Fast Mixing Markov Chains for Strongly Rayleigh Measures, DPPs, and Constrained Sampling

Inference for determinantal point processes without spectral knowledge

Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel $K$. DPPs possess desirable properties, such as exact sampling or analyticity of the moments, but learning the parameters of kernel $K$ through likelihood-based inference is not straightforward. First, the kernel that appears in the likelihood is not $K$, but another kernel $L$ related to $K$ through an often intractable spectral decomposition. This issue is typically bypassed in machine learning by directly parametrizing th…

Markov Properties of Discrete Determinantal Point Processes

Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and direct way. Discrete DPPs have become popular and computationally tractable models for solving several machine learning tasks that require the selection of diverse objects, and have been successfully applied in numerous real-life problems. Despite their popularity, the statistical properties of such models have not been adequately explored. In this note, we deri…

Scalable MCMC Sampling for Nonsymmetric Determinantal Point Processes

A determinantal point process (DPP) is an elegant model that assigns a probability to every subset of a collection of $n$ items. While conventionally a DPP is parameterized by a symmetric kernel matrix, removing this symmetry constraint, resulting in nonsymmetric DPPs (NDPPs), leads to significant improvements in modeling power and predictive performance. Recent work has studied an approximate Markov chain Monte Carlo (MCMC) sampling algorithm for NDPPs restricted to size-$k$ subsets (called $k$-NDPPs). However, the runtime of this approach is quadratic in $n$, making it infeasible for large-s…

单位广义瑞利分布下多分量应力强度可靠性的最优设计

Optimal Designs in Multicomponent Stress Strength Reliability for the Unit Generalized Rayleigh Distribution

本文针对逐步II型删失下多分量系统的应力强度可靠性问题，构建统一推断框架，结合多种估计方法与贝叶斯分析，经模拟验证后用实际数据应用，并确定最优逐步删失策略。

Fast Sampling for Strongly Rayleigh Measures with Application to Determinantal Point Processes

In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures. As an important corollary, we obtain a fast mixing Markov Chain sampler for Determinantal Point Processes.

使用Wiener混沌展开和Malliavin微分的衰落持续时间随机分析：基于自适应SGD的最优重要性采样

Stochastic Analysis of Fade Duration Using Wiener Chaos Expansion and Malliavin Calculus: Optimal Importance Sampling via Adaptive SGD

提出结合Wiener混沌展开、Malliavin微分和自适应重要性采样的框架，高精度估计无线信道衰落持续时间分布，实现方差降低839-2516倍，相对误差低于0.5%。