Related papers: Structure Learning in Graphical Models from Indire…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…
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…
Probabilistic graphical models (PGMs) provide a compact and flexible framework to model very complex real-life phenomena. They combine the probability theory which deals with uncertainty and logical structure represented by a graph which…
Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…
We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…
A central machine is interested in estimating the underlying structure of a sparse Gaussian Graphical Model (GGM) from datasets distributed across multiple local machines. The local machines can communicate with the central machine through…
We study the problem of detecting the presence of an underlying high-dimensional geometric structure in a random graph. Under the null hypothesis, the observed graph is a realization of an Erd\H{o}s-R\'enyi random graph $G(n,p)$. Under the…
We propose a method for learning Markov network structures for continuous data without invoking any assumptions about the distribution of the variables. The method makes use of previous work on a non-parametric estimator for mutual…
We consider the problem of estimating an undirected Gaussian graphical model when the underlying distribution is multivariate totally positive of order 2 (MTP2), a strong form of positive dependence. Such distributions are relevant for…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…
Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for learning graphical models with least amount of data remains an active research topic.…
Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved,…
We consider the problem of reconstructing the graph underlying an Ising model from i.i.d. samples. Over the last fifteen years this problem has been of significant interest in the statistics, machine learning, and statistical physics…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
The problem of learning structural equation models (SEMs) from data is a fundamental problem in causal inference. We develop a new algorithm --- which is computationally and statistically efficient and works in the high-dimensional regime…
Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration…
Let $G$ be an undirected graph with $m$ edges and $d$ vertices. We show that $d$-dimensional Ising models on $G$ can be learned from $n$ i.i.d. samples within expected total variation distance some constant factor of $\min\{1, \sqrt{(m +…
The graphical structure of Probabilistic Graphical Models (PGMs) encodes the conditional independence (CI) relations that hold in the modeled distribution. Graph algorithms, such as d-separation, use this structure to infer additional…