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We address the task of probabilistic anomaly attribution in the black-box regression setting, where the goal is to compute the probability distribution of the attribution score of each input variable, given an observed anomaly. The training…

Object counting models suffer when deployed across domains with differing density variety, since density shifts are inherently task-relevant and violate standard domain adaptation assumptions. To address this, we propose a theoretical…

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…

Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…

Predicting diverse human motions given a sequence of historical poses has received increasing attention. Despite rapid progress, existing work captures the multi-modal nature of human motions primarily through likelihood-based sampling,…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier,…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…

In this work, an adaptive predictive control scheme for linear systems with unknown parameters and bounded additive disturbances is proposed. In contrast to related adaptive control approaches that robustly consider the parametric…

It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…

The aim of this paper is to propose diffusion strategies for distributed estimation over adaptive networks, assuming the presence of spatially correlated measurements distributed according to a Gaussian Markov random field (GMRF) model. The…

Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…

This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and…