Related papers: Bures-Wasserstein Importance-Weighted Evidence Low…

We present a Bayesian framework based on a new exponential likelihood function driven by the quadratic Wasserstien metric. Compared to conventional Bayesian models based on Gaussian likelihood functions driven by the least-squares norm…

A long-standing belief holds that Bayesian Optimization (BO) with standard Gaussian processes (GP) -- referred to as standard BO -- underperforms in high-dimensional optimization problems. While this belief seems plausible, it lacks both…

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying…

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods…

We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which…

We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…

Bayesian Optimisation (BO) is a state-of-the-art global optimisation technique for black-box problems where derivative information is unavailable, and sample efficiency is crucial. However, improving the general scalability of BO has proved…

Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs…

Effective uncertainty quantification is important for training modern predictive models with limited data, enhancing both accuracy and robustness. While Bayesian methods are effective for this purpose, they can be challenging to scale. When…

We consider statistical methods which invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning…

Distributionally robust supervised learning (DRSL) is emerging as a key paradigm for building reliable machine learning systems for real-world applications -- reflecting the need for classifiers and predictive models that are robust to the…

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…

We establish new lower bounds for the normal approximation in the Wasserstein distance of random variables that are functionals of a Poisson measure. Our results generalize previous findings by Nourdin and Peccati (2012, 2015) and Bierm\'e,…

This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures. The classical estimation method, restricted maximum likelihood (REML), requires repeated…

The performance of machine learning (ML) models critically depends on the quality and representativeness of the training data. In applications with multiple heterogeneous data generating sources, standard ML methods often learn spurious…

We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a…

Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…

Estimation of reliability and hazard rate is one of the most important problems raised in many applications especially in engineering studies as well as human lifetime. In this regard, different methods of estimation have been used. Each…

We explore a new research direction in Bayesian variational inference with discrete latent variable priors where we exploit Kronecker matrix algebra for efficient and exact computations of the evidence lower bound (ELBO). The proposed…

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…