A Method for Finding Independently Distributed Probability Models that Satisfy Order Contraints

This research investigates a method that attempts to represent a database of expert decisions as an independent probability distribution. To implement this representation, our method searches for a simple probability model that exhibits maximum independence property and preserves a given set of inequality constraints. We will show that nding such a representation can be formulated as a search problem over a log probability space with a representational complexity in a linear order of the number of variables. We will show the search can be achieved by employing linear programming technique in combination with a greedy (best rst) search algorithm. Introduction We present a method that takes a joint probability distribution of n variables and a set of inequality constraints to derive a simpler probability distribution. Each inequality in the constraint set is consistent with the probability distribution, and is in the form of either Pr(X) Pr(Y ) or Pr(X) (or ) K ; where X and Y are subsets of the n variables, and K is a constant. Our proposed method identi es an alternative probability distribution with two properties: rst, each variable is independent of each other; second, it preserves the set of inequality constraints. We can apply our technique to the problem of nding simple (by the kolmogrov complexity measure) probability models that mimic the behavior of expert decision makers. Our system can take a set of decisions as its database, where the context (the observations made previous to the decision) and the costs