Probability - Caltech

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Problems with high-‐dim. distribu)ons ! Suppose we have n proposi)onal symbols ! How many parameters do we need to specify P(X 1 =x 1 ,…,X n =x n )? 24
Independent RVs ! What if RVs are independent? RVs X 1 ,…,X n are independent, if for any assignment P(X 1 =x 1 ,…,X n =x n ) = P(x 1 ) P(x 2 ) … P(x n ) ! How many parameters are needed in this case? ! Independence too strong assump)on… Is there something weaker? 25
Page 1 and 2: Introduc)on to Ar)ficial Intellig
Page 3 and 4: Announcements ! Grading: AvianAske
Page 5 and 6: Quan)fying Uncertainty ! So far,
Page 7 and 8: Decision making under uncertaint
Page 9 and 10: Why use probabili)es? Related ev
Page 11 and 12: Interpreta)on of probabili)es ! P
Page 13 and 14: Examples ! Bernoulli distribu)on:
Page 15 and 16: Example: Gaussian distribu)on !
Page 17 and 18: Example: Mul)variate Gaussian 17
Page 19 and 20: Marginal distribu)ons What is P(
Page 21 and 22: Condi)onal distribu)ons ! Formal
Page 23: Posterior inference ! Suppose we

Probability - Caltech

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