Related papers: Ordinal Optimisation for the Gaussian Copula Model

Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…

Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…

The paper considers a distributed algorithm for global minimization of a nonconvex function. The algorithm is a first-order consensus + innovations type algorithm that incorporates decaying additive Gaussian noise for annealing, converging…

Computing sets of high quality solutions has gained increasing interest in recent years. In this paper, we investigate how to obtain sets of optimal solutions for the classical knapsack problem. We present an algorithm to count exactly the…

We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure, analogous to the Johnson-Lindenstrauss lemma. As…

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…

Ordinal regression (OR, also called ordinal classification) is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation for the underlying explanatory variable.…

Recently, there has been rising interest in Bayesian optimization -- the optimization of an unknown function with assumptions usually expressed by a Gaussian Process (GP) prior. We study an optimization strategy that directly uses an…

We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of…

In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even…

Many real-world optimization problems involve an expensive ground-truth oracle (e.g., human evaluation, physical experiments) and a cheap, low-fidelity prediction oracle (e.g., machine learning models, simulations). Meanwhile, abundant…

This paper addresses the problem of model selection in the sequence model $Y=\theta+\varepsilon\xi$, when $\xi$ is sub-Gaussian, for non-euclidian loss-functions. In this model, the Penalized Comparison to Overfitting procedure is studied…

Bayesian optimization (BO) with Gaussian process (GP) surrogate models is a powerful black-box optimization method. Acquisition functions are a critical part of a BO algorithm as they determine how the new samples are selected. Some of the…

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…

We consider the problem of global optimization of a function over a continuous domain. In our setup, we can evaluate the function sequentially at points of our choice and the evaluations are noisy. We frame it as a continuum-armed bandit…

Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…