Deep neural nets optimize kernel parameters for non-parametric two-sample tests.
problem Determining if two samples come from the same distribution.
method Deep kernels trained to maximize test power, adapting to distribution smoothness and shape.
result Deep kernels outperform simpler kernels in high dimensions and complex data.
New method connects distance and kernel tests for better data structure.
problem Connecting distance and kernel methods for hypothesis testing.
method Proposes a new bijective transformation between metrics and kernels.
result Distance methods can be exactly the same as kernel methods for sample statistics and p-value.
New theoretical tools simplify kernel-based tests analysis.
problem Asymptotic behavior of kernel-based tests in various scenarios.
method Avoids complex expansions and limit theorems, works directly with Hilbert spaces random functionals.
result Framework leads to simpler analysis with minimal regularity conditions.
Unified framework for optimal kernel tests across MMD, HSIC, and KSD.
problem Optimal testing in kernel-based hypothesis testing frameworks.
method Unified derivation of minimax rates, adaptive kernel selection methods.
result Unified power results across MMD, HSIC, and KSD.
A new method for kernel tests without data splitting increases power.
problem Lack of power in kernel-based tests due to data splitting.
method Selective inference framework to learn hyperparameters and test on full sample.
result Empirically larger test power without data splitting, regardless of split proportion.
A new kernel-based CI test improves on existing methods.
problem Testing conditional independence (CI) in a broad range of dependencies.
method Regression-model-agnostic kernel-based CI test using reproducing kernel Hilbert spaces.
result GKCM outperforms state-of-the-art CI tests in simulations.
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
A new MMD-based test combines kernels for two-sample testing without splitting data.
problem Efficiently testing if two datasets come from the same distribution without splitting data.
method Proposes a novel statistic based on Maximum Mean Discrepancy (MMD) that combines kernels, proving concentration bounds and showing data-dependent kernel selection.
result Exponential concentration bounds and improved test power compared to existing methods.
Boosts kernel two-sample test power with multiple kernels.
problem Detecting differences between two distributions over metric spaces.
method Combining MMD estimates over multiple kernels using Mahalanobis distance.
result More powerful in detecting a wide range of alternatives in finite samples.
CTT compresses samples to test distributions near-linearly, outperforming existing methods.
problem Efficiently testing distributions with high power and near-linear runtime.
method Sample compression followed by permutation testing.
result CTT achieves near-linear runtime while maintaining high statistical power.
Meta two-sample testing uses auxiliary data to quickly find powerful tests from limited samples.
problem Challenges in identifying powerful kernels for distinguishing complex distributions with limited data.
method Introduces meta two-sample testing (M2ST) to leverage abundant auxiliary data on related tasks.
result Proposed algorithms improve over baselines and identify powerful tests from scarce observations.
New kernel tests detect differences between distributions exponentially quickly.
problem Characterize the asymptotic performance of kernel two-sample tests.
method Established exponentially consistent kernel two-sample tests for unknown distributions.
result Exponential decay rate of type-II error probability is optimal and independent of kernels.
New test assesses probabilistic model calibration without expensive approximations.
problem Assessing calibration of probabilistic models with scores.
method Kernel Calibration Conditional Stein Discrepancy (KCCSD) test using new score-based kernels.
result Control over type-I error with improved scalability and efficiency.
Proposes practical kernel tests for f-divergences with theoretical guarantees.
problem Two-sample testing and machine unlearning evaluation.
method Regularized f-divergence kernel tests, adaptive to hyperparameters. result Different f-divergences highlight localized differences. Gaussian kernel tests are optimal against smooth alternatives.
problem Understanding the statistical properties of nonparametric tests using Gaussian kernels.
method Analysis of Gaussian kernel-based goodness-of-fit, homogeneity, and independence tests.
result Gaussian kernel tests are minimax optimal against smooth alternatives in all three settings.
New KCM tests improve specification testing via RKHS.
problem Improving specification tests for econometric models.
method Kernel conditional moment (KCM) tests based on RKHS.
result KCM tests have better finite-sample performance than existing tests.
Improves two-sample hypothesis testing using kernel divergences and scoring rules.
problem Two-sample hypothesis testing in machine learning.
method Proposes Kernel Scoring Rules and Divergences, including the Maximum Mean Discrepancy.
result Kernel Score provides more information about embedded distributions than Maximum Mean Discrepancy.
A new, fast kernel test for large data.
problem Efficient kernel two-sample tests for high-dimensional, large-scale data.
method A new kernel-based test that is computationally efficient and robust to high dimensions.
result The new test performs well across various alternatives and dimensions.
Two-sample tests using MMD control type I error and achieve optimal power.
problem Developing reliable nonparametric two-sample tests for small sample sizes.
method Maximum Mean Discrepancy (MMD) for constructing novel nonparametric tests, proving non-asymptotic error control and optimality.
result MMDAgg test controls type I error and achieves minimax rate over Sobolev balls, outperforming other tests.
A novel kernel learning framework detects abrupt changes in time series data.
problem Detecting abrupt changes in time series data with fewer assumptions.
method KL-CPD, a novel kernel learning framework that optimizes a lower bound of test power via an auxiliary generative model.
result Significantly outperformed other state-of-the-art methods in benchmark datasets and simulation studies.
A new sequential test for unnormalized densities.
problem Testing unnormalized densities with adaptive stopping.
method Sequential kernelized Stein discrepancy test, using non-uniform Stein kernels.
result Valid test with asymptotic lower bound for growth.
Kernel tests assess equivalence between distributions without assuming specific moments.
problem Traditional goodness-of-fit tests fail to detect meaningful distributional differences.
method Proposes kernel-based tests using kernel Stein discrepancy and Maximum Mean Discrepancy.
result Tests assess the absence of meaningful distributional differences under controlled error rates.
Improved KSD test for better detection of differences in distributions.
problem Low power of KSD test when distributions have same modes but different mixing proportions.
method Perturb the observed sample using Markov transition kernels to improve KSD test power.
result Perturbed KSD test can lead to substantially higher power than the original KSD test.
We introduce kernel nonparametric tests for Lancaster three-variable interaction and for total independence, using embeddings of signed measures into a reproducing kernel Hilbert space. The resulting test statistics are straightforward to compute, and are used in powerful interaction tests, which are consistent against…
Robust hypothesis testing designs a test for worst-case distributions using kernel methods.
problem Design a robust test for hypothesis testing under uncertainty sets.
method Data-driven uncertainty sets constructed using kernel mean embeddings and maximum mean discrepancy (MMD). Bayesian and Neyman-Pearson settings investigated.
result Proposed robust kernel tests are exponentially consistent and asymptotically optimal.
New robustness test for kernel goodness-of-fit tests.
problem Lack of robustness in existing kernel goodness-of-fit tests.
method Proposes a new robust kernel goodness-of-fit test using kernel Stein discrepancy (KSD) balls.
result First robust kernel goodness-of-fit test addressing both qualitative and quantitative robustness.
A new test compares latent variable models with kernel methods.
problem Comparing latent variable models with intractable marginal distributions.
method Kernel Stein Test, calibrated threshold, low-dimensional latent structure exploitation.
result Significantly outperforms Maximum Mean Discrepancy test in certain latent structure cases.
Study on kernel tests for high-dimensional data, focusing on MMD and CLT.
problem Asymptotic behavior of kernel two-sample tests in high dimensions and large samples.
method Maximum mean discrepancy (MMD) with isotropic kernels, deriving asymptotic expansions and CLT.
result Interplay between moment discrepancy and dimension-and-sample orders in kernel tests.
Improved two-sample testing using L1 geometry for analytic kernels.
problem Detecting differences between distributions.
method Use L1 distance between kernel-based distribution representatives to improve testing power. result Better detection of differences between distributions using L1 norm. A new kernel test reduces noise in MMD by focusing on leading eigen-directions.
problem Noise in trailing directional components degrades power of standard kernel two-sample tests.
method Truncate MMD spectral decomposition, retaining only leading eigen-directions.
result Our method achieves superior power and robustness, especially in high-dimensional and unbalanced settings.
Kernel test detects manifold data differences with high-dimensional noise.
problem Detecting differences between manifold data samples.
method Kernel-based two-sample test statistic related to MMD for manifold data.
result The test power exceeds a threshold depending on manifold dimensionality, Hölder order, and squared divergence.
A new method optimizes MMD test power by dynamically selecting kernels, overcoming traditional trade-offs.
problem Fixed kernels fail to distinguish certain distributions, leading to overfitting and variance collapse.
method Complexity-Penalized MMD (CP-MMD) criterion, derived from concentration inequality, optimizes kernel selection.
result CP-MMD maximizes true test power while ensuring unconditional Type-I validity, matching or exceeding state-of-the-art performance.
We develop a privacy-preserving method for kernel two-sample testing.
problem Protecting sensitive data in two-sample testing.
method Differential privacy framework for kernel two-sample testing.
result Our method achieves similar power to non-private tests with modest sample size increase.
Forest-based kernels improve on existing methods for high-dimensional testing.
problem Developing interpretable kernels for high-dimensional data.
method Kernel Mean Embedding Random Forests (KMERF) using leaf-node proximity.
result KMERF kernels are asymptotically characteristic and outperform existing methods.
This paper introduces differentially private permutation tests for hypothesis testing.
problem Privacy concerns in sensitive data analysis.
method Differentially private permutation tests for kernel methods.
result Proposes dpMMD and dpHSIC for two-sample and independence testing, achieving optimal power.
New test for conditional independence using kernel embeddings.
problem Testing conditional independence in high-dimensional settings.
method Analytic kernel embeddings, asymptotic distribution.
result New test outperforms existing methods in high-dimensional settings.
New methods for large-scale kernel independence testing reduce computation time and memory usage.
problem Efficiently testing independence in large datasets with flexible kernel methods.
method Large-scale kernel approximations including block-based, Nystrom, and random Fourier feature approaches.
result Novel large-scale methods provide comparable performance to existing methods but with significantly less computation time and memory usage.
Improved deep kernel machine achieves 94.5% test accuracy on CIFAR-10.
problem Achieving high accuracy on complex tasks like image classification.
method Stochastic kernel regularisation to add noise to learned Gram matrices.
result 94.5% test accuracy on CIFAR-10.
KSDAgg combines multiple KSD tests to improve goodness-of-fit testing without splitting data.
problem Improving goodness-of-fit testing without data splitting.
method KSDAgg aggregates multiple KSD tests with different kernels to maximize power.
result KSDAgg achieves the smallest uniform separation rate of the collection, up to a logarithmic term.
Linear-time kernel test outperforms previous methods in goodness-of-fit.
problem Testing goodness-of-fit for large datasets efficiently.
method Adaptive feature learning via Stein's method to minimize false negatives.
result The new test outperforms previous methods under mean-shift alternatives and high dimensions.
A novel kernel-based test detects equality versus singularity of two probability measures.
problem Detecting equality versus singularity of two probability distributions.
method Combines kernel mean and kernel covariance embeddings to construct a likelihood ratio test statistic.
result The test statistic satisfies a '0/\infty' law, vanishing under the null and diverging under the alternative.
Efficient tests for various statistical problems using incomplete U-statistics.
problem Nonparametric tests for two-sample, independence, and goodness-of-fit problems.
method Proposes MMDAggInc, HSICAggInc, and KSDAggInc tests aggregating over multiple kernel bandwidths.
result Aggregated tests provide a solution to the kernel selection problem and achieve optimal rates.
A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice of block size allows control over the tradeoff between test power and computatio…
New test for binary treatment effects using kernel methods.
problem Testing distributional effects of binary treatments.
method Kernel-based doubly-robust test, avoiding permutations.
result Valid type-I error with computational efficiency.
A new witness two-sample test improves data efficiency and power.
problem Nonparametric two-sample testing.
method Optimizes kernel and defines weights and basis points using training data.
result The new test is consistent, has well-controlled type-I error, and has comparable or higher power.
Kernel-embedding tests can be suboptimal, but a simple modification improves their performance.
problem Optimizing goodness-of-fit tests using kernel embeddings.
method Analyzing and modifying kernel-embedding based goodness-of-fit tests within a minimax framework.
result A moderated kernel-embedding approach provides optimal tests for various deviations and is adaptive over a wide range of spaces.
Test for joint distributions equivalence using kernel embedding.
problem Determining statistical difference between joint distributions.
method Joint kernel distribution embedding to extend kernel two-sample test.
result Can verify dataset-shift in learning frameworks.
Sharp bounds derived for test error of finite-rank kernel ridge regression.
problem Loose bounds on test error for finite-rank kernels in machine learning.
method Sharp non-asymptotic upper and lower bounds for KRR test error.
result Tighter bounds on finite-rank KRR test error, valid for any regularization parameters.