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The problem of maximum-likelihood (ML) estimation of discrete tree-structured distributions is considered. Chow and Liu established that ML-estimation reduces to the construction of a maximum-weight spanning tree using the empirical mutual…
The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both…
In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central…
This paper studies the decentralized learning of tree-structured Gaussian graphical models (GGMs) from noisy data. In decentralized learning, data set is distributed across different machines (sensors), and GGMs are widely used to model…
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…
Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…
The change detection problem is to determine if the Markov network structures of two Markov random fields differ from one another given two sets of samples drawn from the respective underlying distributions. We study the trade-off between…
Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In…
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…
It is known that from purely observational data, a causal DAG is identifiable only up to its Markov equivalence class, and for many ground truth DAGs, the direction of a large portion of the edges will be remained unidentified. The golden…
Knowing the causal structure of a system is of fundamental interest in many areas of science and can aid the design of prediction algorithms that work well under manipulations to the system. The causal structure becomes identifiable from…
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…
We consider the problem of decentralized detection in a network consisting of a large number of nodes arranged as a tree of bounded height, under the assumption of conditionally independent, identically distributed observations. We…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language,…
Despite numerous years of research into the merits and trade-offs of various model selection criteria, obtaining robust results that elucidate the behavior of cross-validation remains a challenging endeavor. In this paper, we highlight the…
We show that $n$-variable tree-structured Ising models can be learned computationally-efficiently to within total variation distance $\epsilon$ from an optimal $O(n \ln n/\epsilon^2)$ samples, where $O(\cdot)$ hides an absolute constant…
Gaussian Bayesian networks (a.k.a. linear Gaussian structural equation models) are widely used to model causal interactions among continuous variables. In this work, we study the problem of learning a fixed-structure Gaussian Bayesian…
Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being…