1. Machine Learning
Learning is “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” (Herbert Simon, 1983)
Different types of AI learning models
Inductive learning
Explanation based learning
Supervised learning
Unsupervised learning
Parallel distributed processing (PDP) models
Neural networks

2. An Inductive Learning Framework
Data and goals of learning task
Representation of learned knowledge
Specific instance of concept “ball”
size(obj1, small) Ù color(obj1,red) Ù shape(obj1, round)
General concept “ball”
size(X, Y) Ù color(X,Z) Ù shape(X, round)
Operations on data
Concept space
Combination of representations and operations
Heursitic search

3. Version Space
Version space is a set of concept descriptions consistent with the training data
Generalization and specialization
shape(box, cube) → shape(X, cube)
size(X, large) Ù shape(X, round) → shape(X, round)
color(X, blue) Ù shape(X, cube) →
color(X, blue) Ù (shape(X, cube) Ú shape(X, rectangle))
“Theory” of Generalization
Given predicate sentences p and q, let P and Q be the set of all sentences that satisfy p and q, respectively. Expression p is more general that q iif. P Ê Q

4. Concept Space Searches
Specific to general
Goal is to create a set S (hypotheses) of maximally specific generalizations
Maintain set NL of previously observed negative examples (initially empty)
Initialize S to first positive training instance in PG
 p : p Î PG
 s : s Î S, if s ≠ p, let s = most specific generalization that matches p
Remove from S all hypotheses more general than other hypotheses in S
Remove from S all hypotheses that match a previously observed negative in NL
 n : n Î NG
Add n to NL
 s : s Î S  s = n, remove s from S
General to specific
Goal is to create a set G of maximally general concepts
Maintain set PL of previously observed positive examples
Initialize G to the most general concepts
 g : g Î G, if g = n, let g = most general specializations that do not match n
Remove from G all hypotheses more specific than other hypotheses in G
Remove from G all hypotheses that fail to match a previously observed positive in PL
Add p to PL
 g : g Î G  g ≠ p, remove g from G

5. Concept Space Search Examples
X = {small, large} Y = {red, white, blue} Z = {ball, cube, brick}
S: {} Positive: obj(small, red, ball)
S: {obj(small, red, ball)} Positive: obj(small, white, ball)
S: {obj(small, Y, ball)} Positive: obj(large, blue, ball)
S: {obj(X, Y, ball)}
Specific => General
G {obj(X, Y, Z)} Negative: obj(small, red, brick)
G: {obj:(large, Y, Z), obj(X, white, Z), obj(X, blue, Z), Positive: obj(large, white, ball)
obj(X, Y, ball), obj(X, Y, cube)}
G: {obj(large, Y, Z), obj(X, white, Z), obj(X, Y, ball)} Negative: obj(large, blue, cube)
G: {obj(large, white, Z), obj(X, white, Z), obj(X, Y, ball)} Positive: obj(small, blue, ball)
G: {obj(X, Y, ball)}
General => Specific

6. Version Space Convergence
Generalization and specialization lead to version space convergence
Specialization of general models
Generalization of specific models
Candidate Elimination Algorithm
Bi-directional search - combines previous two search techniques
If G = S and |S| = |G| = 1, then a single goal concept has been found
Otherwise, there is no single concept that covers all positive instances and none of the negative instances

7. Candidate Elimination Algorithm
G: {obj(X, Y, Z)} Positive: obj(small, red, ball)
S: {}
G: {obj(X, Y, Z)} Negative: obj(small, blue, brick)
S: {obj(small, red, ball)}
G: {obj(X, red, Z), obj(X, Y, ball)} Positive: obj(large, red, ball)
G: {obj(X, red, Z), obj(X, Y, ball)} Negative: obj(large, red, cube)
S: {obj(X, red, ball)}
G: {obj(X, red, ball)}

8. Explanation-Based Learning
Explanation-Based Algorithm
Target concept
Agent must find an effective definition of this concept
Training example
Domain theory (premise(X) → conclusion(X))
liftable(X)  container(X) → cup(X)
part(Z, W)  concave(W)  points_up(W) → container(Z)
light(Y)  part(Y, handle) → liftable(Y)
small(A) → light(A)
made_of(Z, feathers) → light(A)
Operational criteria
Means of describing the form of concept definitions

9. Explanation-Based Learning Example
Specific and Generalized Proof Trees
cup(obj1)
small(obj1)
part(obj1, handle)
owns(bob, obj1)
part(obj1, bottom)
part(obj1, bowl)
points_up(bowl)
concave(bowl)
color(obj1, red)
cup(obj1)
liftable(obj1)
container(obj1)
light(obj1)
part(obj1, handle)
part(obj1, bowl)
points_up(bowl)
concave(bowl)
small(obj1)
cup(X)
liftable(X)
container(X)
light(obj1)
part(X, handle)
part(X, W)
points_up(W)
concave(W)
small(X)

10. Benefits of Explanation-Based Learning
Domain theory allows the learner to select relevant aspects of the training instance
Ignores irrelevant aspects such as color of the cup
EBL forms generalizations that we know to be relevant to specific goals and consistent with the domain theory
Many instances may allow numerous possible generalizations that are either meaningless or wrong
Allows the learner to learn from a single instance
Allows the learner to hypothesize unstated relationships between goals and experiences

11. Unsupervised Learning
Supervised learning assumes the existence of an external method to correctly classify training data
Unsupervised learning require that the learner evaluate concepts on its own
AM is an early example of a discovery program
Discovered natural numbers by modifying its notion of “bags,” or multisets.
Figured out addition, multiplication, division, and prime numbers by evaluating “interesting” concepts
Failed beyond rudimentary number theory – space grew combinatorially and percentage of interesting concepts diminished

12. Concept Clustering
The goal of the clustering problem is to organize a collection of objects into some hierarchy of classes that meet some standard of quality
Necessary to have some means of measuring similarity between objects
Numeric taxonomy represents objects as collections of features and assigns numeric values to these features
Similarity metric treats object as a point in n-dimensional space, where n is the number of features. Similarity between two objects is thus the Euclidean distance between them

13. Agglomerative Clustering
Bottom-up approach to the clustering problem
Examine all pairs of objects, and make the pair with the highest degree of similarity a cluster
Define the features of this cluster as some function (i.e. average) of the features of the members and replace the component objects with this definition
Repeat until all objects have been reduced to a single cluster
Difficult to compare objects defined using symbolic features rather than numeric features
Define similarity as a proportion of common features
However does not adequately take into account underlying semantic knowledge or take into account goals or background knowledge
Traditional algorithms are extensional, enumerate all members. No intensional definition to classify both known and future members

14. Parallel Distributed Processing (PDP)
Also known as subsymbolic approaches/models
View intelligence as the behavior of a collection of large numbers of simple interacting components
Symbolic systems suffer from brittleness
Encompasses phenomena related to the nature of a two-value system
Human performance degrades as a problem gets harder, but almost always generates some answer; expert systems either perform perfectly or not at all
Neural networks
Connectionalist approach inspired by biological brains

15. Neural Networks Neurons Neural network Inputs values: xi Weights: wi
Usually discrete, real values, or within {0, 1} or {-1, 1}
Weights: wi
Usually real valued
Activation values
Output of the neuron
Activation function: F
Neural network
Network topology
Learning algorithm
Environment

16. Simple Neural Networks
McCulloch-Pitts Neuron (McCulloch and Pitts, 1943)
Inputs are either +1 or -1, activation function multiplies each input by its weight as sums the result
If the sum is greater than or equal to 0, the output is 1. Otherwise the output is 0
Output
X  Y
X  Y ⌐X
Weight +1 +1 -2 +1 +1 -1 -1
Inputs X Y +1 X Y +1 X

17. Perceptrons Devised by Frank Rosenblatt in the late 1950s
A single-layer network where all inputs and activation values are either 0 or 1, and the weights are real valued
Activation function is a simple linear threshold
1 if ∑ xiwi > t
0 otherwise
Supervised learning, perceptron changes weights based on correct results
If output is correct, do nothing
If output is 0 and should be 1, increment weights on the active lines (input of 1) by some amount d.
If output is 1 and should be 0, decrement weights on the active lines by some amount d.

18. Limits of Perceptrons
Single-layer networks are only capable of learning classes that are linearly separable
For example, exclusive-or is not linearly separable, and thus cannot be represented by a perceptron
For any n-dimensional space, a classification is linearly separable if these groups can be separated with a single n-1 dimensional hyperplane Y 1
X xor Y = 0
X xor Y = 1 X 1

19. Modern Machine Learning Topics
Asymptotic Model Selection for Naive Bayesian Networks
Dimension Reduction in Text Classification with Support Vector Machines
Stability of Randomized Learning Algorithms
Diffusion Kernels on Statistical Manifolds
Multiclass Boosting for Weak Classifiers
Denoising Source Separation
Learning with Decision Lists of Data-Dependent Features
Generalization Bounds and Complexities Based on Sparsity and Clustering for Convex Combinations of Functions from Random Classes
Characteristics of a Family of Algorithms for Generalized Discriminant Analysis of Undersampled Problems
Journal of Machine Learning Research,