论文标题
用于蒙特卡洛集成的高斯 - 热矿确定点过程的新型采样器
A novel sampler for Gauss-Hermite determinantal point processes with application to Monte Carlo integration
论文作者
论文摘要
确定点过程是机器学习和统计建模的一个有前途但相对较不发达的工具，是具有排斥力的分布的规范统计示例。尽管它们的数学表述优雅且吸引人，但它们的实际用途（例如简单地从中取样）远非直接。 $ \ mathbb {r}^d $通过构建新颖的采样方案。该新过程中的样本被证明可用于针对高斯措施的蒙特卡洛整合，这在机器学习应用中尤其重要。
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.
