Uncertainty-4

# Uncertainty-4 - From Data To Understanding In machine...

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1 From Data To Understanding In machine learning, maintain critical perspective Making predictions is only part of the story Also try to get some understanding of the domain Example True statement: palm size negatively correlates with life expectancy o The larger your palm size, the shorter your life (on average) Why? o Women have smaller palms than men on average o Women live 5 years longer than men on average Sometimes you need better model of your domain! Bayesian Networks Bayesian Network Graphical representation of joint probability distribution o Node: random variable o Arc (X, Y): variable X has direct influence on variable Y Call X a “parent” of Y o Each node X has conditional probability: P(X | parents(X)) o Graph has no cycles (loops by following arcs) Called “Directed Acyclic Graph” (DAG) Palm size Gender Life Expectancy Conditional independence encoded in network Each node (variable) is conditionally independent of its non-descendants, given it parents In network above Palm Size and Life Expectancy are conditionally independent, given Gender o Formally: P(PS, LE | G) = P(PS | G) P(LE | G) Network structure provides insight about domain Network Shows Conditional Independence Palm size Gender Life Expectancy Each node has conditional probability table (CPT) For node X: P(X | Parents(X)) Conditional independence modularizes joint probability: Conditional Probability Tables P(G = M) = 0.49 P(G = F) = 0.51 P(PS = L | G = M) = 0.45 P(PS = M | G = M) = 0.35 P(PS = S | G = M) = 0.20 P(PS = L | G = F) = 0.10 P(PS = M | G = F) = 0.30 P(PS = S | G = F) = 0.60 P(LE = < 70 | G = M) = 0.20 P(LE = 70-80 | G = M) = 0.50 P(LE = > 80 | G = M) = 0.30 P(LE = < 70 | G = F) = 0.10 P(LE = 70-80 | G = F) = 0.35 P(LE = > 80 | G = F) = 0.55 n i i i n X X P X X X P 1 2 1 )) ( Parents | ( ) ,..., , ( Palm size Gender Life Expectancy

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2 Each node has conditional probability table (CPT) Reduces number of parameters needed in model
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## This document was uploaded on 12/24/2011.

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Uncertainty-4 - From Data To Understanding In machine...

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