Related papers: Wasserstein-enabled characterization of designs an…

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…

We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…

The main objective of this paper is to outline a theoretical framework to characterise humans' decision-making strategies under uncertainty, in particular active learning in a black-box optimization task and trading-off between information…

Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…

Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…

This paper introduces a probabilistic framework to estimate parameters of an acquisition function given observed human behavior that can be modeled as a collection of sample paths from a Bayesian optimization procedure. The methodology…

Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…

Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…

We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with…

Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…

A Bayesian design is given by maximising an expected utility over a design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models.…

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during…

Designing experiments that systematically gather data from complex physical systems is central to accelerating scientific discovery. While Bayesian experimental design (BED) provides a principled, information-based framework that integrates…

Bayesian optimization (BO) provides a powerful framework for optimizing black-box, expensive-to-evaluate functions. It is therefore an attractive tool for engineering design problems, typically involving multiple objectives. Thanks to the…

We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…

We analyze the effect of small changes in the underlying probabilistic model on the value of multi-period stochastic optimization problems and optimal stopping problems. We work in finite discrete time and measure these changes with the…

Personalization in marketing aims at improving the shopping experience of customers by tailoring services to individuals. In order to achieve this, businesses must be able to make personalized predictions regarding the next purchase. That…

This study concerns the formulation and application of Bayesian optimal experimental design to symbolic discovery, which is the inference from observational data of predictive models taking general functional forms. We apply constrained…