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Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…

Tuning scientific and probabilistic machine learning models $-$ for example, partial differential equations, Gaussian processes, or Bayesian neural networks $-$ often relies on evaluating functions of matrices whose size grows with the data…

Deep generative models such as GANs, normalizing flows, and diffusion models are powerful regularizers for inverse problems. They exhibit great potential for helping reduce ill-posedness and attain high-quality results. However, the latent…

Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…

Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

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,…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

Deep generative models (e.g. GANs and VAEs) have been developed quite extensively in recent years. Lately, there has been an increased interest in the inversion of such a model, i.e. given a (possibly corrupted) signal, we wish to recover…

This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…

This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…

A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…

Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…

Linear methods are ubiquitous for control and estimation problems. In this work, we present a number of tensor operator norms as a means to approximately bound the error associated with linear methods and determine the situations in which…

We model time-varying network data as realizations from multivariate Gaussian distributions with precision matrices that change over time. To facilitate parameter estimation, we require not only that each precision matrix at any given time…