Related papers: A Distance Covariance-based Kernel for Nonlinear C…
In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…
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…
Contrastive learning is an efficient approach to self-supervised representation learning. Although recent studies have made progress in the theoretical understanding of contrastive learning, the investigation of how to characterize the…
We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors…
To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly…
We use a suitable version of the so-called "kernel trick" to devise two-sample (homogeneity) tests, especially focussed on high-dimensional and functional data. Our proposal entails a simplification related to the important practical…
Modeling multiple sampling densities within a hierarchical framework enables borrowing of information across samples. These density random effects can act as kernels in latent variable models to represent exchangeable subgroups or clusters.…
This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…
Building spatial process models that capture nonstationary behavior while delivering computationally efficient inference is challenging. Nonstationary spatially varying kernels (see, e.g., Paciorek, 2003) offer flexibility and richness, but…
Causal discovery, beyond the inference of a network as a collection of connected dots, offers a crucial functionality in scientific discovery using artificial intelligence. The questions that arise in multiple domains, such as physics,…
Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…
Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…
Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…
Most existing causal structure learning methods assume data collected from one environment and independent and identically distributed (i.i.d.). In some cases, data are collected from different subjects from multiple environments, which…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…
In this paper, we propose an invariant quantile regression (IQR) framework specifically designed for multi-environment datasets, which captures the invariance across different environments. This framework is closely related to transfer…
Debiased collaborative filtering aims to learn an unbiased prediction model by removing different biases in observational datasets. To solve this problem, one of the simple and effective methods is based on the propensity score, which…