Related papers: Bayesian Models of Graphs, Arrays and Other Exchan…

We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks,…

Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on…

Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might…

A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is…

Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to…

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Many biological networks include cyclic structures. In such cases, Bayesian networks (BNs), which must be acyclic, are not sound models for structure learning. Dynamic BNs can be used but require relatively large time series data. We…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Bayesian networks (BN) are directed acyclic graphical (DAG) models that have been adopted into many fields for their strengths in transparency, interpretability, probabilistic reasoning, and causal modeling. Given a set of data, one hurdle…

Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…

Bayesian networks are graphical models to represent the probabilistic relationships between variables in the Bayesian framework. The knowledge of all variables can be updated using new information about some of the variables. We show that…

We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

In ecology, the description of species composition and biodiversity calls for statistical methods that involve estimating features of interest in unobserved samples based on an observed one. In the last decade, the Bayesian nonparametrics…

Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…

Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the…

A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number…

The structure of a Bayesian network encodes most of the information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study the…

Motivated by the need to analyze large, decentralized datasets, distributed Bayesian inference has become a critical research area across multiple fields, including statistics, electrical engineering, and economics. This paper establishes…