[Machinie Learning] 吴恩达机器学习课程笔记——Week5

Machine Learning by Andrew Ng

💡 吴恩达机器学习课程学习笔记——Week 5
🐠 本人学习笔记汇总 合订本
✓ 课程网址 standford machine learning
🍭 参考资源

• 课程笔记
• python版作业

学习提纲

• Cost Function and Back-propagation
• Back-propagation in Practice
• Application of Neural Networks
• Review

Cost Function and Back-propagation

Notation

• L = total number of layers in the network
• $S_l$ = number of units (not counting bias unit) in layer l
• K = number of output units/classes

we denote $h_{\Theta }(x{)}_k$ as being a hypothesis that results in the k-th output
输入x，$h_{\Theta }(x{)}_k$是输出的第k个特征

1.Cost Function
the cost function for regularized logistic regression
and the cost function for neural network are as below

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the cost function for regularized logistic regression was

for neural network, the cost function is

Here, we define ${\delta }_j^l$ as the error for $a_j^l$

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2.Back-propagation Algorithm

Same as other ml algorithms, our goal is to minimize the cost function

Therefor, we need to compute

• $J(\theta )$
• $\frac{\partial }{\partial {\theta }_{i,j}^{(l)}}J(\theta )$

The algorithm to compute $\frac{\partial }{\partial {\theta }_{i,j}^{(l)}}J(\theta )$ is as below

The whole algorithm is as below

step1 and step2, forward propagation

step3, compute ${\delta }^{(L)}$

step4, compute ${\delta }^{(L-1)}$ and so on,



step5, compute the $\frac{\partial }{\partial {\theta }_{i,j}^{(l)}}J(\theta )$

3.Back-propagation Intuition

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Back-propagation in Practice

1.Implementation Note: Unrolling Parameters
use gradient checking to assure everything goes well

2.Gradient Checking

3.Random Initialization

4.Putting It Together

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6 steps to train a network

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Ideally, we want $h_\theta(x^i) \approx y^i$ But remember that $J(\Theta)$ is not a convex function and thus we can end up in a local minima instead.

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Application of Neural Networks

1.Autonomous Driving
skip.

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Review

skip.

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额外阅读

吴恩达机器学习——反向传播算法