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Promising results have driven a recent surge of interest in continuous optimization methods for Bayesian network structure learning from observational data. However, there are theoretical limitations on the identifiability of underlying…

Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected…

Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…

The vast majority of network datasets contains errors and omissions, although this is rarely incorporated in traditional network analysis. Recently, an increasing effort has been made to fill this methodological gap by developing network…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

Bayesian networks have been used as a mechanism to represent the joint distribution of multiple random variables in a flexible yet interpretable manner. One major challenge in learning the structure of a Bayesian network is how to model…

Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive…

We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…

Bayesian networks (BNs) are graphical models that are useful for representing high-dimensional probability distributions. There has been a great deal of interest in recent years in the NP-hard problem of learning the structure of a BN from…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…

We describe a graphical model for probabilistic relationships---an alternative to the Bayesian network---called a dependency network. The graph of a dependency network, unlike a Bayesian network, is potentially cyclic. The probability…

Finding the parameters of a latent variable causal model is central to causal inference and causal identification. In this article, we show that existing graphical structures that are used in causal inference are not stable under…

We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random…

Heterogeneous molecular entities and their interactions, commonly depicted as a network, are crucial for advancing our systems-level understanding of biology. With recent advancements in high-throughput data generation and a significant…

We present a technique to characterize differentially expressed genes in terms of their position in a high-dimensional co-expression network. The set-up of Gaussian graphical models is used to construct representations of the co-expression…

Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…

Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…