Introduction To Artificial Neural Networks

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1 Introduction To Artificial Neural Networks

2 Machine Learning Supervised circle square circle square Unsupervised group these into two categories

3 Supervised Machine Learning

4 Supervised Machine Learning

5 Supervised Machine Learning

6 Supervised Machine Learning

7 Supervised Machine Learning

8 Supervised Machine Learning Accuracy

9 Supervised Machine Learning Accuracy 15/20 = 075

10 Supervised Machine Learning Accuracy 15/20 = 075 Precision

11 Supervised Machine Learning Accuracy 15/20 = 075 Precision 7/12 = 058

12 Supervised Machine Learning Accuracy 15/20 = 075 Precision 7/12 = 058 Recall

13 Supervised Machine Learning Accuracy 15/20 = 075 Precision 7/12 = 058 Recall 7/7 = 10

14 Supervised Machine Learning Accuracy 15/20 = 075 Precision 7/12 = 058 Recall 7/7 = 10 F1 (2PR/(P+R))

15 Supervised Machine Learning Accuracy 15/20 = 075 Precision 7/12 = 058 Recall 7/7 = 10 F1 (2PR/(P+R)) = 073

16

17

18 * / =?

19 * / =

20

21 Neural Networks In order to combine the powers of the machine and the human brain, Neural Networks try to mimic the structure and function of our nervous system

22 Biological Motivation #1 Dendrites Nodes Synapses Axon Synapses (weights)

23 Biological Motivation #2

24 Node A Weight w Node B W is the strength of signal sent between A and B If A is stimulated sufficiently and w is positive, then A stimulates B If A is stimulated sufficiently and w is negative, then A inhibits B If A isn t stimulated sufficiently, nothing happens The amount to which a node must be stimulated is determined by its threshold

25 Neural Networks Node (Neuron) Edge (Interconnection)

26 A Single Perceptron Input x 1 Weight w 1 Input x 2 Weight w 2 Threshold T Output y Input x 3 Weight w 3 Weight w 4 Input x 4

27 A Single Perceptron Input x 1 Weight w 1 Input x 2 Weight w 2 Threshold T Output y Input x 3 Input x 4 Weight w 3 Weight w 4 If w 1 x 1 + w 2 x w n x n T, then the output of n is 1 Otherwise, the output of n is 0

28 Perceptron created in the 1960 s Neural network of a single neuron Trainable: its threshold and input weights can be modified or learned If the neuron doesn t give the desired output, then it has made a mistake Input weights and threshold can be changed according to a learning algorithm

29 X1 = I did my homework X2 = I m well rested y = I will go to class 1 means True 0 means False x 1 x 2 y = x 1 and x

30 AND Input x 1 W 1 =? T =? Output y Input x 2 W 2 =?

31 AND Input x 1 W 1 = 1 T = 2 Output y Output is 1 only if all inputs are 1 Input x 2 W 2 = 1 Inputs are either 0 or 1

32 AND Input x 1 W 1 =? Input x 2 W 2 =? T =? Output y Input x 3 W 3 =? W 4 =? Input x 4

33 AND Input x 1 W 1 = 1 Input x 2 Input x 3 W 2 = 1 W 3 = 1 T = 4 Output y Output is 1 only if all inputs are 1 Input x 4 W 4 = 1 Inputs are either 0 or 1

34 X1 = I did my homework X2 = I m well rested y = I will go to class 1 means True 0 means False x 1 x 2 y = x 1 or x

35 OR Input x 1 W 1 =? T =? Output y Input x 2 W 2 =?

36 OR Input x 1 W 1 = 1 T = 1 Output y Output is 1 if at least 1 input is 1 Input x 2 W 2 = 1 Inputs are either 0 or 1

37 OR Input x 1 W 1 =? Input x 2 W 2 =? T =? Output y Input x 3 W 3 =? W 4 =? Input x 4

38 OR Input x 1 W 1 = 1 Input x 2 W 2 = 1 T = 1 Output y Output is 1 if at least 1 input is 1 Input x 3 W 3 = 1 W 4 = 1 Input x 4 Inputs are either 0 or 1

39 X1 = I did my homework X2 = I m well rested y = I will go to class 1 means True 0 means False x 1 x 2 y = x 1 xor x

40 XOR Input x 1 W 1 =? T =? Output y Input x 2 W 2 =?

41 XOR Input x 1 W 1 = 1 T = 05 Output y If inputs are 0, output is 0 If one input is 0 and one is 1, output is 1 Input x 2 W 2 = 1 Inputs are either 0 or 1

42 XOR Input x 1 W 1 = 1 Input x 2 W 2 = 1 Inputs are either 0 or 1 T = 05 Output y If input are 0, output is 0 If one input is 0 and one is 1, output is 1 If both inputs are 1, output is 1

43 Linearly Separable x 1 x 2 x 1 and x x 1 x 2

44 Linearly Separable x 1 x 2 x 1 and x x 1 x 2

45 Linearly Separable x 1 x 2 x 1 and x x 1 x 2 x 1 or x x 1 x 1 x 2 x 2

46 Linearly Separable x 1 x 2 x 1 and x x 1 x 2 x 1 or x x 1 x 1 x 2 x 2

47 Linearly Separable x 1 x 2 x 1 and x x 1 x 2 x 1 or x x 1 x 2 x 1 xor x x 1 x 1 x 1 x 2 x 2 x 2

48 History of Neural Networks McCulloch and Pitts (1943) introduced model of artificial neurons and suggested they could learn Hebb (1949) Simple updating rule for learning Rosenblatt (1962) - the perceptron model Minsky and Papert (1969) wrote Perceptrons Bryson and Ho (1969, but largely ignored until 1980s) invented back-propogation learning for multilayer networks

49 Perceptrons 1969 book by Marvin Minsky and Seymour Papert The problem is that they can only work for classification problems that are linearly separable Insufficiently expressive Important research problem to investigate multilayer networks although they were pessimistic about their value

50 XOR Input x 1 1 T = T = 1 Output = x 1 xor x 2 1 Input x 2 1 T = 1 x 1 x 2 x 1 xor x

51 Training/Learning Train a perceptron to respond to certain inputs with certain desired outputs After training, the perceptron should give reasonable outputs for any input If it wasn t trained for that input, it should try to find the best possible output depending on how it was trained

52 Perceptron Training Rule Begin with random weights Apply the perceptron to each training example (each pass through examples is called an epoch) If it misclassifies an example, modify the weights Continue until the perceptron classifies all training examples correctly

53 Perceptron Training Rule Begin with random weights Apply the perceptron to each training example (each pass through examples is called an epoch) If it misclassifies an example, modify the weights Continue until the perceptron classifies all training examples correctly

54 Modifying the Weights w i w i + w i w i = LearningRate(DesiredOutput ActualOutput)x i

55 Modifying the Weights w i w i + w i w i = LearningRate(DesiredOutput ActualOutput)x i Usually set to some small value like 01 Moderates the degree to which the weights are changed at each step Keeps it from overshooting

56 Modifying the Weights w i w i + w i w i = LearningRate(DesiredOutput ActualOutput)x i This is the difference between what we wanted the output to be and what it actually was If the desired and actual are equal, then this is 0 and the weight won t change

57 Modifying the Weights w i w i + w i w i = LearningRate(DesiredOutput ActualOutput)x i The value of the input itself If this value was 0, then it had no impact on the error, and so its weight shouldn t be adjusted

58 Perceptron Training Rule Works when cases are linearly separable learning rate is slow enough Other approaches to training perceptrons Delta rule (Gradient Descent Approach) Linear Programming

59 Restaurant Problem: Will I wait for a table? Alternate whether there is a suitable alternative restaurant nearby Bar whether the restaurant has a comfortable bar area to wait in Fri/Sat true on Fridays and Saturdays Hungry whether we are hungry Patrons how many people are in the restaurant (None, Some or Full) Price the restaurants price range ($, $$, $$$) Raining whether its is raining outside Reservation whether we made a reservation Type the kind of restaurant (French, Italian, Thai, or Burger) WaitEstimate the wait estimate by the host (0-10 minutes, 10-30, 30-60, > 60)

60 Multilayer Network

61 Learning in Multilayer Networks Same method as for single layer networks Example inputs are presented to the network If the network computes an output that matches the desired, nothing is done If there is an error, then the weights are adjusted to balance the error

62 Back Propogation Algorithm Approach to dividing the contribution of each weight to the error Like the Perceptron Learning Algorithm, we try to minimize error between each desired output and actual output At the output layer, the weight update rule is very similar to the rule for the perceptron Two differences: The activation of the hidden unit a j is used instead of the input value The rule contains a term for the gradient of the activation function

63 Back Propagation Learning

64 Pattern Recognition Inputs (x 1, x 2,, x n ) are called a pattern If the perceptron gives the desired output for some pattern, the perceptron recognizes or correctly classifies that pattern A pattern could be anything any ideas?

65 Handwritten Character Recognition Le Cun et al (1989) implemented a neural network to read zip codes on hand-addressed envelopes, for sorting purposes To identify the digits, uses a 16x16 array of pixels as input, 3 hidden layers, and a distributed output encoding with 10 output units for digits input nodes, 10 output units (1 for the liklihood of each number)

66

67

68 Neural Nets for Face Recognition

69 Learning Hidden Unit Weights

70 ALVINN Drives 70 mph on a public highway Camera image 30 outputs for steering 4 hidden units 30x32 pixels as inputs 30x32 weights into one out of four hidden unit

71 Interpreting Satellite Imagery for Automated Weather Forecasting

72 Summary Perceptrons, one layer networks, are insufficiently expressive Multi-layer networks are sufficiently expressive and can be trained by error back-propogation Many applications including speech, driving, hand written character recognition, fraud detection, driving, etc

73 Input x 1 W 1 = 1 Input x 2 W 2 = 1 T = 1 Output y Input x 3 W 3 = 1 W 4 = 1 Input x 4

74 XOR Input x 1 1 T = T = 1 Output = x 1 xor x 2 1 Input x 2 1 T = 1 x 1 x 2 x 1 xor x

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