Introduction to Graphical Models

Part 2 of 2

Lecture 31 of 41

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Graphical Models Overview [1]:

Bayesian Networks

P(20s, Female, Low, Non-Smoker, No-Cancer, Negative, Negative)

= P(T) · P(F) · P(L | T) · P(N | T, F) · P(N | L, N) · P(N | N) · P(N | N)

•Conditional Independence

–X is conditionally independent (CI) from Y given Z (sometimes written X Y | Z) iff

P(X | Y, Z) = P(X | Z) for all values of X, Y, and Z

–Example: P(Thunder | Rain, Lightning) = P(Thunder | Lightning) T R | L

•Bayesian (Belief) Network

–Acyclic directed graph model B = (V, E, ) representing CI assertions over

–Vertices (nodes) V: denote events (each a random variable)

–Edges (arcs, links) E: denote conditional dependencies

•Markov Condition for BBNs (Chain Rule):

•Example BBN

n

iiin21 Xparents |XPX , ,X,XP

1

X1 X3

X4

X5

Age

Exposure-To-Toxins

Smoking

Cancer X6

Serum Calcium

X2

Gender X7

Lung Tumor

sDescendantNon

Parents

sDescendant

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