Related papers: Discussion of "A Gibbs sampler for a class of rand…
We present a Gibbs sampler for the Dempster-Shafer (DS) approach to statistical inference for Categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields…
This is a contribution for the discussion on "A Gibbs sampler for a class of random convex polytopes" by Pierre E. Jacob, Ruobin Gong, Paul T. Edlefsen and Arthur P. Dempster to appear in the Journal of American Statistical Association.
In this paper, the Dempster-Shafer method is employed as the theoretical basis for creating data classification systems. Testing is carried out using three popular (multiple attribute) benchmark datasets that have two, three and four…
A new method for multinomial inference is proposed by representing the cell probabilities as unordered segments on the unit interval and following Dempster-Shafer (DS) theory. The resulting DS posterior is then strengthened to improve…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
This paper explores the interplay between statistics and generative artificial intelligence. Generative statistics, an integral part of the latter, aims to construct models that can generate efficiently and meaningfully new data across the…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
We propose a new classifier based on Dempster-Shafer (DS) theory and a convolutional neural network (CNN) architecture for set-valued classification. In this classifier, called the evidential deep-learning classifier, convolutional and…
Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
We describe a provably complete algorithm for the generation of a tight, possibly exact superset of all combinatorially distinct simple n-facet polytopes in R^d, along with their graphs, f-vectors, and face lattices. The technique applies…
We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing…
We present Digenes, a new discovery system that aims to help researchers in graph theory. While its main task is to find extremal graphs for a given (function of) invariants, it also provides some basic support in proof conception. This has…
We study the Gibbs sampling algorithm for continuous determinantal point processes. We show that, given a warm start, the Gibbs sampler generates a random sample from a continuous $k$-DPP defined on a $d$-dimensional domain by only taking…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…
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…
The Gibbs sampler is one of the most popular algorithms for inference in statistical models. In this paper, we introduce a herding variant of this algorithm, called herded Gibbs, that is entirely deterministic. We prove that herded Gibbs…
The Dempster--Shafer (DS) theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence. DS theory has been widely used in computer science and engineering applications, but has yet to reach the…
Deep generative models have achieved great success in areas such as image, speech, and natural language processing in the past few years. Thanks to the advances in graph-based deep learning, and in particular graph representation learning,…