inverted dropout示例

这里是完成的吴恩达的深度学习课程作业中的一个inverted dropout的作业题，是一种很流行的正则化方式。这里做一个记录,重点记录了如何实现前向和后向的inverted dropout，都是代码片段，无法运行；完整的代码请参见吴恩达的第二课的第一周的作业。

1、前向传播

def forward_propagation_with_dropout(X, parameters, keep_prob = 0.5):
    """
    Implements the forward propagation: 
    LINEAR -> RELU + DROPOUT -> 
    LINEAR -> RELU + DROPOUT -> LINEAR -> SIGMOID.
    Arguments:
    X -- input dataset, of shape (2, number of examples)
    parameters -- python dictionary containing your parameters
    "W1", "b1", "W2", "b2", "W3", "b3":
        W1 -- weight matrix of shape (20, 2)
        b1 -- bias vector of shape (20, 1)
        W2 -- weight matrix of shape (3, 20)
        b2 -- bias vector of shape (3, 1)
        W3 -- weight matrix of shape (1, 3)
        b3 -- bias vector of shape (1, 1)
    keep_prob - probability of keeping a neuron active during drop-out,
    scalar
    Returns:
    A3 -- last activation value, output of the forward propagation,
    of shape (1,1)
    cache -- tuple, information stored for computing the backward propagation
    """
    
    np.random.seed(1)
    
    # 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)
    ### START CODE HERE ### (approx. 4 lines)         
    # Steps 1-4 below correspond to the Steps 1-4 described above. 
    # Step 1: initialize matrix D1 = np.random.rand(..., ...)
    D1 = np.random.rand(A1.shape[0], A1.shape[1])
    # Step 2: convert entries of D1 to 0 or 1 
    # (using keep_prob as the threshold)
    D1 = D1 < keep_prob
    # Step 3: shut down some neurons of A1
    A1 = A1 * D1
    # Step 4: scale the value of neurons that haven't been shut down
    A1 = A1 / keep_prob
    ### END CODE HERE ###
    Z2 = np.dot(W2, A1) + b2
    A2 = relu(Z2)
    ### START CODE HERE ### (approx. 4 lines)
    # Step 1: initialize matrix D2 = np.random.rand(..., ...)
    D2 = np.random.rand(A2.shape[0], A2.shape[1])
    # Step 2: convert entries of D2 to 0 or 1 
    # (using keep_prob as the threshold)
    D2 = D2 < keep_prob
    # Step 3: shut down some neurons of A2
    A2 = A2 * D2
    # Step 4: scale the value of neurons that haven't been shut down
    A2 = A2 / keep_prob
    ### END CODE HERE ###
    Z3 = np.dot(W3, A2) + b3
    A3 = sigmoid(Z3)
    cache = (Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3)
    return A3, cache

2、后向传播

def backward_propagation_with_dropout(X, Y, cache, keep_prob):
    """
    Implements the backward propagation of our 
    baseline model to which we added dropout.
    
    Arguments:
    X -- input dataset, of shape (2, number of examples)
    Y -- "true" labels vector, of shape (output size, number of examples)
    cache -- cache output from forward_propagation_with_dropout()
    keep_prob - probability of keeping a neuron
    active during drop-out, scalar
    
    Returns:
    gradients -- A dictionary with the gradients with respect
    to each parameter, activation and pre-activation variables
    """
    
    m = X.shape[1]
    (Z1, D1, A1, W1, b1, Z2, D2, A2, W2, b2, Z3, A3, W3, b3) = cache
    
    dZ3 = A3 - Y
    dW3 = 1./m * np.dot(dZ3, A2.T)
    db3 = 1./m * np.sum(dZ3, axis=1, keepdims = True)
    dA2 = np.dot(W3.T, dZ3)
    ### START CODE HERE ### (≈ 2 lines of code)
    # Step 1: Apply mask D2 to shut down the
    # same neurons as during the forward propagation
    dA2 = dA2 * D2
    # Step 2: Scale the value of neurons that haven't been shut down
    dA2 = dA2 / keep_prob    
    ### END CODE HERE ###
    dZ2 = np.multiply(dA2, np.int64(A2 > 0))
    dW2 = 1./m * np.dot(dZ2, A1.T)
    db2 = 1./m * np.sum(dZ2, axis=1, keepdims = True)
    
    dA1 = np.dot(W2.T, dZ2)
    ### START CODE HERE ### (≈ 2 lines of code)
    # Step 1: Apply mask D1 to shut down the
    # same neurons as during the forward propagation
    dA1 = dA1 * D1
    # Step 2: Scale the value of neurons that haven't been shut down
    dA1 = dA1 / keep_prob    
    ### END CODE HERE ###
    dZ1 = np.multiply(dA1, np.int64(A1 > 0))
    dW1 = 1./m * np.dot(dZ1, X.T)
    db1 = 1./m * 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