arXiv research

Optimizes kernel discrepancies by selecting subsets efficiently.

The article introduces practical estimators for kernel discrepancies.

Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepanc…

Study finds polynomial convergence rate for Farey sequences linked to Riemann hypothesis.

A new framework improves kernel Stein discrepancy tests for validating distributions.

New conditions ensure MMDs separate and converge to target distributions.

A new method for kernel tests without data splitting increases power.

Study on kernel tests for high-dimensional data, focusing on MMD and CLT.

This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine learning problems. As corollaries of the general technique we bound the discrepancy …

Improved KSD test for better detection of differences in distributions.

Kernel tests assess equivalence between distributions without assuming specific moments.

We show in this note that the Sobolev Discrepancy introduced in Mroueh et al in the context of generative adversarial networks, is actually the weighted negative Sobolev norm $||.||_{\dot{H}^{-1}(ν_q)}$, that is known to linearize the Wasserstein $W_2$ distance and plays a fundamental role in the dynamic formulation of…

New method uses kernel Stein discrepancy for measure transport without strict continuity constraints.

Paper proposes kernelized Stein tests for time-to-event data with censoring.

Improved kernel Stein discrepancy for large-scale data.

Study on discrepancy principle for learning algorithms in nonparametric regression.

We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to integral representations of shift-invariant kernel functions (e.g., Gaussian kernel).…

A new method calculates intrinsic effective sample size for manifold-valued data.

New method uses multiple kernels to improve SVGD performance.

MMD test detects adversarial attacks by addressing kernel limitations and non-independence issues.

Semi-parametric framework for nonlinear system identification

The paper shows how MMD metrizes weak convergence for certain kernels.

This thesis improves kernel-based distances for statistical inference and integration.

We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then demonstrate that the Kernel Score includes the Maximum Mean Discrepancy as a special …

New research sets the minimax lower bound for KSD estimation at sqrt(n).

A new method uses neural tangent kernel to efficiently compute MMD statistic.

We propose a framework for synthesis of geological images based on an exemplar image. We synthesize new realizations such that the discrepancy in the patch distribution between the realizations and the exemplar image is minimized. Such discrepancy is quantified using a kernel method for two-sample test called maximum m…

A new sequential test for unnormalized densities.

Efficiently marginalizes over Gaussian Process kernels for better model flexibility and uncertainty.

Fourier representation improves KSD for infinite-dimensional data.

A new measure helps compute suboptimality in entropy-regularized methods.

Paper proposes kernel-based tests for model misspecification.

New KSDs control moments in approximations, improving diagnostics and tests.

Kernelized Taylor diagram visualizes data populations with fewer assumptions.

EVI-MMD approximates target distributions via MMD minimization with adaptive kernel.

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy measures that provably determine the convergence of a sample to its target dist…

Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of this technique is conducted for the previously unconsidered setting where samples…

This work proposes a new method to match distributions across different spaces using cycle-consistent maps.

Kernelized cumulants improve statistical analysis in high-dimensional spaces.

This paper provides a dictionary of closed-form kernel mean embeddings.

Paper explores Fisher-Rao gradient flows and their kernel approximations.

Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.

Kernel thinning compresses distributions more effectively than i.i.d. sampling or standard thinning.

New method reduces computational cost for learning stationary diffusions.

A new measure scales MMD to assess distribution closeness.

Paper develops a minimax optimal test for goodness-of-fit using kernel Stein discrepancy.

New tools evaluate and optimize conditional sequence models in bioinformatics.