Characterizing the principle of minimum cross-entropy within a conditional-logical framework

AbstractThe principle of minimum cross-entropy (ME-principle) is often used as an elegant and powerful tool to build up complete probability distributions when only partial knowledge is available. The inputs it may be applied to are a prior distribution P and some new information R, and it yields as a result the one distribution P∗ that satisfies R and is closest to P in an information-theoretic sense. More generally, it provides a “best” solution to the problem “How to adjust P to R?”In this paper, we show how probabilistic conditionals allow a new and constructive approach to this important principle. Though popular and widely used for knowledge representation, conditionals quantified by probabilities are not easily dealt with. We develop four principles that describe their handling in a reasonable and consistent way, taking into consideration the conditional-logical as well as the numerical and probabilistic aspects. Finally, the ME-principle turns out to be the only method for adjusting a prior distribution to new conditional information that obeys all these principles.Thus a characterization of the ME-principle within a conditional-logical framework is achieved, and its implicit logical mechanisms are revealed clearly

Belief Dynamics: (Epistemo)logical Investigations

C.S. Peirce's and Isaac Levi's accounts of the belief-doubt-belief model are discussed and evaluated. It is argued that the contemporary study of belief change has metamorphosed into a branch of philosophical logic where empirical considerations have become obsolete. A case is made for reformulations of belief change systems that do allow for empirical tests. Last, a belief change system is presented that (1) uses finite representations of information, (2) can adequately deal with inconsistencies, (3) has finite operations of change, (4) can do without extra-logical elements, and (5) only licenses consistent beliefs

A Bayesian Abduction Model For Sensemaking

This research develops a Bayesian Abduction Model for Sensemaking Support (BAMSS) for information fusion in sensemaking tasks. Two methods are investigated. The first is the classical Bayesian information fusion with belief updating (using Bayesian clustering algorithm) and abductive inference. The second method uses a Genetic Algorithm (BAMSS-GA) to search for the k-best most probable explanation (MPE) in the network. Using various data from recent Iraq and Afghanistan conflicts, experimental simulations were conducted to compare the methods using posterior probability values which can be used to give insightful information for prospective sensemaking. The inference results demonstrate the utility of BAMSS as a computational model for sensemaking. The major results obtained are: (1) The inference results from BAMSS-GA gave average posterior probabilities that were 103 better than those produced by BAMSS; (2) BAMSS-GA gave more consistent posterior probabilities as measured by variances; and (3) BAMSS was able to give an MPE while BAMSS-GA was able to identify the optimal values for kMPEs. In the experiments, out of 20 MPEs generated by BAMSS, BAMSS-GA was able to identify 7 plausible network solutions resulting in less amount of information needed for sensemaking and reducing the inference search space by 7/20 (35%). The results reveal that GA can be used successfully in Bayesian information fusion as a search technique to identify those significant posterior probabilities useful for sensemaking. BAMSS-GA was also more robust in overcoming the problem of bounded search that is a constraint to Bayesian clustering and inference state space in BAMSS