arXiv research

New non-separable covariance kernels for spatiotemporal data derived from harmonic oscillator physics.

The paper analyzes how Gaussian kernel parameters affect posterior covariance in Gaussian processes.

This paper improves computational efficiency in kernel ridge regression under covariate shift.

The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.

Novel neural GP kernels learn stable, flexible covariance structures.

A new model DKMPP integrates covariates and uses an integration-free method for spatio-temporal point processes.

To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, …

Kernel $ε$-Greedy optimizes multi-armed bandits with covariates for sub-linear regret.

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) problem using operator-valued kernels. We show that some of the existing formulations of this problem are special cases of our framework. We then propose a c…

Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well…

This monograph develops the theory of covariant Schrödinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. Basis differential operators in Riemannian manifolds IV. Some specif…

KMRCD detects outliers in non-elliptical data using kernel trick.

New kernel models multi-output Gaussian processes accurately.

The paper presents a novel approach to direct covariance function learning for Bayesian optimisation, with particular emphasis on experimental design problems where an existing corpus of condensed knowledge is present. The method presented borrows techniques from reproducing kernel Banach space theory (specifically m-k…

New asymmetric kernel methods improve feature learning.

Active data collection improves convergence rates in operator learning.

Unified analysis of kernel-based methods under covariate shift.

Semi-supervised method boosts two-sample testing with covariate data.

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 perform feature selection via a constrained optimization problem involving the tra…

The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatmen…

Develops efficient inference for noise heterogeneity in machine learning models.

Optimally tackles covariate shift in RKHS-based nonparametric regression.

Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical covariance kernels when the dimension of input increases. In oder to get round the cu…

Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GP with …

Develops a method for kernel ridge regression under covariate shift using pseudo-labels.

A new kernel-based CI test improves on existing methods.

We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of simulations. Our approach is based on Bayesian inference with kernel mean embeddin…

New GP kernels avoid mean reversion without losing smoothness.

Associating genetic markers with a multidimensional phenotype is an important yet challenging problem. In this work, we establish the equivalence between two popular methods: kernel-machine regression (KMR), and kernel distance covariance (KDC). KMR is a semiparametric regression frameworks that models the covariate ef…

Extends Gaussian process theory to Banach spaces.

In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift problem, we derive high probability confidence bounds for the kernel mean matching (…

Framework for domain adaptation using pseudo-labels from unlabeled data.

New GL-GP models learn covariance respecting domain geometry.

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral dens…

Bayesian deep neural networks converge to processes with α-stable marginals under infinite variance weights.

A new kernel-based nonconformity score improves multivariate prediction regions.

New kernels from ELU and GELU networks reveal non-trivial fixed points.

A streaming algorithm estimates quadratic covariation from financial data efficiently.

New method for causal inference with observed covariates improves learning rates.

The paper defines conditions for Gaussian process sample path regularity.

We analyze the size of the dictionary constructed from online kernel sparsification, using a novel formula that expresses the expected determinant of the kernel Gram matrix in terms of the eigenvalues of the covariance operator. Using this formula, we are able to connect the cardinality of the dictionary with the eigen…

Kernel measures similarity of nonlinear causal structures in heterogeneous populations.

Estimates covariance matrices with correlations between samples.

Kernel ridge regression for causal inference with missing data.

RKUM is an R package for robust kernel-based unsupervised methods.

The paper analyzes covariate shift in nonparametric regression with Markovian data.

The paper introduces a new framework to assess generative model uncertainty.

The paper improves sample reweighting methods for adapting to covariate shifts.