By John G. Webster (Editor)
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Extra info for 31.Knowledge and Data Engineering
The choice of prior is somewhat arbitrary since the update process depends only on the prior being a beta. A simple uniform prior in each cell of the table for variable Xi would be ͱ(Ͱ ϭ 1, Ͷ ϭ ͉D Xi͉ Ϫ 1). With the priors established, the induction of the quantitative structure of the network is simply a matter of incrementing the Ͱ and Ͷ statistics of each conditional probability for each relevant sample seen. A sample is relevant to the conditional probability Pr(Xi ϭ xik͉⌸i ϭ i[ j]) if the sample is consistent with ⌸i ϭ i[ j].
The cost of computation can be measured by the time and resource cost or by opportunity cost. Opportunity cost is the value of a lost opportunity. Being able to precisely measure the value of additional thought would provide a firm grasp on when it makes sense to stop thinking and start acting. The reality, however, is that both the cost of additional computation and the expected gain (or loss) in decision quality are values that are inherently uncertain, context-dependent, and highly subjective.
F (s p θi, j,k ) Choose some prior distribution (i, j,k) for i, j,k. The posterior distribution (i, j,k͉s), which is the estimate of i, j,k, is then f p (s θi, j,k )ξ (θi, j,k ) f f p (s θi, j,k )ξ (θi, j,k )dθi, j,k for θi, j,k ∈ which is proportional to f p(s͉i, j,k)(i, j,k). When sampling with replacement from the database D, a standard description of the sample distribution f(sl͉i, j,k) is as a Bernoulli distribution; in a relevant sample, there is a i, j,k chance that the sample will have Xi assigned to xik (given that the parents ⌸i have the assignment i[ j]), and a 1 Ϫ i, j,k chance that Xi will have a different value.
31.Knowledge and Data Engineering by John G. Webster (Editor)