Related papers: Ordinal Optimisation for the Gaussian Copula Model

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves…

Gaussian Process (GP) models have also become extremely useful for optimization under uncertainty algorithms, especially where the objective functions are costly to compute. Yet, the more classical methods usually adopt strategies that, in…

We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…

We propose a safe approximation to joint chance-constrained programming where the constraint functions are additively dependent on a normally-distributed random vector. The approximation is analytical, meaning that it requires neither…

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…

We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…

Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…

We propose a novel, theoretically-grounded, acquisition function for Batch Bayesian optimization informed by insights from distributionally ambiguous optimization. Our acquisition function is a lower bound on the well-known Expected…

Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…

Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by…

Background: The proportional odds (PO) model is the most common analytic method for ordinal outcomes in randomised controlled trials. While parameter estimates obtained under departures from PO can be interpreted as an average odds ratio,…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

In stochastic optimization, the population risk is generally approximated by the empirical risk. However, in the large-scale setting, minimization of the empirical risk may be computationally restrictive. In this paper, we design an…

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

We provide a numerical scheme to approximate as closely as desired the Gaussian or exponential measure $\mu(\om)$ of (not necessarily compact) basic semi-algebraic sets$\om\subset\R^n$. We obtain two monotone (non increasing and non…

Clustering task of mixed data is a challenging problem. In a probabilistic framework, the main difficulty is due to a shortage of conventional distributions for such data. In this paper, we propose to achieve the mixed data clustering with…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…