Wrap-Up and Review

Louis Oliphant

oliphant@cs.wisc.edu

cs540 section 2

Announcements

HW5 Graded

Solution and grades will be up on the web

Projects not yet graded

Team Reviews due today

Final Dec 19th, 10:05am CS&S 1325

What Have We Learned (first half)

Search

Different Global and Local Search Techniques

DFS, BFS, Greedy Search, A* Search

Hill Climbing, Simulated Annealing, Genetic Algorithms

Searching With an Opponent

Game Playing – Mini-Max with alpha beta pruning

Game Theory

Logic

Propositional Logic

First Order Logic

What we have learned (second half)

Learning

Induction of models

Inference with models

Lots of models

K-NN, Decision Trees, Neural Nets, Naïve Bayes, Bayesian Networks, Ensembles, Support Vector Machines, Inductive Logic Programming, etc.

Each model is trying to capture a function: f(x) that is a mapping from feature space to a classification for every possible input

Model Bias

Evaluation of Models: How well have you learned the function

Accuracy, precision, recall, confusion matrix, etc.

Review

For each model know:

How to create the model (Induction)

How to label unseen examples (Inference)

Learning Bias

Types of Learning

Unsupervised

Reinforment learning

Supervised

Converting to Fixed Length Feature Vectors

Review

K-NN

Euclidean Distance

Weighted Features

Choosing K

Decision Trees

Information, Information Gain

Pruning

Ensembles

Boosting

Occam's Razor

Review

Types of Data

Noisy data

Missing Values

Continuous Features

Skewed Data

Irrelevant Features

Feature Subset Selection

Forward chaining

Backward chaining

Review

Methodology

Accuracy

Learning curves

Precision, Recall

N-Fold cross validation

Confusion Matrix

Train/Tune/Test set splits

Laplacian Priors

Review

Perceptrons

Step Function, Sigmoid Function

Perceptron Training Rule, Delta rule

Threshold

Gradient Descent

Perceptrons and Logic

Artificial Neural Networks (ANNs)

BackPropagation Algorithm

Non-boolean features

More than two classes

Overfitting Problems

K-Means Clustering

Review

Basic Probability

Joint probability, Full joint probability

Conditional probability

Marginalization

Bayes Rule

Chain Rule

Independence, Conditional Independence

Naïve Bayes

Review

Bayesian Networks

Exact Methods of Inference

Inference by Enumeration

Variable Elimination

Approximate Methods of Inference

Direct Sampling

Rejection Sampling

Likelihood Weighting

Markov Chain Monte Carlo

Induction

Parameter Learning

Maximum Likelihood (ML)

Maximum A-Posteriori (MAP)

Topology Learning

Review

Inductive Logic Programming

More than fixed length feature vectors

Covering Algorithms in general

Top Down Approaches

FOIL

PROGOL

Seeds and Bottom Clauses

Bottom Up Approaches

GOLEM

Support Vector Machines

Support Vector

Maximizing the margin

Kernels (mapping to higher dimensions)

Information and Gain Example

F1	F2	F3	Class

0	1	0	A

1	2	0	A

1	0	1	B

0	1	1	B

2	1	1	A

1	0	2	C

2	2	0	A

2	2	1	C

Information is:

Calculate Information of the above dataset.

Calculate Information Gain for each F1.

Back-Propagation Example

Calculate Errors:

Output Units:

δk ← ok(1-ok)(tk-ok)

Hidden Units:

δh← oh(1-oh) (wkhδk)

Update each network weight:

wji ← wji+∆wji

where ∆wji = αδhjxji

Sigmoid Function:

Update weights using back-prop and the example: 1,0,1 and the learning rate 0.2

x1

x2

Input

layer

-1

.75

.5

.5

.5

.5

-1

.25

Hidden

layer

.5

-.5

-1

.25

Output

layer

Probability Example

Full Joint Probability is

P(A,B,C)=?

P(A|B,C)=?

P(A)=?

P(A,B)=?

P(A|B)=?

is A independent of B?

Bayes Rule:

P(A|B)=P(B|A)P(A)/P(B)

Chain Rule:

P(A,B,C,...,Z)=

P(A|B,C,...,Z)P(B|C,...,Z)...P(Z)

Bayesian Network Example

P(D|A,E)=

BCP(A)P(B|A)P(C|B)P(D|A,B)P(E|D)=

P(A)P(E|D)BP(B|A)P(D|A,B)CP(C|B)=

Continued on board...

A

B

E

D

C

2005-12-13T12:18:45