1. CS 790
Machine Learning
Introduction
Ali Borji
UWM

2. Motivating Problems
Handwritten Character Recognition

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

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

5. Can Machines Learn to Solve These Problems?
Or, to be more precise
Can we program machines to learn to do these tasks?

6. Definition of Learning
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 E
(Mitchell, Machine Learning, McGraw-Hill, 1997)

7. Definition of Learning
What does this mean exactly?
Handwriting recognition problem
Task T: Recognizing hand written characters
Performance measure P: percent of characters correctly classified
Training experience E: a database of handwritten characters with given classifications

8. Design a Learning System
We shall use handwritten Character recognition as an example to illustrate the design issues and approaches

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

10. 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

11. Design a Learning System
Step 2: Representing Experience
Choose a representation scheme for the experience/examples
The sensor input represented by an n-d vector, called the feature vector, X = (x1, x2, x3, …, xn)
(1,1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,1, 1,1,0, …., 1) 64-d Vector
(1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1, 1,1,0, …., 1) 64-d Vector

12. Design a Learning System
Step 2: Representing Experience
Choose a representation scheme for the experience/examples
The sensor input represented by an n-d vector, called the feature vector, X = (x1, x2, x3, …, xn)
To represent the experience, we need to know what X is.
So we need a corresponding vector D, which will record our knowledge (experience) about X
The experience E is a pair of vectors E = (X, D)

13. Design a Learning System
Step 2: Representing Experience
Choose a representation scheme for the experience/examples
The experience E is a pair of vectors E = (X, D)
So, what would D be like? There are many possibilities.

14. 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)
e.g,
if X is digit 5, then d5=1; all others =0
If X is digit 9, then d9=1; all others =0

15. 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)

16. Design a Learning System
Step 3: Choose a Representation for the Black Box
We need to choose a function F to approximate the block box. For a given X, the value of F will give the classification of X. There are considerable flexibilities in choosing F
Learning System F X
F(X)

17. Design a Learning System
Step 3: Choose a Representation for the Black Box
F will be a function of some adjustable parameters, or weights, W = (w1, w2, w3, …wN), which the learning algorithm can modify or learn
Learning System
F(W) X
F(W,X)

18. Design a Learning System
Step 4: Learning/Adjusting the Weights
We need a learning algorithm to adjust the weights such that the experience/prior knowledge from the training data can be learned into the system:
E=(X,D)
F(W,X) = D

19. Design a Learning System
Step 4: Learning/Adjusting the Weights
Adjust W
E=(X,D)
Learning System
F(W) X
F(W,X) D
Error = D-F(W,X)

20. Design a Learning System
Step 5: Use/Test the System
Once learning is completed, all parameters are fixed. An unknown input X is presented to the system, the system computes its answer according to F(W,X)
Learning System
F(W) X
F(W,X)
Answer

21. Revision of Some Basic Maths
Vector and Matrix
Row vector/column vector/vector transposition
Vector length/norm
Inner/dot product
Matrix (vector) multiplication
Linear algebra
Euclidean space
Basic Calculus
Partial derivatives
Gradient
Chain rule

22. Revision of Some Basic Maths
Inner/dot product
x = [x1, x1, …, xn ]T , y = [y1, y1, …, yn ]T
Inner/dot product of x and y, xTy
Matrix/Vector multiplication

23. Revision of Some Basic Maths
Vector space/Euclidean space
A vector space V is a set that is closed under finite vector addition and scalar multiplication.
The basic example is n-dimensional Euclidean space, where every element is represented by a list of n real numbers
An n-dimensional real vector corresponds to a point in the Euclidean space.
[1, 3] is a point in 2-dimensional space
[2, 4, 6] is point in 3-dimensional space

24. Revision of Some Basic Maths
Vector space/Euclidean space
Euclidean space (Euclidean distance)
Dot/inner product and Euclidean distance
Let x and y are two normalized n vectors, ||x||= 1, ||y||=1, we can write
Minimization of Euclidean distance between two vectors corresponds to maximization of their inner product.
Euclidean distance/inner product as similarity measure

25. Revision of Some Basic Maths
Basic Calculus
Multivariable function:
Partial derivative: gives the direction and speed of change of y, with respect to xi
Gradient
Chain rule: Let y = f (g(x)), u = g(x), then
Let z = f(x, y), x = g(t), y = h(t), then

26. Feature Space x1 x2 x2(i) x1(i)
Representing real world objects using feature vectors
x2(i)
x1(i) i 2 3 1 4 5 6 7 x1 x2 10
X(i) =[x1(i), x2(i)] 9 11 12
Feature Vector
x1(i) 13 14 8 15 16
Feature Space
Elliptical blobs (objects)
x2(i)

27. Feature Space
From Objects to Feature Vectors to Points in the Feature Spaces x1 x2
Elliptical blobs (objects) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
X(15)
X(1)
X(7)
X(16)
X(3)
X(8)
X(25)
X(12)
X(13)
X(6)
X(9)
X(10)
X(4)
X(11)
X(14)

28. Representing General Objects
Feature vectors of
Faces
Cars
Fingerprints
Gestures
Emotions (a smiling face, a sad expression etc) …

29. Further Reading
T. M. Mitchell, Machine Learning, McGraw-Hill International Edition, 1997
Chapter 1

30. Tutorial/Exercise Questions
Describe informally in one paragraph of English, the task of learning to recognize handwriting numerical digits.
Describe the various steps involved in designing a learning system to perform the task of question 1, give as much detail as possible the tasks that have to be performed in each step.
For the tasks of learning to recognize human faces and fingerprints respectively, redo questions 1 and 2.
In the lecture, we used a very long binary vector to represent the handwriting digits, can you think of other representation methods?

31. What is Machine Learning?
Adapt to / learn from data
To optimize a performance function
Can be used to:
Extract knowledge from data
Learn tasks that are difficult to formalise
Create software that improves over time

32. When to learn Learning involves
Human expertise does not exist (navigating on Mars)
Humans are unable to explain their expertise (speech recognition)
Solution changes in time (routing on a computer network)
Solution needs to be adapted to particular cases (user biometrics)
Learning involves
Learning general models from data
Data is cheap and abundant. Knowledge is expensive and scarce
Customer transactions to computer behaviour
Build a model that is a good and useful approximation to the data

33. Applications Speech and hand-writing recognition
Autonomous robot control
Data mining and bioinformatics: motifs, alignment, …
Playing games
Fault detection
Clinical diagnosis
Spam detection
Credit scoring, fraud detection
Web mining: search engines
Market basket analysis,
Applications are diverse but methods are generic

34. Generic methods Learning from labelled data (supervised learning)
Eg. Classification, regression, prediction, function approx.
Learning from unlabelled data (unsupervised learning)
Eg. Clustering, visualisation, dimensionality reduction
Learning from sequential data
Eg. Speech recognition, DNA data analysis
Associations
Reinforcement Learning

35. Statistical Learning
Machine learning methods can be unified within the framework of statistical learning:
Data is considered to be a sample from a probability distribution.
Typically, we don’t expect perfect learning but only “probably correct” learning.
Statistical concepts are the key to measuring our expected performance on novel problem instances.

36. Induction and inference
Induction: Generalizing from specific examples.
Inference: Drawing conclusions from possibly incomplete knowledge.
Learning machines need to do both.

37. Inductive learning Data produced by “target”.
Hypothesis learned from data in order to “explain”, “predict”,“model” or “control” target.
Generalisation ability is essential.
Inductive learning hypothesis:
“If the hypothesis works for enough data
then it will work on new examples.”

38. Example 1: Hand-written digits
Data representation: Greyscale images
Task: Classification (0,1,2,3…..9)
Problem features:
Highly variable inputs from same class including some “weird” inputs,
imperfect human classification,
high cost associated with errors so “don’t know” may be useful.

40. Example 2: Speech recognition
Data representation: features from spectral analysis of speech signals (two in this simple example).
Task: Classification of vowel sounds in words of the form “h-?-d”
Problem features:
Highly variable data with same classification.
Good feature selection is very important.
Speech recognition is often broken into a number of smaller tasks like this.

42. Example 3: DNA microarrays
DNA from ~10000 genes attached to a glass slide (the microarray).
Green and red labels attached to mRNA from two different samples.
mRNA is hybridized (stuck) to the DNA on the chip and green/red ratio is used to measure relative abundance of gene products.

44. DNA microarrays
Data representation: ~10000 Green/red intensity levels ranging from
Tasks: Sample classification, gene classification, visualisation and clustering of genes/samples.
Problem features:
High-dimensional data but relatively small number of examples.
Extremely noisy data (noise ~ signal).
Lack of good domain knowledge.

45. Projection of 10000 dimensional data onto 2D using PCA
effectively separates cancer subtypes.

46. Probabilistic models A large part of the module will deal with methods
that have an explicit probabilistic interpretation:
Good for dealing with uncertainty
eg. is a handwritten digit a three or an eight ?
Provides interpretable results
Unifies methods from different fields

47. Text books E. Alpaydin’s “Introduction to Machine Learning”
T. Mitchell’s “Machine Learning”

48. Supervised Learning: Uses
Prediction of future cases
Knowledge extraction
Compression
Outlier detection

49. Unsupervised Learning
Clustering: grouping similar instances
Example applications
Customer segmentation in CRM
Learning motifs in bioinformatics
Clustering items based on similarity
Clustering users based on interests

50. Reinforcement Learning
Learning a policy: A sequence of outputs
No supervised output but delayed reward
Credit assignment problem
Game playing
Robot in a maze
Multiple agnts, partial observability