cs230 深度学习 Lecture 2 编程作业： Logistic Regression with a Neural Network mindset

1. 将 Logistic 表达为 神经网络 的形式

（关于 Logistic 可以看这两篇文章： Logistic Regression 为什么用极大似然函数 Logistic regression 为什么用 sigmoid ？

2. 构建模型

• 通过前向传播 (forward propagation) 计算当前的损失，
• 通过反向传播 (backward propagation) 计算当前的梯度，

1. 导入包
2. 获得数据
3. 并进行预处理： 格式转换，归一化
4. 整合模型：
• A. 构建模型
• a. 初始化参数：w 和 b 为 0
• b. 前向传播：计算当前的损失
• c. 反向更新：计算当前的梯度
• B. 梯度更新求模型参数
• C. 进行预测
5. 绘制学习曲线

1. 导入包

import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage

%matplotlib inline

#lr_utils.py

import numpy as np
import h5py

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_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))
test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))

return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes 

2. 获得数据

# Loading the data (cat/non-cat)
train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()

# Example of a picture
index = 25
plt.imshow(train_set_x_orig[index])
print ("y = " + str(train_set_y[:,index]) + ", it's a '" + classes[np.squeeze(train_set_y[:,index])].decode("utf-8") +  "' picture.")

3. 进行预处理： 格式转换，归一化

• m_train (训练样本数量)
• m_test (测试样本数量)
• num_px (训练数据集的长和宽)
### START CODE HERE ### (≈ 3 lines of code)### STA
m_train = train_set_y.shape[1]
m_test = test_set_y.shape[1]
num_px = train_set_x_orig.shape[1]
### END CODE HERE ###

print ("Number of training examples: m_train = " + str(m_train))
print ("Number of testing examples: m_test = " + str(m_test))
print ("Height/Width of each image: num_px = " + str(num_px))
print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)")
print ("train_set_x shape: " + str(train_set_x_orig.shape))
print ("train_set_y shape: " + str(train_set_y.shape))
print ("test_set_x shape: " + str(test_set_x_orig.shape))
print ("test_set_y shape: " + str(test_set_y.shape))

# Reshape the training and test examples

### START CODE HERE ### (≈ 2 lines of code)
train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T
### END CODE HERE ###

print ("train_set_x_flatten shape: " + str(train_set_x_flatten.shape))
print ("train_set_y shape: " + str(train_set_y.shape))
print ("test_set_x_flatten shape: " + str(test_set_x_flatten.shape))
print ("test_set_y shape: " + str(test_set_y.shape))
print ("sanity check after reshaping: " + str(train_set_x_flatten[0:5,0]))

train_set_x = train_set_x_flatten / 255.
test_set_x = test_set_x_flatten / 255.

4. 整合模型

- A. 构建模型
- a. 初始化参数：w 和 b 为 0
- b. 前向传播：计算当前的损失
- c. 反向更新：计算当前的梯度
- B. 梯度更新求模型参数
- C. 进行预测

# GRADED FUNCTION: sigmoid

def sigmoid(z):
"""
Compute the sigmoid of z

Arguments:
x -- A scalar or numpy array of any size.

Return:
s -- sigmoid(z)
"""

### START CODE HERE ### (≈ 1 line of code)
s = 1 / (1 + np.exp(-z))
### END CODE HERE ###

return s

a. 初始化参数：w 和 b 为 0

# GRADED FUNCTION: initialize_with_zeros

def initialize_with_zeros(dim):
"""
This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.

Argument:
dim -- size of the w vector we want (or number of parameters in this case)

Returns:
w -- initialized vector of shape (dim, 1)
b -- initialized scalar (corresponds to the bias)
"""

### START CODE HERE ### (≈ 1 line of code)
w = np.zeros(shape=(dim, 1))
b = 0
### END CODE HERE ###

assert(w.shape == (dim, 1))
assert(isinstance(b, float) or isinstance(b, int))

return w, b

b. 前向传播：计算当前的损失 c. 反向更新：计算当前的梯度

# GRADED FUNCTION: propagate

def propagate(w, b, X, Y):
"""
Implement the cost function and its gradient for the propagation explained above

Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of size (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)

Return:
cost -- negative log-likelihood cost for logistic regression
dw -- gradient of the loss with respect to w, thus same shape as w
db -- gradient of the loss with respect to b, thus same shape as b

Tips:
- Write your code step by step for the propagation
"""

m = X.shape[1]

# FORWARD PROPAGATION (FROM X TO COST)
### START CODE HERE ### (≈ 2 lines of code)
A = sigmoid(np.dot(w.T, X) + b)  # compute activation
cost = (- 1 / m) * np.sum(Y * np.log(A) + (1 - Y) * (np.log(1 - A)))  # compute cost
### END CODE HERE ###

# BACKWARD PROPAGATION (TO FIND GRAD)
### START CODE HERE ### (≈ 2 lines of code)
dw = (1 / m) * np.dot(X, (A - Y).T)
db = (1 / m) * np.sum(A - Y)
### END CODE HERE ###

assert(dw.shape == w.shape)
assert(db.dtype == float)
cost = np.squeeze(cost)
assert(cost.shape == ())

"db": db}

return grads, cost

B. 梯度更新求模型参数

# GRADED FUNCTION: optimize

def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):
"""
This function optimizes w and b by running a gradient descent algorithm

Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of shape (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
num_iterations -- number of iterations of the optimization loop
learning_rate -- learning rate of the gradient descent update rule
print_cost -- True to print the loss every 100 steps

Returns:
params -- dictionary containing the weights w and bias b
grads -- dictionary containing the gradients of the weights and bias with respect to the cost function
costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.

Tips:
You basically need to write down two steps and iterate through them:
1) Calculate the cost and the gradient for the current parameters. Use propagate().
2) Update the parameters using gradient descent rule for w and b.
"""

costs = []

for i in range(num_iterations):

# Cost and gradient calculation (≈ 1-4 lines of code)
### START CODE HERE ###
grads, cost = propagate(w, b, X, Y)
### END CODE HERE ###

# update rule (≈ 2 lines of code)
### START CODE HERE ###
w = w - learning_rate * dw  # need to broadcast
b = b - learning_rate * db
### END CODE HERE ###

# Record the costs
if i % 100 == 0:
costs.append(cost)

# Print the cost every 100 training examples
if print_cost and i % 100 == 0:
print ("Cost after iteration %i: %f" % (i, cost))

params = {"w": w,
"b": b}

"db": db}

return params, grads, costs

C. 进行预测

# GRADED FUNCTION: predict

def predict(w, b, X):
'''
Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)

Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of size (num_px * num_px * 3, number of examples)

Returns:
Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X
'''

m = X.shape[1]
Y_prediction = np.zeros((1, m))
w = w.reshape(X.shape[0], 1)

# Compute vector "A" predicting the probabilities of a cat being present in the picture
### START CODE HERE ### (≈ 1 line of code)
A = sigmoid(np.dot(w.T, X) + b)
### END CODE HERE ###

for i in range(A.shape[1]):
# Convert probabilities a[0,i] to actual predictions p[0,i]
### START CODE HERE ### (≈ 4 lines of code)
Y_prediction[0, i] = 1 if A[0, i] > 0.5 else 0
### END CODE HERE ###

assert(Y_prediction.shape == (1, m))

return Y_prediction

# GRADED FUNCTION: model

def model(X_train, Y_train, X_test, Y_test, num_iterations=2000, learning_rate=0.5, print_cost=False):
"""
Builds the logistic regression model by calling the function you've implemented previously

Arguments:
X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)
Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)
X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)
Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)
num_iterations -- hyperparameter representing the number of iterations to optimize the parameters
learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()
print_cost -- Set to true to print the cost every 100 iterations

Returns:
d -- dictionary containing information about the model.
"""

### START CODE HERE ###
# initialize parameters with zeros (≈ 1 line of code)
w, b = initialize_with_zeros(X_train.shape[0])

# Gradient descent (≈ 1 line of code)
parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)

# Retrieve parameters w and b from dictionary "parameters"
w = parameters["w"]
b = parameters["b"]

# Predict test/train set examples (≈ 2 lines of code)
Y_prediction_test = predict(w, b, X_test)
Y_prediction_train = predict(w, b, X_train)

### END CODE HERE ###

# Print train/test Errors
print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))
print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))

d = {"costs": costs,
"Y_prediction_test": Y_prediction_test,
"Y_prediction_train" : Y_prediction_train,
"w" : w,
"b" : b,
"learning_rate" : learning_rate,
"num_iterations": num_iterations}

return d

d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)

Cost after iteration 0: 0.693147
Cost after iteration 100: 0.584508
Cost after iteration 200: 0.466949
Cost after iteration 300: 0.376007
Cost after iteration 400: 0.331463
Cost after iteration 500: 0.303273
Cost after iteration 600: 0.279880
Cost after iteration 700: 0.260042
Cost after iteration 800: 0.242941
Cost after iteration 900: 0.228004
Cost after iteration 1000: 0.214820
Cost after iteration 1100: 0.203078
Cost after iteration 1200: 0.192544
Cost after iteration 1300: 0.183033
Cost after iteration 1400: 0.174399
Cost after iteration 1500: 0.166521
Cost after iteration 1600: 0.159305
Cost after iteration 1700: 0.152667
Cost after iteration 1800: 0.146542
Cost after iteration 1900: 0.140872
train accuracy: 99.04306220095694 %
test accuracy: 70.0 %

# Example of a picture that was wrongly classified.# Exampl
index = 5
plt.imshow(test_set_x[:,index].reshape((num_px, num_px, 3)))
print ("y = " + str(test_set_y[0, index]) + ", you predicted that it is a \"" + classes[d["Y_prediction_test"][0, index]].decode("utf-8") +  "\" picture.")

5. 绘制学习曲线

# Plot learning curve (with costs)# Plot l
costs = np.squeeze(d['costs'])
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations (per hundreds)')
plt.title("Learning rate =" + str(d["learning_rate"]))
plt.show()

learning_rates = [0.01, 0.001, 0.0001]
models = {}
for i in learning_rates:
print ("learning rate is: " + str(i))
models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 1500, learning_rate = i, print_cost = False)
print ('\n' + "-------------------------------------------------------" + '\n')

for i in learning_rates:
plt.plot(np.squeeze(models[str(i)]["costs"]), label= str(models[str(i)]["learning_rate"]))

plt.ylabel('cost')
plt.xlabel('iterations')

frame = legend.get_frame()
frame.set_facecolor('0.90')
plt.show()

0 条评论

相关文章

Ensemble Learners

Udacity Ensemble Learners ---- Boosting Algorithm 不需要绞尽脑汁去想很复杂的 Rules，只需要一些简单的 ...

3557

1692

31810

3696

1913

5012

4986

1366

3815

2394