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.
Interpretable Probabilistic Medical Image Segmentation via Gaussian Process with Explicit Modelling of Annotation Bias and Variability
University College London（伦敦大学学院）；Queen Mary University of London（伦敦玛丽女王大学）；University of Oxford（牛津大学）；University College London Hospitals NHS Trust（伦敦大学学院医院NHS信托基金会）；Imperial College Healthcare（帝国理工学院医疗保健）
Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting
School of Computation, Information and Technology, Technical University of Munich（计算、信息与技术学院，慕尼黑技术大学）；Munich Data Science Institute（慕尼黑数据科学研究所）；Munich Center for Machine Learning（慕尼黑机器学习中心）
