吴恩达 神经网络和深度学习 assignment3 编程作业 构建神经网络模型

1、导入包

# Package imports

import numpy as np

import matplotlib.pyplot as plt

from testCases import *

import sklearn

import sklearn.datasets

import sklearn.linear_model

from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets

%matplotlib inline

np.random.seed(1) # set a seed so that the results are consistent

2、数据集

X, Y = load_planar_dataset()

# Visualize the data:

plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral)


### START CODE HERE ### (≈ 3 lines of code)

shape_X = X.shape

shape_Y = Y.shape

m = shape_X[1]  # training set size

### END CODE HERE ###

print ('The shape of X is: ' + str(shape_X))

print ('The shape of Y is: ' + str(shape_Y))

print ('I have m = %d training examples!' % (m))

输出:

The shape of X is: (2, 400)

The shape of Y is: (1, 400)

I have m = 400 training examples!

3、简单逻辑回归

# Train the logistic regression classifier

clf = sklearn.linear_model.LogisticRegressionCV();

clf.fit(X.T, Y.T);

# Plot the decision boundary for logistic regression

plot_decision_boundary(lambda x: clf.predict(x), X,Y.reshape(X[0,:].shape))

#plt.title("Logistic Regression")

# Print accuracy

LR_predictions = clf.predict(X.T)

print ('Accuracy of logistic regression: %d ' % float((np.dot(Y,LR_predictions) + np.dot(1-Y,1-LR_predictions))/float(Y.size)*100) +

      '% ' + "(percentage of correctly labelled datapoints)")


4、神经网络模型

构建神经网络模型通用方法:

构建神经网络结构

初始化模型参数

循环:

正向传播

计算损失函数

反向传播获得梯度

梯度更新

4.1定义神经网络结构

def layer_sizes(X, Y):

    """

    Arguments:

    X -- input dataset of shape (input size, number of examples)

    Y -- labels of shape (output size, number of examples)


    Returns:

    n_x -- the size of the input layer

    n_h -- the size of the hidden layer

    n_y -- the size of the output layer

    """

    ### START CODE HERE ### (≈ 3 lines of code)

    n_x = X.shape[0] # size of input layer

    n_h = 4

    n_y = Y.shape[0] # size of output layer

    ### END CODE HERE ###

    return (n_x, n_h, n_y

4.2 初始化模型参数

def initialize_parameters(n_x, n_h, n_y):

    """

    Argument:

    n_x -- size of the input layer

    n_h -- size of the hidden layer

    n_y -- size of the output layer


    Returns:

    params -- python dictionary containing your parameters:

                    W1 -- weight matrix of shape (n_h, n_x)

                    b1 -- bias vector of shape (n_h, 1)

                    W2 -- weight matrix of shape (n_y, n_h)

                    b2 -- bias vector of shape (n_y, 1)

    """


    np.random.seed(2) # we set up a seed so that your output matches ours although the initialization is random.


    ### START CODE HERE ### (≈ 4 lines of code)

    W1 = np.random.randn(n_h,n_x)*0.01

    b1 = np.zeros((n_h,1))

    W2 = np.random.randn(n_y,n_h)*0.01

    b2 = np.zeros((n_y,1))

    ### END CODE HERE ###


    assert (W1.shape == (n_h, n_x))

    assert (b1.shape == (n_h, 1))

    assert (W2.shape == (n_y, n_h))

    assert (b2.shape == (n_y, 1))


    parameters = {"W1": W1,

                  "b1": b1,

                  "W2": W2,

                  "b2": b2}


    return parameters

4.3 循环

def forward_propagation(X, parameters):

    """

    Argument:

    X -- input data of size (n_x, m)

    parameters -- python dictionary containing your parameters (output of initialization function)


    Returns:

    A2 -- The sigmoid output of the second activation

    cache -- a dictionary containing "Z1", "A1", "Z2" and "A2"

    """

    # Retrieve each parameter from the dictionary "parameters"

    ### START CODE HERE ### (≈ 4 lines of code)

    W1 = parameters["W1"]

    b1 = parameters["b1"]

    W2 = parameters["W2"]

    b2 = parameters["b2"]

    ### END CODE HERE ###


    # Implement Forward Propagation to calculate A2 (probabilities)

    ### START CODE HERE ### (≈ 4 lines of code)

    Z1 = np.dot(W1 , X) + b1


    A1 = np.tanh(Z1)

    Z2 = np.dot(W2 , A1) + b2


    A2 =sigmoid(Z2)

    ### END CODE HERE ###


    assert(A2.shape == (1, X.shape[1]))


    cache = {"Z1": Z1,

            "A1": A1,

            "Z2": Z2,

            "A2": A2}


    return A2, cache


def compute_cost(A2, Y, parameters):

    """

    Computes the cross-entropy cost given in equation (13)


    Arguments:

    A2 -- The sigmoid output of the second activation, of shape (1, number of examples)

    Y -- "true" labels vector of shape (1, number of examples)

    parameters -- python dictionary containing your parameters W1, b1, W2 and b2


    Returns:

    cost -- cross-entropy cost given equation (13)

    """


    m = Y.shape[1] # number of example

    # Compute the cross-entropy cost

    ### START CODE HERE ### (≈ 2 lines of code)

    logprobs =  np.multiply(np.log(A2),Y)+np.multiply(np.log(1-A2),(1-Y))

    cost = - np.sum(logprobs) / m

    ### END CODE HERE ###


    cost = np.squeeze(cost)    # makes sure cost is the dimension we expect.

                                # E.g., turns [[17]] into 17

    assert(isinstance(cost, float))


    return cost


def backward_propagation(parameters, cache, X, Y):

    """

    Implement the backward propagation using the instructions above.


    Arguments:

    parameters -- python dictionary containing our parameters

    cache -- a dictionary containing "Z1", "A1", "Z2" and "A2".

    X -- input data of shape (2, number of examples)

    Y -- "true" labels vector of shape (1, number of examples)


    Returns:

    grads -- python dictionary containing your gradients with respect to different parameters

    """

    m = X.shape[1]


    # First, retrieve W1 and W2 from the dictionary "parameters".

    ### START CODE HERE ### (≈ 2 lines of code)

    W1 = parameters["W1"]

    W2 = parameters["W2"]

    ### END CODE HERE ###


    # Retrieve also A1 and A2 from dictionary "cache".

    ### START CODE HERE ### (≈ 2 lines of code)

    A1 = cache["A1"]

    A2 = cache["A2"]

    ### END CODE HERE ###


    # Backward propagation: calculate dW1, db1, dW2, db2.

    ### START CODE HERE ### (≈ 6 lines of code, corresponding to 6 equations on slide above)

    dZ2 = A2 - Y

    dW2 = (1 / m) * np.dot(dZ2, A1.T)

    db2 = (1 / m) * np.sum(dZ2, axis=1, keepdims=True)

    dZ1 = np.multiply(np.dot(W2.T, dZ2), 1 - np.power(A1, 2))

    dW1 = (1 / m) * np.dot(dZ1, X.T)

    db1 = (1 / m) * np.sum(dZ1, axis=1, keepdims=True)

    ### END CODE HERE ###


    grads = {"dW1": dW1,

            "db1": db1,

            "dW2": dW2,

            "db2": db2}


    return grads


def update_parameters(parameters, grads, learning_rate = 1.2):

    """

    Updates parameters using the gradient descent update rule given above


    Arguments:

    parameters -- python dictionary containing your parameters

    grads -- python dictionary containing your gradients


    Returns:

    parameters -- python dictionary containing your updated parameters

    """

    # Retrieve each parameter from the dictionary "parameters"

    ### START CODE HERE ### (≈ 4 lines of code)

    W1 = parameters["W1"]

    b1 = parameters["b1"]

    W2 = parameters["W2"]

    b2 = parameters["b2"]

    ### END CODE HERE ###


    # Retrieve each gradient from the dictionary "grads"

    ### START CODE HERE ### (≈ 4 lines of code)

    dW1 = grads["dW1"]

    db1 = grads["db1"]

    dW2 = grads["dW2"]

    db2 = grads["db2"]

    ## END CODE HERE ###


    # Update rule for each parameter

    ### START CODE HERE ### (≈ 4 lines of code)

    W1 = W1 - learning_rate * dW1

    b1 = b1 - learning_rate * db1

    W2 = W2 - learning_rate * dW2

    b2 = b2 - learning_rate * db2

    ### END CODE HERE ###


    parameters = {"W1": W1,

                  "b1": b1,

                  "W2": W2,

                  "b2": b2}


    return parameters


4.4整合

def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):

    """

    Arguments:

    X -- dataset of shape (2, number of examples)

    Y -- labels of shape (1, number of examples)

    n_h -- size of the hidden layer

    num_iterations -- Number of iterations in gradient descent loop

    print_cost -- if True, print the cost every 1000 iterations


    Returns:

    parameters -- parameters learnt by the model. They can then be used to predict.

    """


    np.random.seed(3)

    n_x = layer_sizes(X, Y)[0]

    n_y = layer_sizes(X, Y)[2]


    # Initialize parameters, then retrieve W1, b1, W2, b2. Inputs: "n_x, n_h, n_y". Outputs = "W1, b1, W2, b2, parameters".

    ### START CODE HERE ### (≈ 5 lines of code)

    parameters = initialize_parameters(n_x,n_h,n_y)

    W1 = parameters["W1"]

    b1 = parameters["b1"]

    W2 = parameters["W2"]

    b2 = parameters["b2"]

    ### END CODE HERE ###


    # Loop (gradient descent)

    for i in range(0, num_iterations):


        ### START CODE HERE ### (≈ 4 lines of code)

        # Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache".

        A2, cache = forward_propagation(X,parameters)


        # Cost function. Inputs: "A2, Y, parameters". Outputs: "cost".

        cost = compute_cost(A2,Y,parameters)

        # Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads".

        grads = backward_propagation(parameters,cache,X,Y)

        # Gradient descent parameter update. Inputs: "parameters, grads". Outputs: "parameters".

        parameters = update_parameters(parameters,grads,learning_rate = 1.2)


        ### END CODE HERE ###


        # Print the cost every 1000 iterations

        if print_cost and i % 1000 == 0:

            print ("Cost after iteration %i: %f" %(i, cost))

    return parameters

4.5预测

# GRADED FUNCTION: predict

def predict(parameters, X):

    """

    Using the learned parameters, predicts a class for each example in X


    Arguments:

    parameters -- python dictionary containing your parameters

    X -- input data of size (n_x, m)


    Returns

    predictions -- vector of predictions of our model (red: 0 / blue: 1)

    """


    # Computes probabilities using forward propagation, and classifies to 0/1 using 0.5 as the threshold.

    ### START CODE HERE ### (≈ 2 lines of code)

    A2, cache = forward_propagation(X,parameters)

    predictions =np.round(A2)

    ### END CODE HERE ###


    return predictions

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