Hei Chan

On the revision of probabilistic beliefs using uncertain evidence

We revisit the problem of revising probabilistic beliefs using uncertain evidence, and report results on several major issues relating to this problem: how should one specify uncertain evidence? How should one revise a probability distribution? How should one interpret informal evidential statements? Should, and do, iterated belief revisions commute? And what guarantees can be offered on the amount of belief change induced by a particular revision? Our discussion is focused on two main methods for probabilistic revision: Jeffreys rule of probability kinematics and Pearls method of virtual evidence, where we analyze and unify these methods from the perspective of the questions posed above.

When do numbers really matter

Common wisdom has it that small distinctions in the probabilities quantifying a belief network do not matter much for the results of probabilistic queries. Yet, one can develop realistic scenarios under which small variations in network probabilities can lead to significant changes in computed queries. A pending theoretical question is then to analytically characterize parameter changes that do or do not matter. In this paper, we study the sensitivity of probabilistic queries to changes in network parameters and prove some tight bounds on the impact that such parameters can have on queries. Our analytical results pinpoint some interesting situations under which parameter changes do or do not matter. These results are important for knowledge engineers as they help them identify influential network parameters. They also help explain some of the previous experimental results and observations with regards to network robustness against parameter changes.

A distance measure for bounding probabilistic belief change

We propose a distance measure between two probability distributions, which allows one to bound the amount of belief change that occurs when moving from one distribution to another. We contrast the proposed measure with some well known measures, including KL-divergence, showing how they fail to be the basis for bounding belief change as is done using the proposed measure. We then present two practical applications of the proposed distance measure: sensitivity analysis in belief networks and probabilistic belief revision. We show how the distance measure can be easily computed in these applications, and then use it to bound global belief changes that result from either the perturbation of local conditional beliefs or the accommodation of soft evidence. Finally, we show that two well known techniques in sensitivity analysis and belief revision correspond to the minimization of our proposed distance measure and, hence, can be shown to be optimal from that viewpoint.