Nyström Kernel Stein Discrepancy Tests

• URL: http://arxiv.org/abs/2605.25173v1
• Date: Sun, 24 May 2026 17:10:19 GMT
• Title: Nyström Kernel Stein Discrepancy Tests
• Abstract summary: We show that the Nystrm-accelerated method performs statistically on-par with the quadratic-time approach, while requiring substantially smaller runtime.<n>Our numerical results show that the Nystrm-accelerated method performs statistically on-par with the quadratic-time approach, while requiring substantially smaller runtime.
• Score: 7.456820555256198
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kernel Stein discrepancy (KSD) is among the most popular goodness-of-fit (GoF) measures on general domains with a large number of successful deployments. One of the main applications of KSD is in constructing powerful GoF tests. However, tests relying on the classical U-/V-statistic-based KSD estimators have two major drawbacks. (i) Their runtime scales quadratically in the number of samples. (ii) Their asymptotic null distribution is computationally intractable in most cases, typically handled by bootstrapping. While it is known that the Nyström method permits accelerating KSD estimation with no loss of statistical accuracy under mild conditions, to the best of our knowledge, the fundamental question of its impact on bootstrap-based GoF testing is open; resolving this question is the focus of the current paper. In particular, we prove that the key properties of the quadratic-time bootstrapped KSD-based GoF test (asymptotic level and local consistency) are preserved by its Nyström acceleration. We numerically demonstrate the efficiency of the accelerated KSD estimator and bootstrap in the context of GoF testing of spherical and functional data. Our numerical results show that the Nyström-accelerated method performs statistically on-par with the quadratic-time approach, while requiring substantially smaller runtime.

Related papers

• From Signals to Transfer: A Factorised Study of Probe-Based Uncertainty Estimation in Large Language Models [51.470637128942336]
  We propose a factorised study of probe-based uncertainty estimation (UE) under matched conditions.<n>Our results show that raw hidden states and attention features are difficult to outperform in-domain.<n>We train benchmark-based pretrained probes that transfer reasonably well to open-ended factual generation.
  arXiv  Detail & Related papers  (2026-06-26T03:23:15Z)
• Semiparametric KSD test: unifying score and distance-based approaches for goodness-of-fit testing [0.0]
  We show that a score-based Goodness-of-fit (GoF) test is equivalent to tests based on integral probability metrics (IPMs) indexed by a function class.<n>We propose a new nonparametric score-based GoF test through a special class of IPM induced by kernelized Stein's function class.<n>Our method achieves power comparable to task-specific normality tests such as Anderson-Darling and Lilliefors.
  arXiv  Detail & Related papers  (2025-12-23T03:05:26Z)
• Nyström Kernel Stein Discrepancy [4.551160285910023]
  We propose a Nystr"om-based KSD acceleration -- with runtime $mathcal Oleft(mn+m3right)$ for $n$ samples and $mll n$ Nystr"om points.<n>We also show the $sqrt n$-consistency of the quadratic-time KSD estimator.
  arXiv  Detail & Related papers  (2024-06-12T16:50:12Z)
• Minimax Optimal Goodness-of-Fit Testing with Kernel Stein Discrepancy [13.429541377715298]
  We explore the minimax optimality of goodness-of-fit tests on general domains using the kernelized Stein discrepancy (KSD)<n>KSD is a powerful framework for goodness-of-fit testing, but its statistical optimality remains largely unexplored.<n>We introduce an adaptive test capable of achieving minimax optimality up to a logarithmic factor by adapting to unknown parameters.
  arXiv  Detail & Related papers  (2024-04-12T07:06:12Z)
• A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport [92.96250725599958]
  Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. We show that our SSN method achieves a global convergence rate of $O (1/sqrtk)$, and a local quadratic convergence rate under standard regularity conditions.
  arXiv  Detail & Related papers  (2023-10-21T18:48:45Z)
• On the Theories Behind Hard Negative Sampling for Recommendation [51.64626293229085]
  We offer two insightful guidelines for effective usage of Hard Negative Sampling (HNS) We prove that employing HNS on the Personalized Ranking (BPR) learner is equivalent to optimizing One-way Partial AUC (OPAUC) These analyses establish the theoretical foundation of HNS in optimizing Top-K recommendation performance for the first time.
  arXiv  Detail & Related papers  (2023-02-07T13:57:03Z)
• Controlling Moments with Kernel Stein Discrepancies [74.82363458321939]
  Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation.<n>We first show that standard KSDs used for weak convergence control fail to control moment convergence.<n>We then provide sufficient conditions under which alternative diffusion KSDs control both moment and weak convergence.
  arXiv  Detail & Related papers  (2022-11-10T08:24:52Z)
• A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spaces [6.437931786032493]
  Kernel Stein discrepancy (KSD) is a kernel-based measure of discrepancy between probability measures. We provide the first analysis of KSD in the generality of data lying in a separable Hilbert space. This allows us to prove that KSD can separate measures and thus is valid to use in practice.
  arXiv  Detail & Related papers  (2022-06-09T15:04:18Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Critical Parameters for Scalable Distributed Learning with Large Batches and Asynchronous Updates [67.19481956584465]
  It has been experimentally observed that the efficiency of distributed training with saturation (SGD) depends decisively on the batch size and -- in implementations -- on the staleness. We show that our results are tight and illustrate key findings in numerical experiments.
  arXiv  Detail & Related papers  (2021-03-03T12:08:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.