Evidence Propagation and Value of Evidence on Influence Diagrams

Abstract

In this paper, we introduce evidence propagation operations on influence diagrams, a concept of the value of evidence to measure the impact/value of new observations/experimentation, and a concept of the value of revelation. Evidence propagation operations are critical for the computation of the value of evidence, general update and inference operations in normative expert systems that are based on the influence diagram (generalized Bayesian network) paradigm. The value of evidence allows us to compute the outcome sensitivity directly defined as the maximum difference among the values of evidence, and the value of perfect information, as the expected value of the values of evidence. We define the value of revelation as the optimal value of the values of evidence. We discuss the relationship between the value of revelation and the value of control. We also discuss implementation issues related to computation of the value of evidence and the value of perfect information.

Explanation of Bayesian Networks and Influence Diagrams in Elvira

“…In order to avoid confusions, we must mention that the meaning of evidence in Elvira is very different from its meaning in some methods oriented to the computation of the value of information in IDs, such as [36], [37], [38]. For those methods, the introduction of evidence e leads to a different decision problem in which the values of the variables in E would be known with certainty before making any decision.…”

“…For instance, introducing evidence {+x} in the ID in Fig. 1 would mean that X were known when making decisions T and D. Therefore, the expected utility of the new decision problem, which we call "Ezawa's scenario" [38], would be…”

“…As mentioned above, we also intend to implement new facilities for introducing evidence in Ezawa's style [38] and for computing the value of information-see Sec. IV-D.1.…”

Influence Diagrams for Neonatal Jaundice Management

“…In our last version of IctNeo, we take advantage of the evidence propagation operation [2], once again reducing complexity. Moreover, the system is able to avoid the computation of many expected utilities by incorporating knowledge about the constraints on decisions in the grammar script: at the time when the first decision node is removed during the process, the value node has already inherited all the decision nodes, and its table is cut by looking for the sequences that do not meet the constraints.…”

Efficient non-myopic value-of-information computation for influence diagrams

“…In the past several years, a few methods have been proposed to compute VOI in IDs. Ezawa [8] introduces some basic concepts about VOI and evidence propagation in IDs. Dittmer and Jensen [7] present a method for calculating myopic VOI in IDs based on the strong junction tree framework [15].…”