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The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…

Fast inference of numerical model parameters from data is an important prerequisite to generate predictive models for a wide range of applications. Use of sampling-based approaches such as Markov chain Monte Carlo may become intractable…

We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…

A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an…

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…

Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…

In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols,…

We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model.…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

In this work, a fully nonparametric geostatistical approach to estimate threshold exceeding probabilities is proposed. To estimate the large-scale variability (spatial trend) of the process, the nonparametric local linear regression…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…

Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…

Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically…