parameters["b" + str(k+1)] - learning_rate * grads["db" + str(k+1)]
+        
+    return parameters
+
+def compute_loss(a3, Y):
+    
+    """
+    Implement the loss function
+    
+    Arguments:
+    a3 -- post-activation, output of forward propagation
+    Y -- "true" labels vector, same shape as a3
+    
+    Returns:
+    loss - value of the loss function
+    """
+    
+    m = Y.shape[1]
+    logprobs = np.multiply(-np.log(a3),Y) + np.multiply(-np.log(1 - a3), 1 - Y)
+    loss = 1./m * np.nansum(logprobs)
+    
+    return loss
+
+def load_cat_dataset():
+    train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")
+    train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features
+    train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels
+
+    test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")
+    test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features
+    test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels
+
+    classes = np.array(test_dataset["list_classes"][:]) # the list of classes
+    
+    train_set_y = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))
+    test_set_y = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))
+    
+    train_set_x_orig = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
+    test_set_x_orig = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T
+    
+    train_set_x = train_set_x_orig/255
+    test_set_x = test_set_x_orig/255
+
+    return train_set_x, train_set_y, test_set_x, test_set_y, classes
+
+
+def predict(X, y, parameters):
+    """
+    This function is used to predict the results of a  n-layer neural network.
+    
+    Arguments:
+    X -- data set of examples you would like to label
+    parameters -- parameters of the trained model
+    
+    Returns:
+    p -- predictions for the given dataset X
+    """
+    
+    m = X.shape[1]
+    p = np.zeros((1,m), dtype = np.int)
+    
+    # Forward propagation
+    a3, caches = forward_propagation(X, parameters)
+    
+    # convert probas to 0/1 predictions
+    for i in range(0, a3.shape[1]):
+        if a3[0,i] > 0.5:
+            p[0,i] = 1
+        else:
+            p[0,i] = 0
+
+    # print results
+    print("Accuracy: "  + str(np.mean((p[0,:] == y[0,:]))))
+    
+    return p
+
+def plot_decision_boundary(model, X, y):
+    # Set min and max values and give it some padding
+    x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1
+    y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1
+    h = 0.01
+    # Generate a grid of points with distance h between them
+    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
+    # Predict the function value for the whole grid
+    Z = model(np.c_[xx.ravel(), yy.ravel()])
+    Z = Z.reshape(xx.shape)
+    # Plot the contour and training examples
+    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
+    plt.ylabel('x2')
+    plt.xlabel('x1')
+    plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral)
+    plt.show()
+    
+def predict_dec(parameters, X):
+    """
+    Used for plotting decision boundary.
+    
+    Arguments:
+    parameters -- python dictionary containing your parameters 
+    X -- input data of size (m, K)
+    
+    Returns
+    predictions -- vector of predictions of our model (red: 0 / blue: 1)
+    """
+    
+    # Predict using forward propagation and a classification threshold of 0.5
+    a3, cache = forward_propagation(X, parameters)
+    predictions = (a3>0.5)
+    return predictions
+
+def load_dataset():
+    np.random.seed(1)
+    train_X, train_Y = sklearn.datasets.make_circles(n_samples=300, noise=.05)
+    np.random.seed(2)
+    test_X, test_Y = sklearn.datasets.make_circles(n_samples=100, noise=.05)
+    # Visualize the data
+    plt.scatter(train_X[:, 0], train_X[:, 1], c=train_Y, s=40, cmap=plt.cm.Spectral);
+    train_X = train_X.T
+    train_Y = train_Y.reshape((1, train_Y.shape[0]))
+    test_X = test_X.T
+    test_Y = test_Y.reshape((1, test_Y.shape[0]))
+    return train_X, train_Y, test_X, test_Y