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Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes

arXiv 1602.05242 ↗First posted 16 Feb 2016cs.LG cs.DS math.PRcited by 24

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Abstract (arXiv)

Strongly Rayleigh distributions are natural generalizations of product and determinantal probability distributions and satisfy strongest form of negative dependence properties. We show that the "natural" Monte Carlo Markov Chain (MCMC) is rapidly mixing in the support of a em homogeneous strongly Rayleigh distribution. As a byproduct, our proof implies Markov chains can be used to efficiently generate approximate samples of a k-determinantal point process. This answers an open question raised by Deshpande and Rademacher.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Feb 2016.

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Citing papers per year: 2021: 5; 2022: 8; 2023: 4; 2024: 2; 2025: 3; 2026: 2.

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  1. 2022Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluationscited by 31
  2. 2021Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processescited by 23
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  7. 2024Recent and Upcoming Developments in Randomized Numerical Linear Algebra for Machine Learningcited by 11
  8. 2022Optimal Sublinear Sampling of Spanning Trees and Determinantal Point Processes via Average-Case Entropic Independencecited by 8
  9. 2024Batch Active Learning of Reward Functions from Human Preferencescited by 8
  10. 2021Batch Bayesian Optimization on Permutations using the Acquisition Weighted Kernelcited by 5
  11. 2022Lazy and Fast Greedy MAP Inference for Determinantal Point Processcited by 5
  12. 2022Dual Representation Learning for Out-of-Distribution Detectioncited by 4
12 more
  1. 2021From Sampling to Optimization on Discrete Domains with Applications to Determinant Maximizationcited by 3
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  3. 2022Scalable Sampling for Nonsymmetric Determinantal Point Processescited by 2
  4. 2022Scalable MCMC Sampling for Nonsymmetric Determinantal Point Processescited by 2
  5. 2023Designing Data: Proactive Data Collection and Iteration for Machine Learningcited by 2
  6. 2025A Sketch-and-Project Analysis of Subsampled Natural Gradient Algorithmscited by 2
  7. 2022One-pass additive-error subset selection for ℓp subspace approximationcited by 1
  8. 2025Establishing Reliability Metrics for Reward Models in Large Language Modelscited by 1
  9. 2021On Subspace Approximation and Subset Selection in Fewer Passes by MCMC Samplingcited by 0
  10. 2025Decentralized Gaussian Process Classification and an Application in Subsea Roboticscited by 0
  11. 2026Greedy Volume Maximization of Gradient Embeddings for Long-Tailed Frame-Level Bioacoustic Active Learningcited by 0
  12. 2026Fair Multi-View Determinantal Coresets via Adaptive NEPvcited by 0