吴恩达第一课logistic Regress编程练习（学习笔记）

目标：利用logisitic Regression来预测图片是否有猫咪，即简单的二分类问题。

过程：初始化（向量输入，归一化），前向和反向传播，梯度下降，优化，预测，输出与可视化

初始化:1.明确输入集数量；测试集数量dim；

    2.输入向量化n*n*nc；

A trick when you want to flatten a matrix X of shape (a,b,c,d) to a matrix X_flatten of shape (b ∗∗ c ∗∗ d, a) is to use:
X_flatten = X.reshape(X.shape[0], -1).T # X.T is the transpose of X
    3.确定batch-size，输入归一化，压缩到【0,1】之间，便于计算。

    4.初始化权值、偏差

w = np.zeros((dim, 1))
b = 0

前向与反向传播：

       1.激活函数sigmoid

       2.z = w.T * X + b

       3.激活函数sigmoid

       4.损失函数cost = -y*log(pred_y) -(1-y)*log(1-pred_y)

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

反向传播梯度下降：根据链式法则有：损失函数对w的偏导为（a-y）*X,损失函数对b的偏导为（a-y）

dw = np.dot(X, (A - Y).T)/m
db = np.sum(A - Y)/m
优化（多次迭代）：

w = w - learning_rate*dw

预测：
将新的输入与模型参数运算得到结果Pred-y，若大于0.5则输出1，反之输出0

模型整合：

1.初始化参数；2.正反向传播；3.优化；4.预测；5.打印显示与绘图可视化

超参数调试：

尝试不同的学习速率、batch-size和迭代次数，观察训练和测试准确率问题。

What you need to remember:

Common steps for pre-processing a new dataset are:

Figure out the dimensions and shapes of the problem (m_train, m_test, num_px, ...)
Reshape the datasets such that each example is now a vector of size (num_px * num_px * 3, 1)
"Standardize" the data

What to remember: You've implemented several functions that:

Initialize (w,b)Optimize the loss iteratively to learn parameters (w,b):
computing the cost and its gradient
updating the parameters using gradient descent
Use the learned (w,b) to predict the labels for a given set of examples

What to remember from this assignment:

Preprocessing the dataset is important.You implemented each function separately: initialize(), propagate(), optimize(). Then you built a model().Tuning the learning rate (which is an example of a "hyperparameter") can make a big difference to the algorithm. You will see more examples of this later in this course!