arXiv research

The paper explores a new type of kernel using Wasserstein distance for better classification of shapes.

We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing …

The paper improves error bounds for Bayesian quadrature in noisy settings.

Guyon-Lekeufack model accurately predicts market volatility.

Paper improves regret bounds for Gaussian process upper confidence bound in Bayesian optimization.

The paper analyzes the statistical cost of tuning kernel hyperparameters in robust regression.

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-expo…

Kernel method outperforms deep neural networks in speech enhancement.

Quantum LS-SVM simplifies matrix inversion for faster machine learning.

A quantum-inspired classical algorithm speeds up LS-SVM classification.

Enhanced kernel framework for advanced data forecasting.

New algorithm estimates transport maps with nearly optimal error.

This paper addresses Gaussian Process regression over probability measures, revealing a non-stationarity issue between Euclidean and Wasserstein kernels.

SNEPPPs use squared neural networks to efficiently model Poisson point processes.

The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.

Study on learning properties of scale-dependent kernels controlling stability and error.

Squared families are a new model class derived from linear transformations, offering convenient properties and universal approximation.

Unified analysis of kernel-based and locally adaptive bandit optimization methods.

Paper introduces kernel deformed exponential families for sparse continuous attention.

Let $(M, g)$ be a real analytic Kaehler manifold. We say that a smooth map $E_p:W\to M$ from a neighborhood $W$ of the origin of $T_pM$ into $M$ is a {\em diastatic exponential} at $p$ if it satisfies $$(d \E_p)_0=\id_{T_pM},$$ $$D_p(\E_p (v))=g_p(v, v), \forall v\in W,$$ where $D_p$ is Calabi's diastasis function at $…

Improved Gaussian process approximations reduce computational cost.

We consider the problem of Bayesian optimization (BO) in one dimension, under a Gaussian process prior and Gaussian sampling noise. We provide a theoretical analysis showing that, under fairly mild technical assumptions on the kernel, the best possible cumulative regret up to time $T$ behaves as $Ω(\sqrt{T})$ and $O(\s…

New Hida-Matérn kernels enable flexible process priors and efficient GP inference.

Study proves existence, uniqueness, and positivity of solutions to a complex volatility model.

Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in thei…

GPs' decisions can vary significantly with different kernels, even if kernels are qualitatively similar.

New method finds global minima using function evaluations and kernel approximations.

Study on Wasserstein gradient flow for MMD between Coulomb measures.

Paper evaluates squared-exponential covariance function for Gaussian processes with integral observations.

New analysis explains pathology of deep Gaussian processes.

Volterra square-root process boundary behavior and martingale measures

Paper tackles non-stationary kernelized bandits with near-optimal algorithm.

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order interactions. However, until recently, there has been a strong reliance on a limi…

Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.

Sparse LR-LSSVM improves kernel machine performance.

The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), and feature selection (mutual information). Recently, several methods of directly estimating the density ratio have been deve…

Estimates exponential family distributions using a novel doubly dual embedding technique.

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…

Study compares exponential and power-law kernels in modeling high-frequency trading data.

New stability theory for Sinkhorn semigroups with explicit decay rates.

Quantum kernel methods can lead to trivial models due to exponential concentration of kernel values.

We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…

Improves probability distribution compression with KT algorithm.

Bayesian optimization under heavy-tailed noise with improved regret bounds.

Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still an open important issue especially for learning with small sample s…

Study of regularized least squares in RKKS with indefinite kernels.

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line b…

Optimal Biweight kernel and computationally efficient Epanechnikov kernel for modal linear regression.