Related papers: A Generator for Generalized Inverse Gaussian Distr…
In this paper we introduce five different algorithms based on method of moments, maximum likelihood and full Bayesian estimation for learning the parameters of the Inverse Gamma distribution. We also provide an expression for the KL…
In this paper, we study Bayesian approach for solving large scale linear inverse problems arising in various scientific and engineering fields. We propose a fused $L_{1/2}$ prior with edge-preserving and sparsity-promoting properties and…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
Any explicit functional representation $f$ of a density is hampered by two main obstacles when we wish to use it as a generative model: designing $f$ so that sampling is fast, and estimating $Z = \int f$ so that $Z^{-1}f$ integrates to 1.…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
Inverse classification is the process of perturbing an instance in a meaningful way such that it is more likely to conform to a specific class. Historical methods that address such a problem are often framed to leverage only a single…
In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The Gibbs posterior formulation is a generalization of standard…
Region-of-Interest (ROI)-based image compression allocates bits unevenly according to the semantic importance of different regions. Such differentiated coding typically induces a sharp-peaked and heavy-tailed distribution. This distribution…
Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…
Generalized feed-forward Gaussian models have achieved significant progress in sparse-view 3D reconstruction by leveraging prior knowledge from large multi-view datasets. However, these models often struggle to represent high-frequency…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…
The calculation of the underground density field from measured gravity data has been done by a variety of methods of varied types. The use of the vector gravity components is here addressed in order to develop one accurate gravity inversion…
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…
We develop an efficient posterior sampling scheme for the Poisson INGARCH models. The proposed method is based on the approximation of the posterior density that exploits the Poisson limit of the negative binomial distribution. It allows us…
A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of…
Generative adversarial networks constitute a powerful approach to generative modeling. While generated samples often are indistinguishable from real data, there is no guarantee that they will follow the true data distribution. For…
Conventional meta-atom designs rely heavily on researchers' prior knowledge and trial-and-error searches using full-wave simulations, resulting in time-consuming and inefficient processes. Inverse design methods based on optimization…
The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…