In previous section, we studied about Implementing Intermediate outputs in R
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 \({W_j}\) and \({w_(jk)}\) 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.
The next post is The Neural Network Algorithm.
