A Parallel Algorithm for Statistical Belief Refinement and its use in Causal Reasoning

This paper presents a new approach to efficient parallel computation of statistical inferences. This approach involves two heuristics, highest impact first and highest impact remaining , which control the speed of convergence and error estimation for an algorithm that iteratively refines degrees of belief. When applied to causal reasoning, this algorithm provides a performance solution to the qualification problem. This algorithm has been implemented and tested by a program called HITEST, which runs on parallel hardware. 1 Introduction A useful form of statistical inference derives a belief that an object is a member of a hypothesis set, given that the object is a known member of other sets. For example, we might wish to derive the probability that Tweety is in the set flyers, given that she is in the set birds. This probability can be obtained from the value of the statistic %(ilyers | birds), which captures the proportion of The set on the right-hand side of the conditional bar, birds in this case, is called the reference class [Kyburg, 1983] since it provides a reference from which to ascribe probabilities to assertions about its members belonging to other sets. It is generally agreed that a more specific reference class will tend to derive a more appropriate probability 1 In the case of Tweety, if we also know that she lives in Antarctica, it is prudent to incorporate this fact in the reference class, using the value of the statistic %(f lyers | birds Pi antarcticans) instead. However, if we take the principle of specificity to its logical extreme, we must incorporate all available knowledge about her into our reference class, including her size, color, age, parentage, etc. In complex domains, it Provided that the relevant statistics are believed with equal confidence. This paper ignores this issue in the interests of clarity and economy. See Kyburg [1989] and Loui [1987] for more details. may not be practical for a reasoner to consider all these potentially relevant factors. When choosing a reference class, an important consideration is the cost of computing (or indexing to) the statistic corresponding to that class. This aspect has not been addressed by any of the above approaches. This paper presents a solution to this problem. Given a set of primitive object-properties, this approach incre-mentally builds more specific reference classes by considering these properties in order of decreasing magnitude of their statistical impacts. As more properties …