KSD Aggregated Goodness-of-fit Test

• URL: http://arxiv.org/abs/2202.00824v6
• Date: Wed, 20 Dec 2023 23:49:03 GMT
• Title: KSD Aggregated Goodness-of-fit Test
• Authors: Antonin Schrab and Benjamin Guedj and Arthur Gretton
• Abstract summary: We introduce a strategy to construct a test, called KSDAgg, which aggregates multiple tests with different kernels. We provide non-asymptotic guarantees on the power of KSDAgg. We find that KSDAgg outperforms other state-of-the-art adaptive KSD-based goodness-of-fit testing procedures.
• Score: 38.45086141837479
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We investigate properties of goodness-of-fit tests based on the Kernel Stein Discrepancy (KSD). We introduce a strategy to construct a test, called KSDAgg, which aggregates multiple tests with different kernels. KSDAgg avoids splitting the data to perform kernel selection (which leads to a loss in test power), and rather maximises the test power over a collection of kernels. We provide non-asymptotic guarantees on the power of KSDAgg: we show it achieves the smallest uniform separation rate of the collection, up to a logarithmic term. For compactly supported densities with bounded model score function, we derive the rate for KSDAgg over restricted Sobolev balls; this rate corresponds to the minimax optimal rate over unrestricted Sobolev balls, up to an iterated logarithmic term. KSDAgg can be computed exactly in practice as it relies either on a parametric bootstrap or on a wild bootstrap to estimate the quantiles and the level corrections. In particular, for the crucial choice of bandwidth of a fixed kernel, it avoids resorting to arbitrary heuristics (such as median or standard deviation) or to data splitting. We find on both synthetic and real-world data that KSDAgg outperforms other state-of-the-art quadratic-time adaptive KSD-based goodness-of-fit testing procedures.

Related papers

• Supervised Kernel Thinning [6.6157730528755065]
  kernel thinning algorithm of Dwivedi & Mackey (2024) provides a better-than-i.i.d. compression of a generic set of points. We generalize the KT algorithm to speed up supervised learning problems involving kernel methods.
  arXiv  Detail & Related papers  (2024-10-17T16:48:51Z)
• 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. We show its $sqrtn$-consistency with a classical sub-Gaussian assumption, and demonstrate its applicability for goodness-of-fit testing on a suite of benchmarks.
  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) The KSD framework offers a flexible approach for goodness-of-fit testing, avoiding strong distributional assumptions. 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)
• Byzantine-resilient Federated Learning With Adaptivity to Data Heterogeneity [54.145730036889496]
  This paper deals with Gradient learning (FL) in the presence of malicious attacks Byzantine data. A novel Average Algorithm (RAGA) is proposed, which leverages robustness aggregation and can select a dataset.
  arXiv  Detail & Related papers  (2024-03-20T08:15:08Z)
• Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels [57.46832672991433]
  We propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS) We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We develop an expectation-propagation expectation-maximization algorithm for efficient posterior inference and function estimation.
  arXiv  Detail & Related papers  (2023-10-09T03:55:09Z)
• Controlling Moments with Kernel Stein Discrepancies [74.82363458321939]
  Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation. We first show that standard KSDs used for weak convergence control fail to control moment convergence. 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)
• Efficient Aggregated Kernel Tests using Incomplete $U$-statistics [22.251118308736327]
  Three proposed tests aggregate over several kernel bandwidths to detect departures from the null on various scales. We show that our proposed linear-time aggregated tests obtain higher power than current state-of-the-art linear-time kernel tests.
  arXiv  Detail & Related papers  (2022-06-18T12:30:06Z)
• 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)
• Optimal policy evaluation using kernel-based temporal difference methods [78.83926562536791]
  We use kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process. We derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator. We prove minimax lower bounds over sub-classes of MRPs.
  arXiv  Detail & Related papers  (2021-09-24T14:48:20Z)
• Learning Deep Kernels for Non-Parametric Two-Sample Tests [50.92621794426821]
  We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power.
  arXiv  Detail & Related papers  (2020-02-21T03:54:23Z)

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.