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This paper focuses on Bayesian Optimization in combinatorial spaces. In many applications in the natural science. Broad applications include the study of molecules, proteins, DNA, device structures and quantum circuit designs, a on…
We tackle the extension to the vector-valued case of consistency results for Stepwise Uncertainty Reduction sequential experimental design strategies established in [Bect et al., A supermartingale approach to Gaussian process based…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially…
The goal of this paper is to understand the conditional law of a stochastic process once it has been observed over an interval. To make this precise, we introduce the notion of a continuous disintegration: a regular conditional probability…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
We present a novel framework for conditional sampling of probability measures, using block triangular transport maps. We develop the theoretical foundations of block triangular transport in a Banach space setting, establishing general…
We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and…
In this paper we show that the conditional distribution of perturbed chi-quare risks can be approximated by certain distributions including the Gaussian ones. Our results are of interest for conditional extreme value models and multivariate…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
This paper discusses a new notion of quadratic variation and covariation for Banach space valued processes (not necessarily semimartingales) and related It\^o formula. If $\X$ and $\Y$ take respectively values in Banach spaces $B_{1}$ and…
In this paper, we establish $\mathcal B$-valued variational inequalities for differential operators, ergodic averages and symmetric diffusion semigroups under the condition that Banach space $\mathcal B$ has martingale cotype property.…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…
We study the generic behavior of the method of successive approximations for set-valued mappings in Banach spaces. We consider, in particular, the case of those set-valued mappings which are defined by pairs of nonexpansive mappings and…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…