cse 5331/7331 f'07© prentice hall1 cse 5331/7331 fall 2007 machine learning margaret h. dunham...

CSE 5331/7331 F'07 © Prentice Hall 1

CSE 5331/7331CSE 5331/7331Fall 2007Fall 2007

Machine LearningMachine Learning

Margaret H. DunhamMargaret H. DunhamDepartment of Computer Science and EngineeringDepartment of Computer Science and Engineering

Southern Methodist UniversitySouthern Methodist University

Some Slides extracted from Some Slides extracted from Data Mining, Introductory and Advanced TopicsData Mining, Introductory and Advanced Topics , Prentice Hall, 2002., Prentice Hall, 2002.Other slides from CS 545 at Colorado State University, Chuck AndersonOther slides from CS 545 at Colorado State University, Chuck Anderson

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Table of ContentsTable of Contents

Introduction (Chuck Anderson)Introduction (Chuck Anderson) Statistical Machine Learning ExamplesStatistical Machine Learning Examples

– EstimationEstimation– EMEM– Bayes TheoremBayes Theorem

Decision Tree LearningDecision Tree Learning Neural Network LearningNeural Network Learning

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The slides in this introductory section are The slides in this introductory section are from from

CS545: Machine LearningCS545: Machine Learning

By Chuck AndersonBy Chuck Anderson

Department of Computer ScienceDepartment of Computer Science

Colorado State UniversityColorado State University

Fall 2006Fall 2006

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What is Machine Learning?

Statistics ≈ the science of inference from data Machine learning ≈ multivariate statistics +

computational statistics Multivariate statistics ≈ prediction of values of

a function assumed to underlie a multivariate dataset

Computational statistics ≈ computational methods for statistical problems (aka statistical computation) + statistical methods which happen to be computationally intensive

Data Mining ≈ exploratory data analysis, particularly with massive/complex datasets

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Kinds of Learning Learning algorithms are often categorized

according to the amount of information provided:

Least Information:– Unsupervised learning is more exploratory.– Requires samples of inputs. Must find regularities.

More Information:– Reinforcement learning most recent.– Requires samples of inputs, actions, and rewards

or punishments. Most Information:

– Supervised learning is most common.– Requires samples of inputs and desired outputs.

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Examples of Algorithms

Supervised learning– Regression

» multivariate regression» neural networks and kernel methods

– Classification» linear and quadratic discrimination analysis» k-nearest neighbors» neural networks and kernel methods

Reinforcement learning– multivariate regression– neural networks

Unsupervised learning– principal components analysis– k-means clustering– self-organizing networks

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Point EstimationPoint Estimation Point Estimate:Point Estimate: estimate a population estimate a population

parameter.parameter. May be made by calculating the parameter for a May be made by calculating the parameter for a

sample.sample. May be used to predict value for missing data.May be used to predict value for missing data. Ex: Ex:

– R contains 100 employeesR contains 100 employees– 99 have salary information99 have salary information– Mean salary of these is $50,000Mean salary of these is $50,000– Use $50,000 as value of remaining employee’s Use $50,000 as value of remaining employee’s

salary. salary. Is this a good idea?Is this a good idea?


Estimation ErrorEstimation Error

Bias: Bias: Difference between expected value and Difference between expected value and actual value.actual value.

Mean Squared Error (MSE):Mean Squared Error (MSE): expected value expected value of the squared difference between the of the squared difference between the estimate and the actual value:estimate and the actual value:

Why square?Why square? Root Mean Square Error (RMSE)Root Mean Square Error (RMSE)


Jackknife EstimateJackknife Estimate Jackknife Estimate:Jackknife Estimate: estimate of parameter is estimate of parameter is

obtained by omitting one value from the set of obtained by omitting one value from the set of observed values.observed values.

Ex: estimate of mean for X={xEx: estimate of mean for X={x1, … , x, … , xn}}


Maximum Likelihood Maximum Likelihood Estimate (MLE)Estimate (MLE)

Obtain parameter estimates that maximize Obtain parameter estimates that maximize the probability that the sample data occurs for the probability that the sample data occurs for the specific model.the specific model.

Joint probability for observing the sample Joint probability for observing the sample data by multiplying the individual probabilities. data by multiplying the individual probabilities. Likelihood function: Likelihood function:

Maximize L.Maximize L.


MLE ExampleMLE Example

Coin toss five times: {H,H,H,H,T}Coin toss five times: {H,H,H,H,T}

Assuming a perfect coin with H and T equally Assuming a perfect coin with H and T equally

likely, the likelihood of this sequence is: likely, the likelihood of this sequence is:

However if the probability of a H is 0.8 then:However if the probability of a H is 0.8 then:


MLE Example (cont’d)MLE Example (cont’d) General likelihood formula:General likelihood formula:

Estimate for p is then 4/5 = 0.8Estimate for p is then 4/5 = 0.8


Expectation-Maximization Expectation-Maximization (EM)(EM)

Solves estimation with incomplete data.Solves estimation with incomplete data. Obtain initial estimates for parameters.Obtain initial estimates for parameters. Iteratively use estimates for missing Iteratively use estimates for missing

data and continue until convergence.data and continue until convergence.


EM ExampleEM Example


EM AlgorithmEM Algorithm


Bayes TheoremBayes Theorem

Posterior Probability:Posterior Probability: P(hP(h1|x|xi)) Prior Probability:Prior Probability: P(h P(h1)) Bayes Theorem:Bayes Theorem:

Assign probabilities of hypotheses given a data Assign probabilities of hypotheses given a data value.value.


Bayes Theorem ExampleBayes Theorem Example Credit authorizations (hypotheses): Credit authorizations (hypotheses):

hh11=authorize purchase, h=authorize purchase, h2 = authorize after = authorize after further identification, hfurther identification, h3=do not authorize, =do not authorize, hh4= do not authorize but contact police= do not authorize but contact police

Assign twelve data values for all Assign twelve data values for all combinations of credit and income:combinations of credit and income:

From training data: P(hFrom training data: P(h11) = 60%; P(h) = 60%; P(h22)=20%; )=20%;

P(h P(h33)=10%; P(h)=10%; P(h44)=10%.)=10%.

1 2 3 4 Excellent x1 x2 x3 x4 Good x5 x6 x7 x8 Bad x9 x10 x11 x12


Bayes Example(cont’d)Bayes Example(cont’d) Training Data:Training Data:

ID Income Credit Class xi 1 4 Excellent h1 x4 2 3 Good h1 x7 3 2 Excellent h1 x2 4 3 Good h1 x7 5 4 Good h1 x8 6 2 Excellent h1 x2 7 3 Bad h2 x11 8 2 Bad h2 x10 9 3 Bad h3 x11 10 1 Bad h4 x9


Bayes Example(cont’d)Bayes Example(cont’d) Calculate P(xCalculate P(xii|h|hjj) and P(x) and P(xii))

Ex: P(xEx: P(x77|h|h11)=2/6; P(x)=2/6; P(x44|h|h11)=1/6; P(x)=1/6; P(x22|h|h11)=2/6; P(x)=2/6; P(x88||

hh11)=1/6; P(x)=1/6; P(xii|h|h11)=0 for all other x)=0 for all other xii.. Predict the class for xPredict the class for x44::

– Calculate P(hCalculate P(hjj|x|x44) for all h) for all hjj. . – Place xPlace x4 4 in class with largest value.in class with largest value.– Ex: Ex:

»P(hP(h11|x|x44)=(P(x)=(P(x44|h|h11)(P(h)(P(h11))/P(x))/P(x44)) =(1/6)(0.6)/0.1=1. =(1/6)(0.6)/0.1=1.

»xx4 4 in class hin class h11..

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Twenty Questions GameTwenty Questions Game


Decision TreesDecision Trees Decision Tree (DT):Decision Tree (DT):

– Tree where the root and each internal node is Tree where the root and each internal node is labeled with a question. labeled with a question.

– The arcs represent each possible answer to The arcs represent each possible answer to the associated question. the associated question.

– Each leaf node represents a prediction of a Each leaf node represents a prediction of a solution to the problem.solution to the problem.

Popular technique for classification; Leaf Popular technique for classification; Leaf node indicates class to which the node indicates class to which the corresponding tuple belongs.corresponding tuple belongs.


Decision Tree ExampleDecision Tree Example


Decision TreesDecision Trees

How do you build a good DT?How do you build a good DT? What is a good DT?What is a good DT? Ans: Supervised LearningAns: Supervised Learning


Comparing DTsComparing DTs

BalancedDeep


Decision Tree Induction is often based on Decision Tree Induction is often based on Information TheoryInformation Theory

SoSo


InformationInformation


DT Induction DT Induction

When all the marbles in the bowl are When all the marbles in the bowl are mixed up, little information is given. mixed up, little information is given.

When the marbles in the bowl are all When the marbles in the bowl are all from one class and those in the other from one class and those in the other two classes are on either side, more two classes are on either side, more information is given.information is given.

Use this approach with DT Induction !Use this approach with DT Induction !


Information/EntropyInformation/Entropy Given probabilitites pGiven probabilitites p11, p, p22, .., p, .., pss whose sum is whose sum is

1, 1, EntropyEntropy is defined as:is defined as:

Entropy measures the amount of randomness Entropy measures the amount of randomness or surprise or uncertainty.or surprise or uncertainty.

Goal in classificationGoal in classification– no surpriseno surprise– entropy = 0entropy = 0

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Neural Networks Neural Networks Based on observed functioning of human Based on observed functioning of human

brain. brain. (Artificial Neural Networks (ANN)(Artificial Neural Networks (ANN) Our view of neural networks is very simplistic. Our view of neural networks is very simplistic. We view a neural network (NN) from a We view a neural network (NN) from a

graphical viewpoint.graphical viewpoint. Alternatively, a NN may be viewed from the Alternatively, a NN may be viewed from the

perspective of matrices.perspective of matrices. Used in pattern recognition, speech Used in pattern recognition, speech

recognition, computer vision, and recognition, computer vision, and classification.classification.


Neural NetworksNeural Networks Neural Network (NN)Neural Network (NN) is a directed graph is a directed graph

F=<V,A> with vertices V={1,2,…,n} and arcs F=<V,A> with vertices V={1,2,…,n} and arcs A={<i,j>|1<=i,j<=n}, with the following A={<i,j>|1<=i,j<=n}, with the following restrictions:restrictions:– V is partitioned into a set of input nodes, VV is partitioned into a set of input nodes, V II, ,

hidden nodes, Vhidden nodes, VHH, and output nodes, V, and output nodes, VOO..– The vertices are also partitioned into layers The vertices are also partitioned into layers – Any arc <i,j> must have node i in layer h-1 Any arc <i,j> must have node i in layer h-1

and node j in layer h.and node j in layer h.– Arc <i,j> is labeled with a numeric value wArc <i,j> is labeled with a numeric value w ijij..– Node i is labeled with a function fNode i is labeled with a function f ii..


Neural Network ExampleNeural Network Example


NN NodeNN Node


NN Activation FunctionsNN Activation Functions

Functions associated with nodes in Functions associated with nodes in graph.graph.

Output may be in range [-1,1] or [0,1]Output may be in range [-1,1] or [0,1]


NN Activation FunctionsNN Activation Functions


NN LearningNN Learning

Propagate input values through graph.Propagate input values through graph. Compare output to desired output.Compare output to desired output. Adjust weights in graph accordingly.Adjust weights in graph accordingly.

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