Inference over distributions

• Inference / Reasoning


  THe process of derviing the truth or probability of a hyptoheses from a knowledge base and from specfici observations
• The constant P(y) serves as a normalisation factor Z that makes the resulting condtional distribution P(X|y) sum to 1.0
• The general inference by enumeration algorithm :

  Goal : compute P(X|y)

  Starting Point : P(X|y) = \frac{P(X,y)}{P(y)}
• The general inference by enumeration algorithm :

  (1) For each possible value combiation x \in Val(X), compute P(x,y) via enumeration

  (2) Compute denominator = normalisation constant P(y) from these P(x,y)

  (3) normalise P(X,y) to obtain conditional distribution P(X|y)
• The genreral inference-by-enumeration Algortihm :

  1. Compute P(X,y) = \sum_{z \in val(Z)} P(X,y,z)
  2. Compute normalisation const Z as $Z =$$P(y) =$$\sum_x P(x,y)$
  3. conditioning via renormalisation $P(X|y) =$$\frac{1}{Z} P(X,y)$