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Graphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…
We present a new method for estimating multivariate, second-order stationary Gaussian Random Field (GRF) models based on the Sparse Precision matrix Selection (SPS) algorithm, proposed by Davanloo et al. (2015) for estimating scalar GRF…
Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on…
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…
Solving inverse problems with the reverse process of a diffusion model represents an appealing avenue to produce highly realistic, yet diverse solutions from incomplete and possibly noisy measurements, ultimately enabling uncertainty…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
While continuous diffusion models have achieved remarkable success, discrete diffusion offers a unified framework for jointly modeling text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…