Probabilistic Constraint Satisfaction with Non-Gaussian Noise
This work addresses a specific bottleneck in molecular structure determination by enabling more flexible uncertainty modeling, but it is incremental as it builds directly on a previous method.
The paper tackles the limitation of requiring normally distributed uncertainty in a Bayesian algorithm for 3D coordinate determination from constraints, by extending it to handle arbitrary distributions using Gaussian mixtures, resulting in a much more accurate solution in molecular structure determination.
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.