【Stanford ML Exercise4 Week5】Neural Networks Learning

Implement the backpropagation algorithm for neural networks and apply it to the task of hand-written digit recognition.

1. Neural Networks

  • implement the backpropagation algorithm to learn the parameters for the neural network.

1.1 Visualizing the data

Screen Shot 2017-06-26 at 10.24.42 PM.png

  • 5000 training examples

    each training example is a 20 pixel by 20 pixel grayscale image of the digit

    The 20 by 20 grid of pixels is “unrolled” into a 400-dimensional vector


1.2 Model representation

  • 3 layers – an input layer, a hidden layer and an output layer

Screen Shot 2017-06-26 at 10.29.10 PM.png

1.3 Feedforward and cost function

  • implement the cost function and gradient for the neural network
  • should not be regularizing the terms that correspond to the bias

Cost function with regularization:

Screen Shot 2017-07-06 at 10.44.14 PM

2. Backpropagation

  • compute the gradient for the neural network cost function


2.1 Sigmoid gradient

Gradient for the sigmoid function:


2.2 Random initialization

  • When training neural networks, it is important to randomly initialize the parameters for symmetry breaking.
epsilon init = 0.12;
W = rand(L out, 1 + L in) * 2 * epsilon init − epsilon init;

2.3 Backpropagation

Intuition behind the backpropagation algorithm:

  • Given a training example (x(t),y(t)), first run a “forward pass” to compute all the activations throughout the network
  • for each node j in layer l, compute an “error term” δ(l) that measures how much that node was “responsible” j for any errors in our output


Step 1-4 to implement backpropagation:



Author: Lisa.zxiaoc

Data scientist and learner.

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