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Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process,…

Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…

In this paper, we propose an analytical method for performing tractable approximate Gaussian inference (TAGI) in Bayesian neural networks. The method enables the analytical Gaussian inference of the posterior mean vector and diagonal…

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…

Full waveform inversion (FWI) commonly stands for the state-of-the-art approach for imaging subsurface structures and physical parameters, however, its implementation usually faces great challenges, such as building a good initial model to…

As Deep Learning continues to yield successful applications in Computer Vision, the ability to quantify all forms of uncertainty is a paramount requirement for its safe and reliable deployment in the real-world. In this work, we leverage…

Gaussian processes are employed for non-parametric regression in a Bayesian setting. They generalize linear regression, embedding the inputs in a latent manifold inside an infinite-dimensional reproducing kernel Hilbert space. We can…

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,…

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…

Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In…

We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…

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…

Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…

For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational…

This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The…

The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural…

Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…