Probabilistic Constraint Satisfaction with Non-Gaussian Noise

TL;DR

This paper extends a Bayesian algorithm for 3D point determination from uncertain constraints by allowing non-Gaussian noise, specifically mixtures of Gaussians, improving accuracy and enabling parallel computation.

Contribution

It introduces a mixture-of-Gaussians approach to handle arbitrary constraint distributions in Bayesian 3D structure determination.

Findings

Multicomponent constraint representation yields more accurate solutions.

The algorithm decomposes problems into unimodal subproblems for efficiency.

Parallel implementation is well-suited for the new method.

Abstract

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.