Probabilistic Constraint Satisfaction with Non-Gaussian Noise
Russ Altman, Cheng Chen, William Poland, Jaswinder Singh
We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited, however, by the requirement that the uncertainty in the constraints be normally distributed. In this paper, we present an extension of the original algorithm that allows constraint uncertainty to be represented as a mixture of Gaussians, and thereby allows arbitrary constraint distributions. We illustrate the performance of this algorithm on a problem drawn from the domain of molecular structure determination, in which a multicomponent constraint representation produces a much more accurate solution than the old single component mechanism. The new mechanism uses mixture distributions to decompose the problem into a set of independent problems with unimodal constraint uncertainty. The results of the unimodal subproblems are periodically recombined using Bayes' law, to avoid combinatorial explosion. The new algorithm is particularly suited for parallel implementation.
Keywords: constraint satisfaction, Bayesian measurement update, distance constraints, Kalman Fi
PS Link: file://camis.stanford.edu/pub/altman/UAI94.RTF
PDF Link: /papers/94/p15-altman.pdf
AUTHOR = "Russ Altman
and Cheng Chen and William Poland and Jaswinder Singh",
TITLE = "Probabilistic Constraint Satisfaction with Non-Gaussian Noise",
BOOKTITLE = "Proceedings of the Tenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-94)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1994",
PAGES = "15--22"