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Statistical network models are useful for understanding the underlying formation mechanism and characteristics of complex networks. However, statistical models for \textit{signed networks} have been largely unexplored. In signed networks,…
Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables…
We describe an efficient and scalable spherical graph embedding method. The method uses a generalization of the Euclidean stress function for Multi-Dimensional Scaling adapted to spherical space, where geodesic pairwise distances are…
Learning latent structure in complex networks has become an important problem fueled by many types of networked data originating from practically all fields of science. In this paper, we propose a new non-parametric Bayesian…
Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…
Interactions between actors are frequently represented using a network. The latent position model is widely used for analysing network data, whereby each actor is positioned in a latent space. Inferring the dimension of this space is…
Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA).…
Latent space model plays a crucial role in network analysis, and accurate estimation of latent variables is essential for downstream tasks such as link prediction. However, the large number of parameters to be estimated presents a…
In a dynamic network, the neighborhood of the vertices evolve across different temporal snapshots of the network. Accurate modeling of this temporal evolution can help solve complex tasks involving real-life social and interaction networks.…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
We propose a directed acyclic hypergraph framework for a probabilistic graphical model that we call Bayesian hypergraphs. The space of directed acyclic hypergraphs is much larger than the space of chain graphs. Hence Bayesian hypergraphs…
Latent space models (LSM) for network data were introduced by Hoff et al. (2002) under the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance…
The study of network data in the social and health sciences frequently concentrates on two distinct tasks (1) detecting community structures among nodes and (2) associating covariate information to edge formation. In much of this data, it…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
Understanding network functionality requires integrating structure and dynamics, and emergent latent geometry induced by network-driven processes captures the low-dimensional spaces governing this interplay. Here, we focus on…
Spatial generalized linear mixed-effects models are popularly used to analyze spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of…
State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…