arXiv research

Paper derives uniform error bounds for Gaussian process regression for safer control applications.

New method identifies Gaussian SEMs with varying error variances.

Enhances reinforcement learning uncertainty estimation with a generalized Gaussian error model.

Paper bounds prediction error for misspecified Gaussian process models.

Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.

The study examines the universality of Gaussian data in high-dimensional generalized linear estimation.

Robust estimators for Gaussian sparse tasks with optimal error under contamination.

This paper addresses error bounds and posterior variance for Gaussian process regression.

Diffusion models generate data with Gaussian Universality, matching linear model test errors.

This work approximates finite neural networks with Gaussian processes, providing error bounds and applications in prior selection.

Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language, information retrieval and others. Gaussian graphical model selection is a statist…

Optimal Gaussian noise mechanisms achieve nearly optimal error in unbiased mean estimation.

Theoretical analysis of entropy approximation for Gaussian mixtures.

Bayesian method identifies causal DAG structure from non-Gaussian errors.

Study improves least squares estimation for heavy-tailed errors.

In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…

Gaussian process regression helps approximate Bayesian inverse problems efficiently.

Improved BO algorithms reduce prediction error under Gaussian noise.

A new error bound improves safety in Bayesian optimization.

Study predicts Gaussian Volterra processes with noisy Brownian motion.

Improved estimator for least squares using random projections achieves smaller error.

New bounds for kernel regression under non-Gaussian noise.

A new asymmetric correntropy method improves robust adaptive filtering for asymmetric error distributions.

The paper develops generalization bounds for deep compound Gaussian neural networks.

New approach uses Gaussian processes to learn and track complex systems with guaranteed accuracy.

The paper bounds estimation and prediction errors in time series using entropy.

This paper analyzes error in SKI for Gaussian Processes, providing conditions for linear time inference.

Study Gaussian-process limits of neural networks using tensor programs.

The paper provides tighter error bounds for GPR under bounded support noise.

Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.

New bound matches exact generalization error for quadratic Gaussian problem.

This paper considers the quantification of the prediction performance in Gaussian process regression. The standard approach is to base the prediction error bars on the theoretical predictive variance, which is a lower bound on the mean square-error (MSE). This approach, however, does not take into account that the stat…

The study proves Gaussian universality of deep random features learning.

Study on linear regression with dependent covariates, proving universality and error characterization.

Paper analyzes GP derivatives for error propagation in geoscience.

Proposes a new model for mixed membership in Gaussian mixture.

Study improves error bounds for sparse regression with heavy-tailed covariates.

Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method - within the best …

This paper improves active learning for Gaussian process regression to handle distributional uncertainty.

New GaussianSketch approximates kernel distances with almost relative error and small additive term.

For binary classification we establish learning rates up to the order of $n^{-1}$ for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions: Tsybakov's noise assumption to establish a small estimation error, and a new geometr…

The article analyzes high-dimensional classification using empirical risk minimization with precise error predictions.

Study precise sample covariance error for Gaussian centered data.

Proposes SGELU for neural networks to improve performance and convergence.

Paper analyzes holdout cross-validation for large non-Gaussian covariance estimation.

The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the learning rate as the number of samples increases is discussed. Specifically, the error…

A method to improve sequential learning by keeping past data errors in check.