Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore the connection between conditional independence measures induced by distances on …
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48 results for “kernel independence”
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.
This work develops a non-parametric test for relational independence in non-i.i.d. data.
problem Testing independence in relational systems where data samples are not i.i.d.
method Kernel mean embedding for relational variables, consistent non-parametric scalable kernel test.
result Empirically validated effectiveness compared to state-of-the-art tests.
A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the product of the marginals, in a Reproducing Kernel Hilbert Space (RKHS). It has …
Discusses MultiFIT for multivariate dependence, comparing it to HSIC tests.
problem Comparing Multiscale Fisher's Independence Test (MultiFIT) to HSIC tests for multivariate dependence.
method Compares MultiFIT to HSIC tests, highlighting exact level control and performance limitations.
result Observes performance limitations of MultiFIT in terms of test power.
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. T…
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional independence. We describe some conditional independencies through the conditions on t…
This work improves fair tensor decomposition using a kernel criterion.
problem Learning fair low-rank tensor decompositions with statistical parity.
method Regularizes Canonical Polyadic Decomposition with KHSIC to ensure approximate statistical parity.
result The proposed algorithm achieves better fairness and fit than state-of-the-art FATR.
Sequential Kernel-based Conditional Independence Testing via Adaptive Betting
problem Testing conditional independence
method Testing-by-betting on an adaptively optimized Kernel Conditional Independence statistic
result Significantly reduces Type I error inflation while preserving high power
Efficiently fine-tunes patient-independent seizure detection models with tensor kernel machine.
problem Improving seizure detection accuracy for wearable devices.
method Transfer learning with tensor kernel machine using canonical polyadic decomposition.
result Patient fine-tuned model achieves high performance with smaller model size.
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned ke…
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.
Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with the Perron-Frobenius operators in vector-valued reproducing kernel Hilbert space…
We show that the error probability of reconstructing kernel matrices from Random Fourier Features for the Gaussian kernel function is at most , where is the number of random features and is the diameter of the data domain. We also provide an information-theoretic method-independen…
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including nonlinear associations and multivariate interactions. However, these approaches come wi…
New research optimizes HSIC estimation rate for translation-invariant kernels.
problem Optimizing the rate of HSIC estimation for translation-invariant kernels.
method Proved minimax optimal rate of for HSIC estimation.
result Optimality of various HSIC estimators proven.
FastKCI speeds up KCI tests for causal inference on large datasets.
problem Cubic computational complexity of kernel-based conditional independence tests.
method Mixture-of-experts approach with parallel Gaussian process inference.
result Substantial computational speedups with maintained statistical power.
New test detects independence in streaming data, adapting to data complexity.
problem Independence testing in streaming data with adaptive stopping.
method Sequential kernelized independence tests using betting principles.
result Valid inference in streaming data with improved power.
Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Seriesstat.ME
Kernel-based tests detect dependencies in multivariate time series, including stationary and non-stationary data.
problem Detecting dependencies in multivariate time series data, especially non-stationary data.
method Kernel-based statistical tests of joint independence, extending dHSIC to handle both stationary and non-stationary processes.
result Robustly uncovers significant higher-order dependencies in synthetic and real-world data.
Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernelsstat.ML
Gaussian processes adapted for Riemannian manifolds using gauge-independent kernels.
problem Deploying Gaussian processes on non-Euclidean domains like Riemannian manifolds.
method Developed techniques to generalize Gaussian processes to vector fields on Riemannian manifolds using gauge-independent kernels.
result Enabled training of vector-valued Gaussian processes on Riemannian manifolds using standard Gaussian process methods.
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by con…
Kernelized cumulants improve statistical analysis in high-dimensional spaces.
problem Statistical analysis in high-dimensional spaces with low variance estimators.
method Extending cumulants to RKHS using tensor algebra and kernel trick.
result Kernelized cumulants provide new all-purpose statistics with computational tractability.
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample and independence tests from the machine learning community. A fixed-point transf…
Faster convergence of kernel mean embeddings using variance information.
problem Speeding up the convergence rate of kernel mean embeddings.
method Leveraging variance information in reproducing kernel Hilbert space and estimating variance from data.
result Efficiently estimate variance information from data to achieve distribution-agnostic convergence bounds.
MixCIT tests conditional independence for mixed data types efficiently and reliably.
problem Testing conditional independence for mixed data types, especially when at least one is continuous.
method Graph-based test statistic comparing kernel similarities, debiased local-polynomial approach for continuous variables.
result Unified, efficient, and statistically guaranteed solution across heterogeneous data types.
A new kernel test avoids permutations for independence testing.
problem Intractable null distributions of kernel statistics.
method Developed xHSIC and xdCov, avoiding permutations.
result New tests have limiting Gaussian distributions under null.
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…
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…
New insights into CI tests reveal key factors for practical performance.
problem Understanding and improving CI tests in practical applications.
method Investigation of the Kernel-based Conditional Independence (KCI) test and analysis of its practical behavior.
result Errors in conditional mean embedding estimates and appropriate conditioning kernel selection are crucial for CI tests.
New statistics improve kernel independence testing efficiency.
problem Improving efficiency in kernel independence testing.
method Adapting martingale MMD construction to joint independence problem.
result Two new statistics achieve finite-sample consistency with linear per-test cost.
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.
Paper introduces EO_k for quantifying accuracy-fairness trade-offs in FRL.
problem Tackles the trade-off between accuracy and fairness in FRL.
method Kernel-based formulation of EO criterion for FRL.
result Offers a unified analytical characterization of fairness tradeoffs.
Paper introduces a new test for conditional independence using weighted partial copulas.
problem Testing conditional independence between variables.
method The approach uses a weighted partial copula function and a bootstrap procedure to compute regions of rejection.
result The proposed test has competitive power compared to existing methods.
Entropy analysis via kernel methods for probabilistic inference.
problem Entropy analysis of probability distributions.
method Kernel methods and reproducing kernel Hilbert spaces for entropy estimation.
result New upper-bounds on log partition functions for probabilistic inference.
We introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We examine the case of the undercomplete BSSD (uBSSD). Applying temporal concatenation we reduce this problem to ISA. The associated `high …
New method tests conditional independence using spectral representations.
problem Untestable conditional independence in many settings.
method Spectral representations of partial covariance operators, bi-level contrastive learning.
result Asymptotic validity and power guarantees for CI testing.
New bounds for KRR condition number reveal overfitting phenomena.
problem Characterizing overfitting in KRR with varying kernel spectral decay.
method Derived new bounds for kernel matrices, enhanced test error bounds, and identified feature independence role.
result Identified tempered and catastrophic overfitting phenomena.
Kernel methods and MLPs perform similarly to linear models in high dimensions.
problem Understanding the performance of kernel methods and MLPs in high-dimensional settings.
method Analysis of kernel methods and MLPs in a high-dimensional regime with proportional asymptotics.
result Linear models are optimal in high-dimensional settings when data is generated by kernel models with nonlinear relationships.
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.
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as establ…
A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on…
Invariant kernels reduce rank and improve generalization across dimensions.
problem Symmetry in high-dimensional data impacts kernel matrix rank and learning algorithms.
method Compute invariant polynomial kernel ranks under various groups acting on data.
result Symmetry decreases kernel rank, making it independent of data dimension.
New unsupervised learning technique learns independent kernels for better machine learning tasks.
problem Improving unsupervised representation learning for machine learning tasks.
method Stacking convolutional transforms using alternating proximal minimization scheme.
result DCTL outperforms shallow version CTL on benchmark datasets.
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.
The article introduces practical estimators for kernel discrepancies.
problem Estimating kernel discrepancies accurately and efficiently.
method Presented various estimators for MMD, HSIC, and KSD, including V-statistics, U-statistics, and incomplete U-statistics. Stressed the importance of kernel bandwidth and introduced adaptive estimators.
result Adaptive estimators combining multiple estimators with various kernels address the problem of kernel selection.
The Mondrian Kernelstat.ML
We introduce the Mondrian kernel, a fast random feature approximation to the Laplace kernel. It is suitable for both batch and online learning, and admits a fast kernel-width-selection procedure as the random features can be re-used efficiently for all kernel widths. The features are constructed by sampling trees via a…
Sequential tests for two-sample and independence testing using betting strategies.
problem Testing sequential data for two-sample and independence without kernel selection issues.
method Prediction-based betting strategies that adaptively determine distribution and joint distribution.
result Prediction-based tests outperform kernel-based approaches in high-dimensional or structured data settings.
We investigate the problem of testing whether random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but allows for an arbitrary number of variables. We embed the -dimensional joint …