Session 4 and 5_Artificial Neural Network_Contemporary Business Anaytics_24 July.pptx

business analytics machile learning neural network

1. Contemporary Business Analytics Artificial Neural Network

2. Non-linear Relationships x 1 x 2 …)  

3. Computer Vision 188 104 187 101 127 95 195 97 178 139 109 162 66 217 65 238 170 195 141 97 206 234 64 128 128 93 109 129 63 202 124 177 113 108 91 139 67 126 174 146 160 175 129 59 158 214 87 148 51 101 246 89 93 144 98 215 49 55 35 66 33 31 39 26 44 33 61 45 34 37 65 65 47 64 56 21 36 39 59 31 21 64 51 41 60 69 53 27 64 59 66 61 61 40 69 60 66 70 52 46 23 21 69 66 52 39 48 65 46 28 67 20

4. Computer Vision – Car Detection

5. Computer Vision – Car Detection x 1 x 2 x 1 x 2

6. ANN Architecture 6 Activation function Weighted sum Connection weights Input features a = = σ (z)   z = w T x + b weight vector , w Feature vector , x bias b Neuron

7. Simple Linear Regression y a y p e 1 y x e 2 x 1 e 3 e 4 e 6 e 5    

8. = σ (z), where z = wx + b , x is the feature vector , w and b are the parameter vectors = 0 if a< 0.5, 1 if a ≥ 0.5 The objective of training is to set the parameter vectors w , b so that the model estimates high probabilities for positive instances ( y = 1) and low probabilities for negative instances ( y = 0)   Logistic Regression

9. Logistic Regression Loss function of a single training instance –log( ) grows very large when approaches 0, so the cost will be large if the model estimates a probability close to 0 for a positive instance It will also be very large if the model estimates a probability close to 1 for a negative instance The cost function over the whole training set is the average cost over all training instances Logistic Regression cost function (L( , )) L = - ) + ) ]  

10. Gradient Descent Gradient Descent is a generic optimization algorithm capable of finding optimal solutions to a wide range of problems The general idea of Gradient Descent is to tweak parameters iteratively in order to minimize a cost function -  

11. Gradient Descent

12. Gradient Descent – Learning Rate 12 The learning rate is too small The learning rate is too large

13. ANN Architecture 13 Activation function Weighted sum Connection weights Input features a = σ (z) z = w T x + b weight vector , w Feature vector , x bias b Neuron

14. Artificial Neural Network 14 x 3 x 2 x 1 W [1] x a [1] = σ (z [1] ) = W [1] x + b [1]   b [1] L( a [2] , )     [1] [2] a [2] = σ (z [2] ) = W [2] a [1] + b [2]   W [2] b [2] Activation function Weighted sum Connection weights Input features Neuron Layer [1] Computation Perceptron Multi-layered Perceptron Layer [2] Computation Output W [1] a [1] W [2] a [2] [0]

15. Forward Propagation X 3 X 2 X 1 = a   [1] [2] x =   W [1] =   0.9 0.3 0.4 1.16 0.761 0.3 0.6 0.8 0.2 0.8 0.2 0.1 0.5 0.6 0.62 0.650 0.42 0.603 1.11 0.75

16. ANN: Forward Propagation 16 x 3 x 2 x 1 W [1] x a [1] = σ (z [1] ) = W [1] x + b [1]   b [1] L( a [2] , )   [1] [2] a [2] = σ (z [2] ) = W [2] a [1] + b [2]   W [2] b [2] Multi-layered Perceptron x =   W [1] =   z [1] = W [1] x =   a [1] = σ (z [1] ) =   W [2] =   z [2] = W [2] a [1] =   a [2] = σ (z [2] ) = 0.75   [0]

17. Backpropagation X 2 X 1 = a = σ (z)   w 1 w 2 b Z = w 1 X 1 + w 2 X 2 + b × ×   ( a,y )