Related papers: Inverse Filtering for Hidden Markov Models with Ap…

Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…

Sparse representations have proven their efficiency in solving a wide class of inverse problems encountered in signal and image processing. Conversely, enforcing the information to be spread uniformly over representation coefficients…

We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete…

We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

We study Bayesian optimal control of a general class of smoothly parameterized Markov decision problems. Since computing the optimal control is computationally expensive, we design an algorithm that trades off performance for computational…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for…

A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…

In this paper, we address the fusion problem in wireless sensor networks, where the cross-correlation between the estimates is unknown. To solve the problem within the Bayesian framework, we assume that the covariance matrix has a prior…

We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

The Bayesian inference approach is widely used to tackle inverse problems due to its versatile and natural ability to handle ill-posedness. However, it often faces challenges when dealing with situations involving continuous fields or…

This paper develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by adversarial optimization, namely Generative…

In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with…

We define an evolving in-time Bayesian neural network called a Hidden Markov Neural Network, which addresses the crucial challenge in time-series forecasting and continual learning: striking a balance between adapting to new data and…

In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data. The model under consideration is governed by a class of semilinear evolution…

This paper focuses on the state estimation problem in distributed sensor networks, where intermittent packet dropouts, corrupted observations, and unknown noise covariances coexist. To tackle this challenge, we formulate the joint…

Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…

Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…