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Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
The human body consists of microbiomes associated with the development and prevention of several diseases. These microbial organisms form several complex interactions that are informative to the scientific community for explaining disease…
Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods…
Motivated by a neuroscience application we study the problem of statistical estimation of a high-dimensional covariance matrix with a block structure. The block model embeds a structural assumption: the population of items (neurons) can be…
In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to…
We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g.…
The Stochastic Block Model (SBM) is a popular probabilistic model for random graphs. It is commonly used for clustering network data by aggregating nodes that share similar connectivity patterns into blocks. When fitting an SBM to a network…
Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…
In complex systems, the network of interactions we observe between system's components is the aggregate of the interactions that occur through different mechanisms or layers. Recent studies reveal that the existence of multiple interaction…
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…
Traditional approaches to Bayes net structure learning typically assume little regularity in graph structure other than sparseness. However, in many cases, we expect more systematicity: variables in real-world systems often group into…
The Stochastic Block Model (Holland et al., 1983) is a mixture model for heterogeneous network data. Unlike the usual statistical framework, new nodes give additional information about the previous ones in this model. Thereby the…
This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With…
In this paper, we introduce a novel Distributed Markov Chain Monte Carlo (MCMC) inference method for the Bayesian Non-Parametric Latent Block Model (DisNPLBM), employing the Master/Worker architecture. Our non-parametric co-clustering…
A class of models that have been widely used are the exponential random graph (ERG) models, which form a comprehensive family of models that include independent and dyadic edge models, Markov random graphs, and many other graph…
We consider the controllability of large-scale linear networked dynamical systems when complete knowledge of network structure is unavailable and knowledge is limited to coarse summaries. We provide conditions under which average…
The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this…
We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and…
Community detection is an important content in complex network analysis. The existing community detection methods in attributed networks mostly focus on only using network structure, while the methods of integrating node attributes is…