Related papers: A Bayesian Perspective on Uncertainty Quantificati…
Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…
Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
We explore the notion of uncertainty in the context of modern abstractive summarization models, using the tools of Bayesian Deep Learning. Our approach approximates Bayesian inference by first extending state-of-the-art summarization models…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
We give a probabilistic interpretation of sampling theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain…
We propose a sampling algorithm to perform system identification from a set of input-output graph signal pairs. The dynamics of the systems we study are given by a partially known adjacency matrix and a generic parametric graph filter of…
Safe and reliable disclosure of information from confidential data is a challenging statistical problem. A common approach considers the generation of synthetic data, to be disclosed instead of the original data. Efficient approaches ought…
We develop a generative model-based approach to Bayesian inverse problems, such as image reconstruction from noisy and incomplete images. Our framework addresses two common challenges of Bayesian reconstructions: 1) It makes use of complex,…
In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…
The interdependence between nodes in graphs is key to improve class predictions on nodes and utilized in approaches like Label Propagation (LP) or in Graph Neural Networks (GNN). Nonetheless, uncertainty estimation for non-independent…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
We consider the problem of uncertainty quantification for an unknown low-rank matrix $\mathbf{X}$, given a partial and noisy observation of its entries. This quantification of uncertainty is essential for many real-world problems, including…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but…
Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to…
We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over…