Proposes a sparse linear classifier for classification with pairwise dependencies.
problem Classification accuracy is limited by tree-structured graphical models.
method Semi-parametric approach using sparse linear combination of univariate and bivariate log-transformed densities.
result SLB classifier is competitive with popular methods.
Paper develops metrics for random dynamical systems using vector-valued RKHSs.
problem Creating metrics for random nonlinear dynamical systems.
method Develops metrics on random dynamical systems using Perron-Frobenius operators in vector-valued reproducing kernel Hilbert spaces (vvRKHSs). Uses operator-valued kernels and time-wise independence criteria.
result Extends existing metrics for deterministic systems and introduces kernel maximal mean discrepancy for random processes.
Proposes a method to create fair, robust predictors that remain consistent across different scenarios.
problem Creating fair and robust machine learning models that behave consistently across different scenarios.
method Graphical criteria and a model-agnostic framework called CIP based on HSCIC.
result Demonstrates the effectiveness of CIP in enforcing counterfactual invariance across various datasets.
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.
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.
The paper develops robust tests for detecting independence in synchronous stochastic systems with finite sample guarantees.
problem Detecting independence in synchronous stochastic systems with finite sample guarantees.
method Combines confidence region estimates with permutation tests and dependence measures to detect nonlinear dependence.
result Consistent hypothesis tests for detecting independence under mild assumptions.
This work explores the connection between distances and kernels for conditional independence.
problem Measuring conditional independence in various fields like causal discovery and feature selection.
method Investigates the relationship between conditional independence measures induced by distances and reproducing kernels.
result Some kernel-based conditional independence measures are not equivalent to distance-based measures.
Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.
problem Optimizing estimation of Kernel Stein Discrepancy from samples.
method Identifying and comparing minimax scales for U-statistic and V-statistic.
result Hilbert-Schmidt norm of Stein covariance operator gives optimal scale.
A new test detects non-linear independence in censored survival data.
problem Detecting non-linear independence between survival times and covariates.
method A kernel log-rank test using reproducing kernel Hilbert spaces.
result The test correctly rejects the null hypothesis under any alternative.
Paper proposes universally consistent K-sample tests using any dependence measure.
problem Testing whether K groups of data points are drawn from the same distribution.
method Demonstrates the use of any dependence measure for K-sample testing.
result Achieves universally consistent K-sample testing using distance correlation and Hilbert-Schmidt independence criterion.
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.
ICAL improves deep learning model accuracy and NLL with optimized batch labeling.
problem Deep Bayesian Active Learning for efficient model training.
method ICAL uses HSIC to measure dependency and optimizes batch size scaling.
result Significant improvements in model accuracy and NLL on image datasets.
IPGDN learns disentangled node representations in graphs.
problem Learning disentangled node representations in graph convolutional networks (GCNs).
method IPGDN uses neighborhood routing mechanism and HSIC to enforce independence among latent representations.
result IPGDN outperforms state-of-the-arts in graph classification, clustering, and visualization.
Study on estimating distances between covariance operators and Gaussian processes.
problem Estimating distances between covariance operators and Gaussian processes.
method Riemannian distances, concentration results for Hilbert space-valued random variables, RKHS covariance and cross-covariance operators.
result Both distances converge in the Hilbert-Schmidt norm and can be consistently and efficiently estimated.
Paper develops a new method for reducing dimensions in longitudinal data.
problem Challenges in predicting and inferring from high-dimensional longitudinal data.
method Proposes supervised Kernel PCA (sklPCA) for longitudinal data. result Demonstrates superior model accuracy compared to existing methods.
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.
New method speeds up HSIC for multiple variables.
problem Quadratic computational complexity of HSIC for multiple variables.
method Nyström approximation to HSIC for M≥2. result Consistent Nyström HSIC estimator for M≥2. We investigate the problem of testing whether d 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 d-dimensional joint …
GraphITE estimates individual effects of graph-structured treatments.
problem Estimating individual effects of complex treatment structures.
method Graph neural networks and Hilbert-Schmidt Independence Criterion regularization.
result GraphITE outperforms baselines in estimating treatment effects for large numbers of treatments.
A novel disentangled graph autoencoder improves treatment effect estimation from networked observational data.
problem Treatment effect estimation from observational data is challenging due to unconfoundedness assumption and latent confounders.
method Proposes a disentangled variational graph autoencoder to disentangle latent factors and enforce factor independence.
result Extensive experiments show superior performance compared to state-of-the-art approaches.
HSIC loss improves robust regression and classification models.
problem Learning robust models in the absence of target domain data.
method Adapted HSIC loss for unsupervised covariate shift.
result Models outperform standard methods on covariate shift tasks.
This work improves independence tests for high-dimensional data.
problem Detecting subtle dependencies between high-dimensional random variables with complex distributions.
method Develops two approaches to learn powerful independence tests using variational mutual information and HSIC.
result Optimized HSIC tests generally outperform other approaches on detecting structured dependence.
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.
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…
Paper proposes a differentially private test for joint dependence among random vectors.
problem Detecting joint dependence among sensitive data while maintaining privacy.
method Differentially private permutation methodology for dHSIC test.
result Proposed test attains minimax optimal power across privacy regimes.
Framework for generating multiple clusterings from multi-view data.
problem Challenges in finding optimal clustering criteria and handling incomplete multi-view data.
method DiMVMC framework that optimizes multiple decoder deep networks to complete data views and generate shared representations.
result DiMVMC outperforms state-of-the-art competitors in generating multiple clusterings with high diversity and quality.
More powerful feature selection tests using selective inference.
problem Selection bias in feature selection leading to specious analysis.
method Conditioning on minimal selection event using Maximum Mean Discrepancy and Hilbert Schmidt Independence Criterion with multiscale bootstrap.
result Proposed test is more powerful in most scenarios.
This paper improves HSIC-based dimensionality reduction for non-linear kernels.
problem Non-convexity of HSIC objective function for non-linear kernels limits optimization efficiency.
method Spectral optimization algorithm with local guarantees and principled initialization.
result Empirical improvements by a factor of 105 in runtime with lower errors. A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when compu…
Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in closed form just involving linear algebra operations. However, they are hampere…
A novel double-space tensor-product RKHS framework for hybrid uncertainty sensitivity analysis.
problem Quantifying the influence of hybrid aleatory and epistemic uncertainties on high-dimensional system responses.
method A novel double-space tensor-product RKHS framework for sensitivity analysis under hybrid uncertainty.
result Concurrent double Möbius inversion orthogonally decomposes global dependence measure into pure aleatory effects, pure epistemic effects, and their interaction contributions.
We give the twistor description of harmonic maps of the Riemann sphere into the Hilbert-Schmidt Grassmannian. The study of such maps is motivated by the harmonic spheres conjecture formulated in the beginning of this paper.
Study resolvent convergence for random matrices with general covariance profiles.
problem Analyzing resolvent convergence for random matrices with non-identically distributed columns.
method Using moments of quadratic forms and deterministic equivalents, the study provides bounds on the trace of matrix products.
result The trace of matrix products is close to the trace of a deterministic equivalent, controlled by matrix norms.
Maximizes image representation dependence for self-supervised learning.
problem Learning meaningful image representations from unlabeled data.
method Maximizes Hilbert-Schmidt Independence Criterion (HSIC) between image transformations and identity.
result Matches state-of-the-art performance on ImageNet and other vision tasks.
Solves steering problem with continuous time, Hilbert-Schmidt cost, and matrix ODEs.
problem Fixed horizon linear quadratic covariance steering in continuous time with a specific terminal cost.
method Formulates necessary conditions as a coupled matrix ODE two-point boundary value problem, designs a matricial recursive algorithm, and proves convergence.
result Proposes and proves the convergence of a matricial recursive algorithm for solving the steering problem.
Paper develops efficient incomplete U-statistics for degenerate cases.
problem High computational cost and non-standard asymptotic behavior in degenerate U-statistics.
method Characterizes dependence structure using hypergraph theory and combinatorial designs, bypassing traditional Hoeffding decomposition.
result Derives a Berry-Esseen bound for incomplete U-statistics of deterministic designs, enabling Gaussian limiting distributions in degenerate cases.
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.
GraphLIME explains GNN models by selecting key features locally.
problem Explaining the effectiveness of GNN models is challenging due to complex nonlinear transformations.
method GraphLIME uses HSIC Lasso for nonlinear feature selection in GNN models.
result GraphLIME provides more descriptive explanations than existing methods.
Paper introduces a new measure of conditional dependence avoiding matrix inversions.
problem Measuring conditional dependence between two phenomena influenced by a confounder.
method Uses U-statistics pruning to avoid matrix inversions and re-interpret independence.
result Proposes a novel measure of conditional dependence that avoids matrix inversions.
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 …
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation, have been proposed to alleviate the problem. However, the statistic…
Optimizes learning Hilbert-Schmidt operators between Sobolev spaces.
problem Statistical limits of learning mappings between infinite-dimensional function spaces.
method Minimax optimal regularization and multilevel training.
result Multilevel kernel operator learning achieves optimal learning rate.
Parameterizing the approximate posterior of a generative model with neural networks has become a common theme in recent machine learning research. While providing appealing flexibility, this approach makes it difficult to impose or assess structural constraints such as conditional independence. We propose a framework f…
Optimal transport for functional data using Hilbert-Schmidt operators.
problem Optimal transport for distributions on function spaces with partially represented stochastic maps.
method Regularization technique to restrict transport maps to Hilbert-Schmidt operators, developing an efficient algorithm.
result Existence, uniqueness, and consistency of the Hilbert-Schmidt operator estimate for the transport map.
Proposes a new sensitivity measure for optimization problems.
problem Optimization of high-dimensional functions with expensive computer codes.
method Introduces a new influence measure based on the Hilbert-Schmidt Independence Criterion.
result The new measure significantly reduces the number of function evaluations.
The paper develops divergences for Gaussian processes and RKHS settings.
problem Estimating divergences in infinite-dimensional spaces.
method Formulations of Alpha Log-Det divergences, continuity in norm, laws of large numbers, consistent estimation from finite samples.
result Infinite-dimensional divergences can be estimated from finite-dimensional versions with dimension-independent sample complexities.
Proposes a multi-view DR algorithm to improve learning performance.
problem Improving learning performance with multi-view high-dimensional data.
method Smooth Preserve Projection extended to multi-view using Hilbert-Schmidt Independence Criterion.
result Excellent performance on multi-view datasets.
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.