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203.5.6 Neural Network Intuition

Before going further into neural network algorithm, we need to understand and break down how the algorithm is working.

Neural Network Intuition

Final Output

`(y = out(h) = g(sum W_j h_j))`

`(h_j = out(x) = g(sum w_(jk)x_k))`

`(y = out(h) = g(sum W_j g(sum w_(jk) x_k)))`

  • So h is a non linear function of linear combination of inputs – A multiple logistic regression line
  • Y is a non linear function of linear combination of outputs of logistic regressions
  • Y is a non linear function of linear combination of non linear functions of linear combination of inputs

We find W to minimize

`\(\sum_{i=1}^n [y_i – g(\sum W_j h_j)]^2\) We find \({W_j}\)`

and

`\({w_(jk)}\)`

to minimize

`\(\sum_{i=1}^n [y_i – g(\sum W_j g(\sum w_(jk) x_k))]^2\)`

Neural networks is all about finding the sets of weights

`\({W_j}\)[math] and [math]\({w_(jk)}\)`

 using Gradient Descent Method

The Neural Networks

  • The neural networks methodology is similar to the intermediate output method explained above.
  • But we will not manually subset the data to crate the different models.
  • The neural network technique automatically takes care of all the intermediate outputs using hidden layers
  • It works very well for the data with non-linear decision boundaries
  • The intermediate output layer in the network is known as hidden layer
  • In Simple terms, neural networks are multi layer nonlinear regression model.
  • If we have sufficient number of hidden layers, then we can estimate any complex non-linear function

Neural Network and Vocabulary

Why are they called hidden layers?

  • A hidden layer “hides” the desired output.
  • Instead of predicting the actual output using a single model, build multiple models to predict intermediate output
  • There is no standard way of deciding the number of hidden layers.

Algorithm for Finding Weights

  • Algorithm is all about finding the weights/coefficients
  • We randomly initialize some weights; Calculate the output by supplying training input; If there is an error the weights are adjusted to reduce this error.

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