Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature
This addresses sampling inefficiencies in complex statistical models for researchers in computational statistics and machine learning, though it appears incremental as an extension of existing Riemannian slice sampling methods.
The paper tackles the problem of sampling from multimodal distributions with strong curvature, where traditional MCMC methods struggle, by proposing a method that generalizes Hit-and-Run slice sampling to approximate geodesics as solutions to differential equations, enabling exploration of regions with strong curvature and rapid mode transitions.
Traditional Markov Chain Monte Carlo sampling methods often struggle with sharp curvatures, intricate geometries, and multimodal distributions. Slice sampling can resolve local exploration inefficiency issues, and Riemannian geometries help with sharp curvatures. Recent extensions enable slice sampling on Riemannian manifolds, but they are restricted to cases where geodesics are available in a closed form. We propose a method that generalizes Hit-and-Run slice sampling to more general geometries tailored to the target distribution, by approximating geodesics as solutions to differential equations. Our approach enables the exploration of the regions with strong curvature and rapid transitions between modes in multimodal distributions. We demonstrate the advantages of the approach over challenging sampling problems.