Preliminaries: Distributions

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Presentation transcript:

Preliminaries: Distributions Probabilistic Graphical Models Introduction Preliminaries: Distributions

Joint Distribution Intelligence (I) Difficulty (D) Grade (G) I D G Prob. i0 d0 g1 0.126 g2 0.168 g3 d1 0.009 0.045 i1 0.252 0.0224 0.0056 0.06 0.036 0.024 Intelligence (I) i0 (low), i1 (high), Difficulty (D) d0 (easy), d1 (hard) Grade (G) g1 (A), g2 (B), g3 (C) Probability space Parameters and independent parameters

Conditioning condition on g1 I D G Prob. i0 d0 g1 0.126 g2 0.168 g3 d1 0.009 0.045 i1 0.252 0.0224 0.0056 0.06 0.036 0.024 condition on g1

Conditioning: Reduction Prob. i0 d0 g1 0.126 d1 0.009 i1 0.252 0.06

Conditioning: Renormalization Prob. i0 d0 g1 0.126 d1 0.009 i1 0.252 0.06 I D Prob. i0 d0 0.282 d1 0.02 i1 0.564 0.134 P(I, D, g1) P(I, D | g1) 0.447 0.447

Marginalization Marginalize I I D Prob. i0 d0 0.282 d1 0.02 i1 0.564 0.134 D Prob. d0 0.846 d1 0.154