Related papers: Duality in Graphical Models
The popular generalized additive model framework is extended to allow both the mean curves and the response distribution to be nonparametric. The approach is demonstrated to be a flexible yet parsimonious tool for data analysis in its own…
Algorithmic fairness has become an important machine learning problem, especially for mission-critical Web applications. This work presents a self-supervised model, called DualFair, that can debias sensitive attributes like gender and race…
Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…
Graph signal processing uses the graph eigenvector basis to analyze signals. However, these graph eigenvectors are typically linearly ordered (by total variation), which may not be reasonable for many graph structures. There have been…
\emph{Bidirected graphs} (a sort of nonstandard graphs introduced by Edmonds and Johnson) provide a natural generalization to the notions of directed and undirected graphs. By a \emph{weakly (node- or edge-) acyclic} bidirected graph we…
The overdraw problem of scatterplots seriously interferes with the visual tasks. Existing methods, such as data sampling, node dispersion, subspace mapping, and visual abstraction, cannot guarantee the correspondence and consistency between…
Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth).…
Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…
Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implications in diverse fields ranging from matching problems to the…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
The two matrix model is considered, with measure given by the exponential of a sum of polynomials in two different variables. It is shown how to derive a sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding…
Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…
We derive standard imsets for undirected graphical models and chain graphical models. Standard imsets for undirected graphical models are described in terms of minimal triangulations for maximal prime subgraphs of the undirected graphs. For…
A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a…
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…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
Graph representation learning nowadays becomes fundamental in analyzing graph-structured data. Inspired by recent success of contrastive methods, in this paper, we propose a novel framework for unsupervised graph representation learning by…