A novel sampler for Gauss-Hermite determinantal point processes with application to Monte Carlo integration

• URL: http://arxiv.org/abs/2203.08061v1
• Date: Tue, 15 Mar 2022 16:54:03 GMT
• Title: A novel sampler for Gauss-Hermite determinantal point processes with application to Monte Carlo integration
• Authors: Nicholas P Baskerville
• Abstract summary: We show how a new determinantal point process on $mathbbRd$ can be practically sampled and used to improve Monte Carlo integration. Samples from this new process are shown to be useful in Monte Carlo integration against the Gaussian measure.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Determinantal points processes are a promising but relatively under-developed tool in machine learning and statistical modelling, being the canonical statistical example of distributions with repulsion. While their mathematical formulation is elegant and appealing, their practical use, such as simply sampling from them, is far from straightforward.Recent work has shown how a particular type of determinantal point process defined on the compact multidimensional space $[-1, 1]^d$ can be practically sampled and further shown how such samples can be used to improve Monte Carlo integration.This work extends those results to a new determinantal point process on $\mathbb{R}^d$ by constructing a novel sampling scheme. Samples from this new process are shown to be useful in Monte Carlo integration against Gaussian measure, which is particularly relevant in machine learning applications.

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