2014/10/30 by Shirin Golchi, Golchi, Shirin, David A. Campbell +1
Computer Science · Mathematics · #Algorithm #Bayesian Methods and Mixture Models #Computer science #Constraint (computer-aided design) #Distribution (mathematics) #FOS: Computer and information sciences #Filter (signal processing) #Gaussian Processes and Bayesian Inference #Hybrid Monte Carlo #Importance sampling #Markov Chains and Monte Carlo Methods #Markov chain Monte Carlo #Matching (statistics) #Mathematical optimization #Mathematics #Methodology (stat.ME) #Monte Carlo method #Resampling #Sampling (signal processing) #Sequence (biology) #Statistics #Transformation (genetics) #stat.ME
paper · pdf · doi:10.48550/arxiv.1410.8209
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2014/10/30 · arxiv created 2015/02/25 · arxiv updated 2015/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model, transformation of constraints into features on the parameter space may not be possible. Difficulties in sampling from the posterior distribution as a result of incorporation of constraints into the model is a common challenge leading to truncations in the parameter space and inefficient sampling algorithms. We propose a variant of sequential Monte Carlo algorithm for posterior sampling in presence of constraints by defining a sequence of densities through the imposition of the constraint. Particles generated from an unconstrained or mildly constrained distribution are filtered and moved through sampling and resampling steps to obtain a sample from the fully constrained target distribution. General and model specific forms of constraints enforcing strategies are defined. The Sequentially Constrained Monte Carlo algorithm is demonstrated on constraints defined by monotonicity of a function, densities constrained to low dimensional manifolds, adherence to a theoretically derived model, and model feature matching.