Bayes' Nets

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  • Probability
    • Marginal Distribution
    • Conditional Probabilities
      • Normalization Trick
    • Inference
      • Inference by Enumeration
      • Inference with Bayes’ Rules
  • Bayes’ Nets
    • Independence: $X \independent Y \iff \forall x, y: P(x, y) = P(x)P(y)$
      • $\forall x, y: P(x|y) = P(x)$
    • Conditional Independence: $\ConditionallyIndependent{X}{Y}{Z} \iff \forall x, y, z: P(x, y |z)= P(x|z)P(y|z)$
      • $\forall x, y, z: P(x|z,y) = P(x |z)$
    • D-Separation
      • Query: $\ConditionallyIndependent{X_i}{X_j}{{X_{k_1}, \dots, X_{k_n}}}$?
      • Check all (undirected!) paths between $X_i$ and $X_j$
        • if one or more active -> independence not guaranteed
        • all paths are inactive -> independence guaranteed
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