Related papers: Learning High-Dimensional Mixtures of Graphical Mo…

This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…

A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden…

Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are…

Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or…

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…

Recently there has been increased interest in semi-supervised classification in the presence of graphical information. A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first…

The ability to conduct interventions plays a pivotal role in learning causal relationships among variables, thus facilitating applications across diverse scientific disciplines such as genomics, economics, and machine learning. However, in…

In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…

Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…

We propose a new method for detecting changes in Markov network structure between two sets of samples. Instead of naively fitting two Markov network models separately to the two data sets and figuring out their difference, we…

Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…

Physical phenomena in science and engineering are frequently modeled using scalar fields. In scalar field topology, graph-based topological descriptors such as merge trees, contour trees, and Reeb graphs are commonly used to characterize…

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.…

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…

The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the…

Many problems in real-world applications involve predicting several random variables which are statistically related. Markov random fields (MRFs) are a great mathematical tool to encode such relationships. The goal of this paper is to…

Humans perceive the seemingly chaotic world in a structured and compositional way with the prerequisite of being able to segregate conceptual entities from the complex visual scenes. The mechanism of grouping basic visual elements of scenes…