1. Artificial Intelligence
Neural Networks

2. What is Learning
The word "learning" has many different meanings. It is used, at least, to describe
memorizing something
learning facts through observation and exploration
development of motor and/or cognitive skills through practice
organization of new knowledge into general, effective representations

3. Learning
Study of processes that lead to self-improvement of machine performance.
It implies the ability to use knowledge to create new knowledge or integrating new facts into an existing knowledge structure
Learning typically requires repetition and practice to reduce differences between observed and actual performance

4. What is Learning?
Herbert Simon: “Learning is any process by which a system improves performance from experience.”

5. Learning
Definition: A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience.

6. Learning & Adaptation
”Modification of a behavioral tendency by expertise.” (Webster 1984)
”A learning machine, broadly defined as any device whose actions are influenced by past experiences.” (Nilsson 1965)
”Any change in a system that allows it to perform better the second time on repetition of the same task or on another task drawn from the same population.” (Simon 1983)

7. Negative Features of Human Learning
Its slow (5-6 years for motor skills years for abstract reasoning)
Inefficient
Expensive
There is no copy process
Learning strategy is often a function of knowledge available to learner

8. Applications of ML Learning to recognize spoken words
Learning to drive an autonomous vehicle
Learning to classify objects
Learning to play world-class backgammon
Designing the morphology and control structure of electro-mechanical artefacts

9. Motivating Problems
Handwritten Character Recognition

10. Motivating Problems
Fingerprint Recognition (e.g., border control)

11. Motivating Problems
Face Recognition (security access to buildings etc)

12. Different kinds of learning…
Supervised learning:
Someone gives us examples and the right answer for those examples
We have to predict the right answer for unseen examples
Unsupervised learning:
We see examples but get no feedback
We need to find patterns in the data
Reinforcement learning:
We take actions and get rewards
Have to learn how to get high rewards

13. Reinforcement learning
Another learning problem, familiar to most of us, is learning motor skills, like riding a bike. We call this reinforcement learning.
It's different from supervised learning because no-one explicitly tells you the right thing to do; you just have to try things and see what makes you fall over and what keeps you upright.

14. Learning with a Teacher
supervised learning
knowledge represented by a set of input-output examples (xi,yi)
minimize the error between the actual response of the learner and the desired response
desired
response
state x
Environment
Teacher
actual
response +
Learning
system - S
error signal

15. Unsupervised Learning
self-organized learning
no teacher
task independent quality measure
identify regularities in the data and discover classes automatically
state
Environment
Learning
system

16. The red and the black
Imagine that we were given all these points, and we needed to guess a function of their x, y coordinates that would have one output for the red ones and a different output for the black ones.

17. What’s the right hypothesis?
In this case, it seems like we could do pretty well by defining a line that separates the two classes.

18. Now, what’s the right hypothesis
Now, what if we have a slightly different configuration of points? We can't divide them conveniently with a line.

19. Now, what’s the right hypothesis
But this parabola-like curve seems like it might be a reasonable separator.

20. Design a Learning System
Step 0:
Lets treat the learning system as a black box
Learning System Z

21. Design a Learning System
Step 1: Collect Training Examples (Experience).
Without examples, our system will not learn (so-called learning from examples) 2 3 6 7 8 9

22. Design a Learning System
Step 2: Representing Experience
So, what would D be like? There are many possibilities.
Assuming our system is to recognise 10 digits only, then D can be a 10-d binary vector; each correspond to one of the digits
D = (d0, d1, d2, d3, d4, d5, d6, d7, d8, d9)
X = (1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,1, 1,1,0, …., 1); 64-d Vector
D= (0,0,0,0,0,1,0,0,0,0)
X= (1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1, 1,1,0, …., 1); 64-d Vector
D= (0,0,0,0,0,0,0,0,1,0)

23. Example of supervised learning: classification
We lend money to people
We have to predict whether they will pay us back or not
People have various (say, binary) features:
do we know their Address? do they have a Criminal record? high Income? Educated? Old? Unemployed?
We see examples: (Y = paid back, N = not)
+a, -c, +i, +e, +o, +u: Y
-a, +c, -i, +e, -o, -u: N
+a, -c, +i, -e, -o, -u: Y
-a, -c, +i, +e, -o, -u: Y
-a, +c, +i, -e, -o, -u: N
-a, -c, +i, -e, -o, +u: Y
+a, -c, -i, -e, +o, -u: N
+a, +c, +i, -e, +o, -u: N
Next person is +a, -c, +i, -e, +o, -u. Will we get paid back?

24. Learning by Examples
Concept: ”days on which my friend Aldo enjoys his favourite water sports”
Task: predict the value of ”Enjoy Sport” for an arbitrary day based on the values of the other attributes
Sky
Temp
Humid
Wind
Water
Fore-cast
Enjoy Sport
Sunny
Rainy
Warm
Cold
Normal
High
Strong
Cool
Same
Chane
Yes No

25. Decision trees
high Income?
yes no
Criminal record? NO
yes no NO
YES

26. Constructing a decision tree, one step at a time
+a, -c, +i, +e, +o, +u: Y
-a, +c, -i, +e, -o, -u: N
+a, -c, +i, -e, -o, -u: Y
-a, -c, +i, +e, -o, -u: Y
-a, +c, +i, -e, -o, -u: N
-a, -c, +i, -e, -o, +u: Y
+a, -c, -i, -e, +o, -u: N
+a, +c, +i, -e, +o, -u: N
Constructing a decision tree, one step at a time
address?
yes no
-a, +c, -i, +e, -o, -u: N
-a, -c, +i, +e, -o, -u: Y
-a, +c, +i, -e, -o, -u: N
-a, -c, +i, -e, -o, +u: Y
+a, -c, +i, +e, +o, +u: Y
+a, -c, +i, -e, -o, -u: Y
+a, -c, -i, -e, +o, -u: N
+a, +c, +i, -e, +o, -u: N
criminal?
criminal?
yes no
yes no
-a, +c, -i, +e, -o, -u: N
-a, +c, +i, -e, -o, -u: N
-a, -c, +i, +e, -o, -u: Y
-a, -c, +i, -e, -o, +u: Y
+a, -c, +i, +e, +o, +u: Y
+a, -c, +i, -e, -o, -u: Y
+a, -c, -i, -e, +o, -u: N
+a, +c, +i, -e, +o, -u: N
income?
yes no
Address was maybe not the best attribute to start with…
+a, -c, +i, +e, +o, +u: Y
+a, -c, +i, -e, -o, -u: Y
+a, -c, -i, -e, +o, -u: N

27. Different approach: nearest neighbor(s)
Next person is -a, +c, -i, +e, -o, +u. Will we get paid back?
Nearest neighbor: simply look at most similar example in the training data, see what happened there
+a, -c, +i, +e, +o, +u: Y (distance 4)
-a, +c, -i, +e, -o, -u: N (distance 1)
+a, -c, +i, -e, -o, -u: Y (distance 5)
-a, -c, +i, +e, -o, -u: Y (distance 3)
-a, +c, +i, -e, -o, -u: N (distance 3)
-a, -c, +i, -e, -o, +u: Y (distance 3)
+a, -c, -i, -e, +o, -u: N (distance 5)
+a, +c, +i, -e, +o, -u: N (distance 5)
Nearest neighbor is second, so predict N
k nearest neighbors: look at k nearest neighbors, take a vote
E.g., 5 nearest neighbors have 3 Ys, 2Ns, so predict Y

28. Neural Networks
They can represent complicated hypotheses in high-dimensional continuous spaces.
They are attractive as a computational model because they are composed of many small computing units.
They were motivated by the structure of neural systems in parts of the brain. Now it is understood that they are not an exact model of neural function, but they have proved to be useful from a purely practical perspective.

29. If…then rules
If tear production rate = reduced then recommendation = none
If age = young and astigmatic = no then recommendation = soft

30. Approaches to Machine Learning
Numerical approaches
Build numeric model with parameters based on successes
Structural approaches
Concerned with the process of defining relationships by creating links between concepts

31. Learning methods Decision rules: Bayesian network: Neural Network:
If income < $ then reject
Bayesian network:
P(good | income, credit history,….)
Neural Network:
Nearest Neighbor:
Take the same decision as for the customer in the data base that is most similar to the applicant

32. Classification
Assign object/event to one of a given finite set of categories.
Medical diagnosis
Credit card applications or transactions
Fraud detection in e-commerce
Worm detection in network packets
Spam filtering in
Recommended articles in a newspaper
Recommended books, movies, music, or jokes
Financial investments
DNA sequences
Spoken words
Handwritten letters
Astronomical images

33. Problem Solving / Planning / Control
Performing actions in an environment in order to achieve a goal.
Solving calculus problems
Playing checkers, chess, or backgammon
Balancing a pole
Driving a car or a jeep
Flying a plane, helicopter, or rocket
Controlling an elevator
Controlling a character in a video game
Controlling a mobile robot

34. Another Example: Handwriting Recognition
Positive:
This is a letter S:
Negative:
This is a letter Z:
Background concepts:
Pixel information
Categorisations:
(Matrix, Letter) pairs
Both positive & negative
Task
Correctly categorise
An unseen example
Into 1 of 26 categories

35. History Roots of work on NN are in:
Neurobiological studies (more than one century ago):
How do nerves behave when stimulated by different magnitudes of electric current? Is there a minimal threshold needed for nerves to be activated? Given that no single nerve cel is long enough, how do different nerve cells communicate among each other?
Psychological studies:
How do animals learn, forget, recognize and perform other types of tasks?
Psycho-physical experiments helped to understand how individual neurons and groups of neurons work.
McCulloch and Pitts introduced the first mathematical model of single neuron, widely applied in subsequent work.

36. History Widrow and Hoff (1960): Adaline
Minsky and Papert (1969): limitations of single-layer perceptrons (and they erroneously claimed that the limitations hold for multi-layer perceptrons)
Stagnation in the 70's:
Individual researchers continue laying foundations
von der Marlsburg (1973): competitive learning and self-organization
Big neural-nets boom in the 80's
Grossberg: adaptive resonance theory (ART)
Hopfield: Hopfield network
Kohonen: self-organising map (SOM)

37. Applications Classification: Regression: Pattern association:
Image recognition
Speech recognition
Diagnostic
Fraud detection …
Regression:
Forecasting (prediction on base of past history)
Pattern association:
Retrieve an image from corrupted one
Clustering:
clients profiles
disease subtypes

38. Real Neurons Cell structures Cell body Dendrites Axon
Synaptic terminals

39. Non Symbolic Representations
Decision trees can be easily read
A disjunction of conjunctions (logic)
We call this a symbolic representation
Non-symbolic representations
More numerical in nature, more difficult to read
Artificial Neural Networks (ANNs)
A Non-symbolic representation scheme
They embed a giant mathematical function
To take inputs and compute an output which is interpreted as a categorisation
Often shortened to “Neural Networks”
Don’t confuse them with real neural networks (in heads)

40. Complicated Example: Categorising Vehicles
Input to function: pixel data from vehicle images
Output: numbers: 1 for a car; 2 for a bus; 3 for a tank
INPUT INPUT INPUT INPUT
OUTPUT = OUTPUT = OUTPUT = OUTPUT=1

41. Real Neural Learning
Synapses change size and strength with experience.
Hebbian learning: When two connected neurons are firing at the same time, the strength of the synapse between them increases.
“Neurons that fire together, wire together.”

42. Neural Network
Input Layer
Hidden 1
Hidden 2
Output Layer

43. Simple Neuron
Inputs
 f X1 X2 Xn
Output W1 W2 Wn

44. Neuron Model A neuron has more than one input x1, x2,..,xm
Each input is associated with a weight w1, w2,..,wm
The neuron has a bias b
The net input of the neuron is
n = w1 x1 + w2 x2+….+ wm xm + b

45. Neuron output The neuron output is y = f (n)
f is called transfer function

46. Transfer Function We have 3 common transfer functions
Hard limit transfer function
Linear transfer function
Sigmoid transfer function

47. Exercises
The input to a single-input neuron is 2.0, its weight is 2.3 and the bias is –3.
What is the output of the neuron if it has transfer function as:
Hard limit
Linear
sigmoid

48. Architecture of ANN Feed-Forward networks
Allow the signals to travel one way from input to output
Feed-Back Networks
The signals travel as loops in the network, the output is connected to the input of the network

49. Learning Rule
The learning rule modifies the weights of the connections.
The learning process is divided into Supervised and Unsupervised learning

50. Perceptron
It is a network of one neuron and hard limit transfer function
Inputs
 f X1 X2 Xn
Output W1 W2 Wn

51. Perceptron The perceptron is given first a randomly weights vectors
Perceptron is given chosen data pairs (input and desired output)
Preceptron learning rule changes the weights according to the error in output

52. Perceptron
The weight-adapting procedure is an iterative method and should reduce the error to zero
The output of perceptron is
Y = f(n)
= f ( w1x1+w2x2+…+wnxn)
=f (wixi) = f ( WTX)

53. Perceptron Learning Rule
W new = W old + (t-a) X
Where W new is the new weight
W old is the old value of weight
X is the input value
t is the desired value of output
a is the actual value of output

54. Example
Consider a perceptron that has two real-valued inputs and an output unit. All the initial weights and the bias equal Assume the teacher has said that the output should be 0 for the input: x1 = 5 and x2 = - 3. Find the optimum weights for this problem.

55. Example
Covert the classification problem into perceptron neural network model (start w1=1, b=3 and w2=2 or any other values).
X1 = [0 2], t1=1 & x2 = [1 0], t2=1 & x3 = [0 –2] , t3=0 & x4=[2 0], t4=0

56. Example Perceptron Example calculation: x1=-1, x2=1, x3=1, x4=-1
S = 0.25*(-1) *(1) *(1) *(-1) = 0
0 > -0.1, so the output from the ANN is +1
So the image is categorised as “bright”

57. The First Neural Neural Networks
AND Function 1 X1 X2 Y
Threshold(Y) = 2

58. Simple Networks
t = 0.0 y x
W = 1.5
W = 1 -1

59. Exercises Design a neural network to recognize the problem of
X1=[2 2] , t1=0
X=[1 -2], t2=1
X3=[-2 2], t3=0
X4=[-1 1], t4=1
Start with initial weights w=[0 0] and bias =0

60. Problems Four one-dimensional data belonging to two classes are
X = [ ]
T = [ ]
W = [ ]

61. Example -1 +1
- 1

62. Example -1 +1
- 1

63. AND Network
This example means we construct a network for AND operation. The network draw a line to separate the classes which is called Classification

64. Perceptron Geometric View
The equation below describes a (hyper-)plane in the input space consisting of real valued m-dimensional vectors. The plane splits the input space into two regions, each of them describing one class.
decision
region for C1 x2
w1x1 + w2x2 + w0 >= 0
decision
boundary C1 x1 C2
w1x1 + w2x2 + w0 = 0

65. Perceptron: Limitations
The perceptron can only model linearly separable classes, like (those described by) the following Boolean functions:
AND OR
COMPLEMENT
It cannot model the XOR.
You can experiment with these functions in the Matlab practical lessons.

66. Multi-layers Network Let the network of 3 layers
Input layer
Hidden layers
Output layer
Each layer has different number of neurons

67. Multi layer feed-forward NN
FFNNs overcome the limitation of single-layer NN: they can handle non-linearly
separable learning tasks.
Input
layer
Output
layer
Hidden Layer

68. Types of decision regionsx1 1 x2 w2 w1 w0
Network
with a single
node 1 x1 x2
Convex
region L1 L2 L3 L4
One-hidden layer network that realizes the convex region
-3.5

69. Learning rule
The perceptron learning rule can not be applied to multi-layer network
We use BackPropagation Algorithm in learning process

70. Backprop Back-propagation training algorithm illustrated:
Backprop adjusts the weights of the NN in order to minimize the network total mean squared error.
Network activation
Error computation
Forward Step
Error propagation
Backward Step

71. Bp Algorithm The weight change rule is
Where  is the learning factor <1
Error is the error between actual and trained value
f’ is is the derivative of sigmoid function = f(1-f)

72. Delta Rule
Each observation contributes a variable amount to the output
The scale of the contribution depends on the input
Output errors can be blamed on the weights
A least mean square (LSM) error function can be defined (ideally it should be zero)
E = ½ (t – y)2

73. Calculation of Network Error
Could calculate Network error as
Proportion of mis-categorised examples
But there are multiple output units, with numerical output
So we use a more sophisticated measure:
Not as complicated as it looks
Square the difference between target and observed
Squaring ensures we get a positive number
Add up all the squared differences
For every output unit and every example in training set

74. Example
For the network with one neuron in input layer and one neuron in hidden layer the following values are given
X=1, w1 =1, b1=-2, w2=1, b2 =1, =1 and t=1
Where X is the input value
W1 is the weight connect input to hidden
W2 is the weight connect hidden to output
b1 and b2 are bias
t is the training value

75. Momentum in Backpropagation
For each weight
Remember what was added in the previous epoch
In the current epoch
Add on a small amount of the previous Δ
The amount is determined by
The momentum parameter, denoted α
α is taken to be between 0 and 1

76. How Momentum Works If direction of the weight doesn’t change Caution:
Then the movement of search gets bigger
The amount of additional extra is compounded in each epoch
May mean that narrow local minima are avoided
May also mean that the convergence rate speeds up
Caution:
May not have enough momentum to get out of local minima
Also, too much momentum might carry search
Back out of the global minimum, into a local minimum

77. Building Neural Networks
Define the problem in terms of neurons
think in terms of layers
Represent information as neurons
operationalize neurons
select their data type
locate data for testing and training
Define the network
Train the network
Test the network

78. Application: FACE RECOGNITION
The problem:
Face recognition of persons of a known group in an indoor environment.
The approach:
Learn face classes over a wide range of poses using neural network.

79. Navigation of a car
Done by Pomerlau. The network takes inputs from a 34X36 video image and a 7X36 range finder. Output units represent “drive straight”, “turn left” or “turn right”. After training about 40 times on 1200 road images, the car drove around CMU campus at 5 km/h (using a small workstation on the car). This was almost twice the speed of any other non-NN algorithm at the time.
11/17/2018

80. Automated driving at 70 mph on a public highway
Camera
image
30 outputs
for steering
30x32 weights
into one out of
four hidden
unit
4 hidden
units
30x32 pixels
as inputs

81. Exercises
Perform one iteration of backprpgation to network of two layers. First layer has one neuron with weight 1 and bias –2. The transfer function in first layer is f=n2
The second layer has only one neuron with weight 1 and bias 1. The f in second layer is 1/n.
The input to the network is x=1 and t=1

82. X 1 2 W
W13
W23 b2 b1 b3
using the initial weights [b1= - 0.5, w11=2, w12=2, w13=0.5, b2= 0.5, w21= 1, w22 = 2, w23 = 0.25, and b3= 0.5] and input vector [2, 2.5] and t = 8. Process one iteration of backpropagation algorithm.

83. Consider a transfer function as f(n) = n2
Consider a transfer function as f(n) = n2. Perform one iteration of BackPropagation with a= 0.9 for neural network of two neurons in input layer and one neuron in output layer. The input values are X=[1 -1] and t = 8, the weight values between input and hidden layer are w11 = 1, w12 = - 2, w21 = 0.2, and w22 = 0.1. The weight between input and output layers are w1 = 2 and w2= -2. The bias in input layers are b1 = -1, and b2= 3.

84. Kakuro. is a kind of game puzzle
Kakuro is a kind of game puzzle. The object of the puzzle is to insert a digit from 1 to 9 inclusive into each white cell such that the sum of the numbers in each entry matches the clue associated with it and that no digit is duplicated in any entry. Briefly describe how you’d use Constraint Satisfaction Problem methods to solve Kakuro puzzles intelligently.