arXiv research

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

Sharp Gaussian bounds derived for Schrödinger kernel on Ricci solitons.

Sharp sub-Gaussian bounds for subsolutions of Trudinger's equation on Riemannian manifolds.

This paper analyzes regret bounds for Gaussian process Thompson sampling.

Improved Bayesian optimisation method using randomised Gaussian process UCB.

Proves upper bounds for heat kernels evolving on manifolds.

New bounds on AE success probability in GP models.

Improves GP models with known bounds for sampling and optimization.

In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian P…

A new method optimizes robustness measures under input uncertainty using randomized Gaussian process upper confidence bound.

The study bounds heat kernel for manifolds with specific curvature conditions.

Study sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces.

Improved BO algorithms reduce prediction error under Gaussian noise.

Bayesian methods improve drug discovery experiment design.

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

Study precise sample covariance error for Gaussian centered data.

New bounds for private learning of high-dimensional Gaussian distributions.

Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.

Lower bounds on private estimation of Gaussian covariance matrices.

This article shows that under locally uniformly integral bounds of the negative part of Ricci curvature the heat kernel admits a Gaussian upper bound for small times. This provides general assumptions on the geometry of a manifold such that certain function spaces are in the Kato class. Additionally, the results imply …

The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.

The paper studies heat kernels on weighted Riemannian manifolds with curvature bounds.

Upper bound on expected supremum of Bernoulli process.

This paper improves GP-UCB by using a shifted exponential distribution for confidence parameters.

Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for application scenarios. Gaussian process regression represents one approach which provid…

The paper improves bounds on regret in Gaussian process bandits.

Automating statistical modelling is a challenging problem in artificial intelligence. The Automatic Statistician takes a first step in this direction, by employing a kernel search algorithm with Gaussian Processes (GP) to provide interpretable statistical models for regression problems. However this does not scale due …

The paper improves privacy accounting for discrete-valued mechanisms and the subsampled Gaussian mechanism.

This note gives a short, self-contained, proof of a sharp connection between Gittins indices and Bayesian upper confidence bound algorithms. I consider a Gaussian multi-armed bandit problem with discount factor $γ$. The Gittins index of an arm is shown to equal the $γ$-quantile of the posterior distribution of the arm'…

The study bounds the stability of Gaussian mixtures under small perturbations.

In this paper, we consider low rank matrix estimation using either matrix-version Dantzig Selector $\hat{A}_λ^d$ or matrix-version LASSO estimator $\hat{A}_λ^L$. We consider sub-Gaussian measurements, $i.e.$, the measurements $X_1,\ldots,X_n\in\mathbb{R}^{m\times m}$ have $i.i.d.$ sub-Gaussian entries. Suppose $\textrm…

Study lenient regret and good-action identification in Gaussian process bandits.

Signals are submanifolds; bounds on energy calculated.

Unified bounds for iterative algorithms with Gaussian data matrices.

In this paper, we derive a Sobolev inequality along an extended Ricci flow and prove a point-wise Guassian type bound for the fundamental solutions of the conjugate heat equation under the flow.

A batched Gaussian Process bandit optimization method achieves near-optimal regret bounds.

The paper tackles estimating optimal policy value in linear bandits with general context distributions.

We present two algorithms for Bayesian optimization in the batch feedback setting, based on Gaussian process upper confidence bound and Thompson sampling approaches, along with frequentist regret guarantees and numerical results.

The paper improves prediction and testing for signals from a linear combination of translated features with Gaussian noise.

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or …

Paper proposes deep neural networks for nonparametric regression from dependent data.

Proposes CLUB for reliable MI minimization in high dimensions.

This paper proposes a DGP approach with UCBs for point target tracking over WSNs.

New SQ lower bound shows complexity nearly matches known upper bound for smoothed agnostic learning.

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. As an extension of Welling and Teh (2001), we define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals and derive an …

While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely many bits. In this note, we characterise the quality of a code (i. e. a given en…

In this paper, we consider the challenge of maximizing an unknown function f for which evaluations are noisy and are acquired with high cost. An iterative procedure uses the previous measures to actively select the next estimation of f which is predicted to be the most useful. We focus on the case where the function ca…

New acquisition function for extreme rewards in bandits.