Related papers: Ordinal Optimisation for the Gaussian Copula Model

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional…

We discuss the approach to estimate aggregation and adaptive estimation based upon (nearly optimal) testing of convex hypotheses. We show that in the situation where the observations stem from {\em simple observation schemes} and where set…

Consider the sequential optimization of a continuous, possibly non-convex, and expensive to evaluate objective function $f$. The problem can be cast as a Gaussian Process (GP) bandit where $f$ lives in a reproducing kernel Hilbert space…

Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…

We study the limit computability of finding a global optimum of a continuous function. We give a short proof to show that the problem of checking whether a point is a global minimum is not limit computable. Thereby showing the same for the…

This paper deals with robust inference for parametric copula models. Estimation using Canonical Maximum Likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the Maximum Mean…

We derive criteria for the selection of datapoints used for data-driven reduced-order modeling and other areas of supervised learning based on Gaussian process regression (GPR). While this is a well-studied area in the fields of active…

We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant…

In this paper we build provably near-optimal, in the minimax sense, estimates of linear forms and, more generally, "$N$-convex functionals" (the simplest example being the maximum of several fractional-linear functions) of unknown "signal"…

This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…

Bayesian Optimization, the application of Bayesian function approximation to finding optima of expensive functions, has exploded in popularity in recent years. In particular, much attention has been paid to improving its efficiency on…

This paper addresses the Bayesian optimization problem (also referred to as the Bayesian setting of the Gaussian process bandit), where the learner seeks to minimize the regret under a function drawn from a known Gaussian process (GP).…

This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise. Our approach combines a series of basis changes with Bayes' rule, transforming the singular estimation problem into a…

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…

Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However,…

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…

In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…

We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let $\mathrm{OPT}:=\max_{\sigma_1,\cdots,\sigma_n}\mathbb{E}\left[\sum_{j=1}^{m}\max_{i\in…

In this paper, we obtain bounds on the probability of convergence to the optimal solution for the compact Genetic Algorithm (cGA) and the Population Based Incremental Learning (PBIL). We also give a sufficient condition for convergence of…