文章目录
- 神经网络的初始化
- 初始化数据
- 模型搭建
- 简单函数
- 零初始化——initialize_parameters_zeros
- 随机初始化——initialize_parameters_random
- He初始化
- 三种初始化结果对比
- 在神经网络中使用正则化
- 导入数据
- 模型搭建
- 非正则化模型
- L2正则化
- dropout
- 三种模型的对比
- 怎么说呢
神经网络的初始化
主要是看权重的不同初始化方法的影响
导包
import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
%matplotlib inline
plt.rcParams['figure.figsize'] = (7.0, 4.0)
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'这里使用的是sklearn中的函数来当作数据集使用，该函数介绍如下
sklearn.datasets.make_circles（n_samples = 100，shuffle = True，noise = None，random_state = None，factor = 0.8 )
#n_samples：整数 可选 默认为100.生成的总点数。（如果是奇数，内圆比外圆多一点，但是测试输入5后，内圆和外圆均是两个点）
#shuffle：布尔变量 可选 默认为True,是否打乱样本
#noise：double 或None 默认为None。将高斯噪声的标准差加入到数据中
#random_state：整数 RandomState instance or None。确定数据集变换和噪声的随机数生成。
#factor：0 < double < 1 默认值0.8。内外圆之间的比例因子、
#返回值：X：[n_samples, 2]形状的数组，生成的样本 y：[n_samples]形状的数组，每个样本的标签（0或1）初始化数据
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)
# 可视化
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_Ytrain_X, train_Y, test_X, test_Y = load_dataset()
模型搭建
模型主要框架如下代码所示：
要实现三种初始化方法，并逐步完善该模型
零初始化 ：在输入参数中设置initialization = “zeros”。
随机初始化 ：在输入参数中设置initialization = “random”，这会将权重初始化为较大的随机值。
He初始化 ：在输入参数中设置initialization = “he”，这会根据He等人（2015）的论文将权重初始化为按比例缩放的随机值。
def model(X, Y, learning_rate = 0.01, num_iterations = 15000, print_cost = True, initialization = "he"):
grads = {}
costs = []
m = X.shape[1] # train 300,test 100
layers_dims = [X.shape[0], 10, 5, 1]#两个隐藏层 10 、5 ，输出层为1
# 初始化参数w、b
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)
for i in range(0, num_iterations):
# 前向传播: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.
a3, cache = forward_propagation(X, parameters)
# 计算该次循环的损失，通过A和Y
cost = compute_loss(a3, Y)
# 反向传播计算导数.
grads = backward_propagation(X, Y, cache)
# 通过grads更新w、b
parameters = update_parameters(parameters, grads, learning_rate)
if print_cost and i % 1000 == 0:
print("Cost after iteration {}: {}".format(i, cost))
costs.append(cost)
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations (per hundreds)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters简单函数
#sigmoid
def sigmoid(x):
s = 1/(1+np.exp(-x))
return s
#relu
def relu(x):
s = np.maximum(0,x)
return s
#前向传播
def forward_propagation(X, parameters):
# 取出数据
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
#反向传播计算导数
def backward_propagation(X, Y, cache):
m = X.shape[1]# train 300，test 100
(z1, a1, W1, b1, z2, a2, W2, b2, z3, a3, W3, b3) = cache
# dz3通过dj/da3和da3/dz3计算出来的，后者为sigmoid的导数
dz3 = 1./m * (a3 - Y)#这里乘1/m让后面梯度下降不需要再除m
dW3 = np.dot(dz3, a2.T)
db3 = np.sum(dz3, axis=1, keepdims = True)
#np.int64(a2 > 0 为relu的导数
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):
L = len(parameters) // 2 # 参数中有w、b，除以2代表层数
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
#经典损失函数
def compute_loss(a3, Y):
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
#通过训练得到的parameters进行预测
def predict(X, y, parameters):
m = X.shape[1]
p = np.zeros((1,m), dtype = np.int32)# 网上教程给的是np.int,不安全
a3, caches = forward_propagation(X, parameters)
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
#绘制决策边界
def plot_decision_boundary(model, X, y):
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
# np.arange为生成等差数列
#np.arange(0, 6, 2) ————array([0, 2, 4])
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
# 语法：X,Y = numpy.meshgrid(x, y)
#输入的x，y，就是网格点的横纵坐标列向量（非矩阵）
#输出的X，Y，就是坐标矩阵。
#简单介绍就是：将x、y的笛卡尔积坐标分别放到X、Y中
#np.r_：是按列连接两个矩阵，就是把两矩阵上下相加，要求列数相等
#np.c_：是按行连接两个矩阵，就是把两矩阵左右相加，要求行数相等
Z = model(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
#matplotlib一直不懂，www
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
plt.ylabel('x2')
plt.xlabel('x1')
plt.scatter(X[0, :], X[1, :], c=np.squeeze(y), cmap=plt.cm.Spectral)
plt.show()
def predict_dec(parameters, X):
a3, cache = forward_propagation(X, parameters)
predictions = (a3>0.5)
return predictions零初始化——initialize_parameters_zeros
将所有参数初始化为零
由于参数都为0的话，训练的时候所有的权重都相同，导致所有的神经元中所蕴藏的函数都相同
def initialize_parameters_zeros(layers_dims):
parameters = {}
L = len(layers_dims)
for l in range(1, L):
parameters['W' + str(l)] = np.zeros((layers_dims[l],layers_dims[l-1]))
parameters['b' + str(l)] = np.zeros((layers_dims[l],1))
return parametersparameters = 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)
plt.title("Model with Zeros initialization")
axes = plt.gca()
axes.set_xlim([-1.5,1.5])
axes.set_ylim([-1.5,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)
如果我们输出一下预测结果的话，会发现它预测都为0，将所有权重初始化为零会导致网络无法打破对称性。 这意味着每一层中的每个神经元都将学习相同的东西，就好像nl=1
随机初始化——initialize_parameters_random
将权重初始化为较大的随机值（按*10缩放），并将偏差设为0。
将 np.random.randn(…,…) * 10用于权重，将np.zeros((…, …))用于偏差。
使用固定的np.random.seed(…)，以确保你的“随机”权重与我们的权重匹配。运行几次代码后参数初始值始终相同
def initialize_parameters_random(layers_dims):
np.random.seed(3) # This seed makes sure your "random" numbers will be the as ours
parameters = {}
L = len(layers_dims) # integer representing the number of layers
for l in range(1, L):
parameters['W' + str(l)] = np.random.randn(layers_dims[l],layers_dims[l-1])*10
parameters['b' + str(l)] = np.zeros((layers_dims[l],1))
return parametersparameters = 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)
plt.title("random initialization")
axes = plt.gca()
axes.set_xlim([-1.5,1.5])
axes.set_ylim([-1.5,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)
训练较长时间的网络，将会看到更好的结果，但是使用太大的随机数进行初始化会降低优化速度
初始化为较小的随机值会更好,也就是使用He初始化，或者是Xavier初始化
He初始化
在上一节作业中使用过Xavier初始化，He初始化与之类似
Xavier初始化使用比例因子sqrt(1./layers_dims[l-1])来表示权重 ，而He初始化使用sqrt(2./layers_dims[l-1])）
def initialize_parameters_he(layers_dims):
np.random.seed(3)
parameters = {}
L = len(layers_dims) - 1
for l in range(1, L + 1):
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))
return parametersparameters = 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)
plt.title("Model with He initialization")
axes = plt.gca()
axes.set_xlim([-1.5,1.5])
axes.set_ylim([-1.5,1.5])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)
三种初始化结果对比
在神经网络中使用正则化
导入数据
import numpy as np
import matplotlib.pyplot as plt
import sklearn
import scipy.io
import sklearn.datasets
%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'def load_2D_dataset():
data = scipy.io.loadmat('./data.mat')
#mat格式也是类似于字典，我们可以遍历.keys()来看里面的标签
#X、y、yval、Xval
train_X = data['X'].T
train_Y = data['y'].T
test_X = data['Xval'].T
test_Y = data['yval'].T
plt.scatter(train_X[0, :], train_X[1, :], c=np.squeeze(train_Y), s=40, cmap=plt.cm.Spectral)
return train_X, train_Y, test_X, test_Ytrain_X, train_Y, test_X, test_Y = load_2D_dataset()
模型搭建
def model(X, Y, learning_rate = 0.3, num_iterations = 30000, print_cost = True, lambd = 0, keep_prob = 1):
grads = {}
costs = []
m = X.shape[1]
layers_dims = [X.shape[0], 20, 3, 1]
parameters = initialize_parameters(layers_dims)
for i in range(0, num_iterations):
# LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SIGMOID.
if keep_prob == 1:
a3, cache = forward_propagation(X, parameters)
elif keep_prob < 1:
a3, cache = forward_propagation_with_dropout(X, parameters, keep_prob)
# 代价函数
if lambd == 0:
cost = compute_cost(a3, Y)
else:
cost = compute_cost_with_regularization(a3, Y, parameters, lambd)
# 反向传播
assert(lambd==0 or keep_prob==1)
if lambd == 0 and keep_prob == 1:
grads = backward_propagation(X, Y, cache)
elif lambd != 0:
grads = backward_propagation_with_regularization(X, Y, cache, lambd)
elif keep_prob < 1:
grads = backward_propagation_with_dropout(X, Y, cache, keep_prob)
# 梯度下降
parameters = update_parameters(parameters, grads, learning_rate)
# Print the loss every 10000 iterations
if print_cost and i % 10000 == 0:
print("Cost after iteration {}: {}".format(i, cost))
if print_cost and i % 1000 == 0:
costs.append(cost)
# 绘制代价曲线
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations (x1,000)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters非正则化模型
传统模型，没有添加lambd、dropout
def relu(x):
return np.maximum(0,x)
def sigmoid(x):
return 1/(1+np.exp(-x))
def initialize_parameters(layers_dims):
parameters={}
np.random.seed(3)
for i in range(1,len(layers_dims)):
parameters['W'+str(i)]=np.random.randn(layers_dims[i],layers_dims[i-1])/ np.sqrt(layers_dims[i-1])
parameters['b'+str(i)]=np.zeros((layers_dims[i],1))
return parameters
def forward_propagation(X, parameters):
#可以使用之前的L层模型操作，但是放到这里的话，有点麻烦
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 compute_cost(A3,Y):
m=Y.shape[1]
# 对应np.dot、np.mutiply、*可以看
return 1/m*np.nansum(np.multiply(-np.log(A3),Y) + np.multiply(-np.log(1 - A3), 1 - Y))
def backward_propagation(X,Y,cache):
m = X.shape[1]
(Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3) = cache
dZ3= 1./m * (A3-Y)#np.multiply(A3,sigmoid的关于Z的导数)
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):
for i in range(len(parameters)//2):
parameters['W'+str(i+1)]=parameters['W'+str(i+1)]-learning_rate*grads['dW'+str(i+1)]
parameters["b" + str(i+1)] = parameters["b" + str(i+1)] - learning_rate * grads["db" + str(i+1)]
return parameters
def predict(X,y,parameters):
m = X.shape[1]
p = np.zeros((1,m), dtype = np.int64)
a3,cache=forward_propagation(X,parameters)
for i in range(0, a3.shape[1]):
if a3[0,i] > 0.5:
p[0,i] = 1
else:
p[0,i] = 0
print("Accuracy: " + str(np.mean((p[0,:] == y[0,:]))))
return p
def plot_decision_boundary(model, X, y):
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
# np.arange为生成等差数列
#np.arange(0, 6, 2) ————array([0, 2, 4])
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
# 语法：X,Y = numpy.meshgrid(x, y)
#输入的x，y，就是网格点的横纵坐标列向量（非矩阵）
#输出的X，Y，就是坐标矩阵。
#简单介绍就是：将x、y的笛卡尔积坐标分别放到X、Y中
#np.r_：是按列连接两个矩阵，就是把两矩阵上下相加，要求列数相等
#np.c_：是按行连接两个矩阵，就是把两矩阵左右相加，要求行数相等
Z = model(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
#matplotlib一直不懂，www
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
plt.ylabel('x2')
plt.xlabel('x1')
plt.scatter(X[0, :], X[1, :], c=np.squeeze(y), cmap=plt.cm.Spectral)
plt.show()
def predict_dec(parameters, X):
#看不懂了这里，先跳过
a3, cache = forward_propagation(X, parameters)
predictions = (a3>0.5)
return predictionsparameters = model(train_X, train_Y)
print ("On the training set:")
predictions_train = predict(train_X, train_Y, parameters)
print ("On the test set:")
predictions_test = predict(test_X, test_Y, parameters)
plt.title("Model without regularization")
axes = plt.gca()
axes.set_xlim([-0.75,0.40])
axes.set_ylim([-0.75,0.65])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)
#
# 关于lambda表达式可以看上面连接
L2正则化
更改损失函数之后，必须更改反向传播，针对新损失函数计算所有梯度
添加的正则项只包含W权重矩阵，所以只需要对dW1,dW2,dW3添加正则化项的梯度即可
def compute_cost_with_regularization(A3, Y, parameters, lambd):
m = Y.shape[1]
W1 = parameters["W1"]
W2 = parameters["W2"]
W3 = parameters["W3"]
cross_entropy_cost = compute_cost(A3, Y)
#np.sum(np.square(Wl)) 矩阵所有元素平方和
L2_regularization_cost = (1./m*lambd/2)*(np.sum(np.square(W1)) + np.sum(np.square(W2)) + np.sum(np.square(W3)))
cost = cross_entropy_cost + L2_regularization_cost
return costdef backward_propagation_with_regularization(X, Y, cache, lambd):
m = X.shape[1]
(Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3) = cache
dZ3 = A3 - Y
dW3 = 1./m * np.dot(dZ3, A2.T) + lambd/m * W3
db3 = 1./m * np.sum(dZ3, axis=1, keepdims = True)
dA2 = np.dot(W3.T, dZ3)
dZ2 = np.multiply(dA2, np.int64(A2 > 0))
dW2 = 1./m * np.dot(dZ2, A1.T) + lambd/m * W2
db2 = 1./m * np.sum(dZ2, axis=1, keepdims = True)
dA1 = np.dot(W2.T, dZ2)
dZ1 = np.multiply(dA1, np.int64(A1 > 0))
dW1 = 1./m * np.dot(dZ1, X.T) + lambd/m * W1
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使用lambd为0.7时候的模型调用
parameters = model(train_X, train_Y, lambd = 0.7)
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)
plt.title("Model with L2-regularization")
axes = plt.gca()
axes.set_xlim([-0.75,0.40])
axes.set_ylim([-0.75,0.65])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)
与传统网络相比，方差减小了，不再过拟合训练数据了
lambd变大，w必须减小才能缩小损失函数，w减小，Z减小，Z减小之后取值范围小，在relu中对应可能就为线性，也就是曲线更加平滑
dropout
它会在每次迭代中随机关闭一些神经元。
你将训练仅使用神经元子集的不同模型。通过Dropout，你的神经元对另一种特定神经元的激活变得不那么敏感，因为另一神经元可能随时关闭。
实现带有Dropout的正向传播，为第一和第二隐藏层添加Dropout。不会将Dropout应用于输入层或输出层
步骤：
1、创建与A矩阵维度相同的[0,1]之间取值的矩阵D
2、对矩阵D中进行阈值设置，将矩阵X的所有条目设置为0（如果概率小于0.5）或1（如果概率大于0.5），则可以执行：X = (X < 0.5)。注意0和1分别对应False和True
3、A=A*D，关闭一些神经元
4、A=A/dropout，这样可以保证损失结果仍有与未丢弃神经元时的期望。也就是在减少一些神经元影响的同时又加强另外神经元的影响（也称为反向dropout）
def forward_propagation_with_dropout(X, parameters, keep_prob = 0.5):
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)
D1 = np.random.rand(A1.shape[0],A1.shape[1])
D1 = D1 < keep_prob
A1 = A1 * D1
A1 = A1 / keep_prob
Z2 = np.dot(W2, A1) + b2
A2 = relu(Z2)
D2 = np.random.rand(A2.shape[0],A2.shape[1])
D2 = D2 < keep_prob
A2 = A2 * D2
A2 = A2 / keep_prob
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反向传播：
1、通过D1关闭的A1中的某些神经元，在反向传播中，我们必须通过D1再次关闭
2.在正向传播过程中，你已将A1除以keep_prob。 因此，在反向传播中，必须再次将dA1除以keep_prob（计算的解释是，如果被keep_prob缩放，则其派生的也由相同的keep_prob缩放）。
教程中给出反向传播也需要除以keep_prob，但是我感觉不需要，不知道为什么需要，A已经除以了，再除的话相当于除了两次，希望有大佬解惑
def backward_propagation_with_regularization(X, Y, cache, lambd):
m = X.shape[1]
(Z1, A1, W1, b1, Z2, A2, W2, b2, Z3, A3, W3, b3) = cache
dZ3 = A3 - Y
dW3 = 1./m * np.dot(dZ3, A2.T) + lambd/m * W3
db3 = 1./m * np.sum(dZ3, axis=1, keepdims = True)
dA2 = np.dot(W3.T, dZ3)
dZ2 = np.multiply(dA2, np.int64(A2 > 0))
dW2 = 1./m * np.dot(dZ2, A1.T) + lambd/m * W2
db2 = 1./m * np.sum(dZ2, axis=1, keepdims = True)
dA1 = np.dot(W2.T, dZ2)
dZ1 = np.multiply(dA1, np.int64(A1 > 0))
dW1 = 1./m * np.dot(dZ1, X.T) + lambd/m * W1
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 gradientsdef backward_propagation_with_dropout(X, Y, cache, keep_prob):
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)
dA2 = dA2 * D2
dA2 = dA2 / keep_prob
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)
dA1 = dA1 * D1
dA1 = dA1 / keep_prob
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 gradientsparameters = model(train_X, train_Y, keep_prob = 0.86, learning_rate = 0.3)
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)
plt.title("Model with dropout")
axes = plt.gca()
axes.set_xlim([-0.75,0.40])
axes.set_ylim([-0.75,0.65])
plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)
仅在训练期间使用dropout，在测试期间不要使用
正则化会损害训练集的性能,这是因为它限制了网络过拟合训练集的能力。 但它最终可以提供更好的测试准确性
三种模型的对比
怎么说呢
第三个作业检验梯度下降，没有做，感觉没时间了，要到下一个组会了，赶快学
matplotlib，只要碰到这个相关的代码，都看不懂，现在不知道要不要学一下，但是感觉专门去学一个库没有必要，纠结
赶快学完这些看pytorch了，自己实现模型细节好麻烦，赶快调库调库，调参侠重现人间
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