A Probabilistic Algorithm for Calculating Structure: Borrowing from Simulated Annealing

TL;DR

This paper introduces a Bayesian algorithm utilizing an extended, iterated Kalman filter combined with a simulated annealing heuristic to determine 3D point structures from probabilistic constraints, applicable to molecular modeling.

Contribution

It presents a novel probabilistic method that integrates Bayesian inference, Kalman filtering, and simulated annealing for 3D structure calculation from noisy data.

Findings

Demonstrates convergence on synthetic data

Shows applicability to molecular structure determination

Provides a flexible framework for probabilistic constraints

Abstract

We have developed a general Bayesian algorithm for determining the coordinates of points in a three-dimensional space. The algorithm takes as input a set of probabilistic constraints on the coordinates of the points, and an a priori distribution for each point location. The output is a maximum-likelihood estimate of the location of each point. We use the extended, iterated Kalman filter, and add a search heuristic for optimizing its solution under nonlinear conditions. This heuristic is based on the same principle as the simulated annealing heuristic for other optimization problems. Our method uses any probabilistic constraints that can be expressed as a function of the point coordinates (for example, distance, angles, dihedral angles, and planarity). It assumes that all constraints have Gaussian noise. In this paper, we describe the algorithm and show its performance on a set of synthetic data to illustrate its convergence properties, and its applicability to domains such ng molecular structure determination.