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In general, neural networks are trained to as classifier to make classifications. But, in supervised machine learning, we usually need to make regression or make predictions, such as predict tomorrow's stock index or temperature.

So, my question are what is the relationship between classification and regression in Neural Network? And how can I train a neural network to train a regression model to make predictions?

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The difference between a classification and regression is that a classification outputs a prediction probability for class/classes and regression provides a value. We can make a neural network to output a value by simply changing the activation function in the final layer to output the values.

By changing the activation function such as sigmoid,relu,tanh,etc. we can use a function ($f(x) = x$). So while back propagation simply derive $f(x)$

For illustration I will provide you the forward and back ward pass for a single layer neural network regression below:

forward pass: $inputs -> x $

$weights input to hidden -> w1$

$weights hidden to output ->w2$

$z2 = w1*x$

$a2 = sigmoid(z2)$

$z3 = w2*a2$

$a3 = f(z3)$

backward pass:

$targets -> Y$

$f(x) = x -> f'(x) = 1$

$sigmoid'(x) -> sigmoid(x)(1-sigmoid(x))$

$d3 = Y - a3$

$d2 = w2*d3$

$w2' = a2*d3$

$w1' = d2*a2'*x$

Here the d3 and d2 are layer wise errors.

Please make sure the dimensions are properly addressed while implementing in code for the above equations.

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