Neural network viewed as a tool for Function approximation

4. Learning Problem

5. Optimization Technique: Steepest Descent The steepest descent algorithm: w (n+1)= w (n)-  g (n)

6. Least-Mean-Square (LMS) Algorithm e(n) is the error signal measured at time n.

7. Model of a Simple Perceptron and Let b k =w k0 and x 0 =+1

8. Activation Functions Threshold Function Sigmoid Function

10. Multi Layer Perceptron

19. Linearly Non Separable data

23. Back-propagation Algorithm

24. Back-propagation Algorithm Contd... Local Gradient

25. Case 1: Neuron j is an Output Node

26. Case 2: Neuron j is a Hidden Node

27. Case 2: Neuron j is a Hidden Node (Contd…)

32. Learning with a Teacher (Supervised Learning)

33. Learning without a Teacher Reinforcement Learning

34. Learning Tasks Function Approximation d = f ( x ) x : input vector d : output vector f (  ) is assumed to be unknown Given a set of labeled examples: Requirement: Design a neural network to approximate this unknown function f(  ) such that F(  ). || F ( x )- f ( x )||<  for all x , where  is a small positive number