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goplayer:betanode [2013/10/09 09:30]
aiartificer Better define variance for Dirichlet formula for large numbers
goplayer:betanode [2013/12/12 12:16] (current)
aiartificer [Beta Distribution as Fundamental Bayesian Network Node]
Line 98: Line 98:
 for large K, only one hyperparameter being updated, and that one hyperparameter is large: for large K, only one hyperparameter being updated, and that one hyperparameter is large:
  
-<m>Var[X_{i}] = {alpha}_{i}/{{alpha}_{i}^3}</m>+<m>Var[X_{i}] = {alpha}_{i}/{{{alpha}_{i}}^3} = 1/{{alpha}_{i}}^2</m>
  
 What if I defined Bayesian networks only using Bernoulli distributions?  What expressive power would I loose?  What would be the computational cost?  Nodes would have to be deterministic.  Essential would be subjective logic.  Would have binomial distributions and beta priors.  When beta prior reaches near certainty of 1, propositional clause could be promoted.  Set of propositional clauses of the same "pattern" could be promoted to predicate clause where subjective logic is applied to clause and whether observations show clause to be predominantly true. What if I defined Bayesian networks only using Bernoulli distributions?  What expressive power would I loose?  What would be the computational cost?  Nodes would have to be deterministic.  Essential would be subjective logic.  Would have binomial distributions and beta priors.  When beta prior reaches near certainty of 1, propositional clause could be promoted.  Set of propositional clauses of the same "pattern" could be promoted to predicate clause where subjective logic is applied to clause and whether observations show clause to be predominantly true.

goplayer/betanode.1381336211.txt.gz · Last modified: 2013/10/09 09:30 by aiartificer