arXiv research

Random Machines improves SVM performance with free kernel choice.

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

Study evaluates RKHS choices for assessing graph models using KSD tests.

Optimal kernel in KR can be data-dependent, improving model performance.

Improves kernel ridge regression by optimizing scale and feature parameters.

Gaussian kernel fails on circle and related spaces.

Neural Kernel Network (NKN) learns flexible kernels from neural networks.

Develops UKP for comparing feature representations in multitask learning.

This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline smoothing or locally weighted regression, and the choice of a kernel in multiple kern…

Develops a fast Bayesian optimisation method that reduces computational overhead.

NVGD uses neural networks to infer distributions without kernel choices.

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of kernel mean embeddings of probability measures. For characteristic kernels, which inc…

Alternative proof of coisotropic embedding theorem for pre-symplectic manifolds.

New ensemble SVM model reduces prediction error without choosing best kernel.

A new framework improves kernel Stein discrepancy tests for validating distributions.

Kernel Dynamic Mode Decomposition reconstructs dynamical systems using Laplacian kernel.

Bayesian Optimization (BO) has become a core method for solving expensive black-box optimization problems. While much research focussed on the choice of the acquisition function, we focus on online length-scale adaption and the choice of kernel function. Instead of choosing hyperparameters in view of maximum likelihood…

This paper tackles scalability issues in kernel logistic regression for large datasets.

The article introduces practical estimators for kernel discrepancies.

Interpolation with Laplace kernel fails in low dimensions but succeeds in high dimensions.

Bayesian distance clustering improves robustness to kernel choice.

New framework explains neural network bias in solving differential equations.

Stein Variational Gradient Descent optimizes particle sets to match distribution expectations.

New kernel HMK improves Gaussian process expressiveness and supports harmonizable covariances.

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

Optimizes kernel methods by adapting regularization parameters.

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce a new algorithm for kernel learning that combines a {\em continuous set of base …

Machine learning with kernels for portfolio valuation and risk management.

A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice of block size allows control over the tradeoff between test power and computatio…

The paper examines how kernel approximations affect Gaussian process regression in large data applications.

Bayesian Gaussian Processes improve exoplanet transit and Hubble constant inference.

Identifies a gradient flow to solve kernel learning problems with noise reduction.

Clarifies bias in GAN loss functions and improves MMD GAN training.

Support Vector Machine (SVM) is powerful classification technique based on the idea of structural risk minimization. Use of kernel function enables curse of dimensionality to be addressed. However, proper kernel function for certain problem is dependent on specific dataset and as such there is no good method on choice …

Kernel K-means clusters probability distributions.

Nonasymptotic error bounds and strong consistency rates for survival analysis methods.

New method controls false discoveries in structured hypothesis spaces.

Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that constructs an approximation to the true likelihood based on the similarity between …

The paper examines Gaussian process means under misspecified likelihoods and smoothness.

Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly affected by the choice of kernel. Furthermore, when direc…

A new kernel for probability measures based on optimal transport.

Geometric theory connects machine learning classifiers to differential geometry.

This thesis improves kernel-based distances for statistical inference and integration.

A new method learns hyperparameters for conditional kernel mean embeddings using Rademacher complexity bounds.

Study provides guarantees for kernel clustering under non-parametric mixtures.

High-dimensional kernel regression struggles due to rotational invariance.

Many investment models in discrete or continuous-time settings boil down to maximizing an objective of the quantile function of the decision variable. This quantile optimization problem is known as the quantile formulation of the original investment problem. Under certain monotonicity assumptions, several schemes to so…

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