2.1 参数初始化（deep_ai）

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本节主要说的是，深度学习参数（ W, b）权重初始化方法不一样， 得到的模型效果不一样。
主要初始化方法：
1）全部初始化为0
2) 随机初始化
3）He initialization

好的初始化方法：
1）加速梯度收敛
2）增加梯度收益(odds)，降低训练集误差

总结
3-layer NN with zeros initialization ： 没有打破均匀性
3-layer NN with random initialization ： 权重太大
3-layer NN with He initialization： 推荐方法

可学习到东西：
不同参数初始化方法可导致不同的结果。
随机初始化打破参数同一性，确保每个隐藏层可学到不同的东西，但是，权重不能初始化太大。
He initilaztion 在激活函数层表现较好，推荐。

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import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
from init_utils import sigmoid, relu, compute_loss, forward_propagation, backward_propagation
from init_utils import update_parameters, predict, load_dataset, plot_decision_boundary, predict_dec

%matplotlib inline
plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'

# load image dataset: blue/red dots in circles
train_X, train_Y, test_X, test_Y = load_dataset()


def model(X, Y, learning_rate=0.01, num_iterations=15000, print_cost=True, initialization="he"):
    """
    Implements a three-layer neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SIGMOID.

    Arguments:
    X -- input data, of shape (2, number of examples)
    Y -- true "label" vector (containing 0 for red dots; 1 for blue dots), of shape (1, number of examples)
    learning_rate -- learning rate for gradient descent
    num_iterations -- number of iterations to run gradient descent
    print_cost -- if True, print the cost every 1000 iterations
    initialization -- flag to choose which initialization to use ("zeros","random" or "he")

    Returns:
    parameters -- parameters learnt by the model
    """

    grads = {
     }
    costs = []  # to keep track of the loss
    m = X.shape[1]  # number of examples
    layers_dims = [X.shape[0], 10, 5, 1]

    # Initialize parameters dictionary.
    if initialization == "zeros":
        parameters = initialize_parameters_zeros(layers_dims)
    elif initialization == "random":
        parameters = initialize_parameters_random(layers_dims)
    elif initialization == "he":
        parameters = initialize_parameters_he(layers_dims)

    # Loop (gradient descent)

    for i in range(0, num_iterations):

        # Forward propagation: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.
        a3, cache = forward_propagation(X, parameters)

        # Loss
        cost = compute_loss(a3, Y)

        # Backward propagation.
        grads = backward_propagation(X, Y, cache)

        # Update parameters.
        parameters = update_parameters(parameters, grads, learning_rate)

        # Print the loss every 1000 iterations
        if print_cost and i % 1000 == 0:
            print("Cost after iteration {}: {}".format(i, cost))
            costs.append(cost)

    # plot the loss
    plt.plot(costs)
    plt.ylabel('cost')
    plt.xlabel('iterations (per hundreds)')
    plt.title("Learning rate =" + str(learning_rate))
    plt.show()

    return parameters


# GRADED FUNCTION: initialize_parameters_zeros

def initialize_parameters_zeros(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.

    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """

    parameters = {
     }
    L = len(layers_dims)  # number of layers in the network

    for l in range(1, L):
        ### START CODE HERE ### (≈ 2 lines of code)
        parameters['W' + str(l)] = np.zeros((layers_dims[l], layers_dims[l - 1]))
        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))
        ### END CODE HERE ###
    return parameters

# GRADED FUNCTION: initialize_parameters_random
def initialize_parameters_random(layers_dims):
    """
    Args:
        layers_dims: python array(list) containing the size of each layer
    Returns:
    parameters -- python dictionary containing your parameters "W1","b1", "W2"...
                  WL ---weight matrix of shape(layers_dims[L], layers_dim[L-1])
                  bL ---bias vector of shape (layers_dims[L],1)

    """
    parameters = {
     }
    L = len(layers_dims)
    for l in range(1, L):
        parameters["W" + str(l)] = np.random.randn(layers_dims[l], layers_dims[l-1]) * 0.01
        parameters["b" + str(l)] = np.zeros((layers_dims[l], 1))
# GRADED FUNCTION: initialize_parameters_he #He 为一个作者名
"""
He initializtion : sqrt(2./layers_dims[l-1])
与随机初始化区别： 随机初始化是 随机数* 10
                而He初始化是随机数 * sqrt(2./layers_dims[l-1])， 激活层参数初始化依赖该层的单元数。
"""
def initialize_parameters_he(layers_dims):
    """
    Arguments:
    layer_dims -- python array (list) containing the size of each layer.

    Returns:
    parameters -- python dictionary containing your parameters "W1", "b1", ..., "WL", "bL":
                    W1 -- weight matrix of shape (layers_dims[1], layers_dims[0])
                    b1 -- bias vector of shape (layers_dims[1], 1)
                    ...
                    WL -- weight matrix of shape (layers_dims[L], layers_dims[L-1])
                    bL -- bias vector of shape (layers_dims[L], 1)
    """

    np.random.seed(3)
    parameters = {
     }
    L = len(layers_dims) - 1  # integer representing the number of layers

    for l in range(1, L + 1):
        ### START CODE HERE ### (≈ 2 lines of code)
        parameters['W' + str(l)] = np.random.randn(layers_dims[l], layers_dims[l - 1]) * np.sqrt(2 / layers_dims[l - 1])
        parameters['b' + str(l)] = np.zeros((layers_dims[l], 1))
        ### END CODE HERE ###

    return parameters
if __name__ == '__main__':
    #参数初始化为0， 效果差，类似随机猜测， 准确率0.5
    parameters = model(train_X, train_Y, initialization="zeros")
    print("On the train set:")
    predictions_train = predict(train_X, train_Y, parameters)
    print("On the test set:")
    predictions_test = predict(test_X, test_Y, parameters)
    """
    原因分析: 
    1)参数没有打破匀称。
    2）每层的神经元都在做相同的训练。 
    3）相当于训练一个n层的1维度神经网络，甚至都没有线性分类器好。
    因此需要注意： 需要随机初始化参数W. 参数b可以初始化为0
    """
    #参数随机化后，效果有明显提升，准确率0.9
    parameters = model(train_X, train_Y, initialization = "random")
    print ("On the train set:")
    predictions_train = predict(train_X, train_Y, parameters)
    print ("On the test set:")
    predictions_test = predict(test_X, test_Y, parameters)
    #参数通过He随机化，在小数据量上迭代效果更好些。 一般推荐这样
    parameters = model(train_X, train_Y, initialization="he")
    print("On the train set:")
    predictions_train = predict(train_X, train_Y, parameters)
    print("On the test set:")
    predictions_test = predict(test_X, test_Y, parameters)