arXiv research

Graph neural networks speed up nonnegative matrix factorization.

Study abelian factors in Lie algebras from graph edge labels.

Extends graph factor system to quasi-median graphs.

A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to plate diagrams for directed graphical models. To exploit efficient t…

Extract common latent factors from graphs for better representation learning.

The free factor graph for Aut(F_N) is not hyperbolic.

DGA and DVGA learn disentangled graph representations to improve graph analysis.

Data-driven factor graphs improve BCJR detection robustness.

End-to-end graph-based SSL learns all graph factors dynamically.

Efficiently learns deep factor graphs using Gaussian belief propagation.

Develops a deep multi-factor model for factor investing with clear financial insights.

The paper refines 2-factor homology to a stable homotopy type for planar trivalent graphs with perfect matchings.

The paper extends NUP representations to factor graphs for better estimation.

EPFGNN models graph connections for better node classification.

Learned factor graphs improve inference from time sequences using neural networks.

PGMax automates PGM inference on GPUs, improving quality and speed.

Study on factorizations of knot polynomials for up to 12 crossings.

Improved error correction using neural networks and belief propagation.

Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformati…

Method solves Gaussian graphical models on ladder graphs efficiently.

We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It estimates observed graphs as GW barycenters constructed by a se…

Improves scalability and robustness of dynamic graph clustering.

New Ricci flow method for directed graphs with balancing factor.

We show that the Gromov boundary of the free factor graph for the free group Fn with n>2 generators is the space of equivalence classes of minimal very small indecomposable projective Fn-trees without point stabilizer containing a free factor equipped with a quotient topology. Here two such trees are equivalent if the …

Enhances knowledge graph completion with mixed geometry tensor factorization.

A new framework models and simulates multibody systems using factor graphs.

GRU-PFG model extracts inter-stock correlations from stock factors using graph neural networks.

Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. …

In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as linear transformations of tree models. This is a new way to decompose the covariance…

Proposes a new tensor factorization model for better link prediction in knowledge graphs.

The paper discusses a pooling mechanism to induce subsampling in graph structured data and introduces it as a component of a graph convolutional neural network. The pooling mechanism builds on the Non-Negative Matrix Factorization (NMF) of a matrix representing node adjacency and node similarity as adaptively obtained …

The set of factorizations of permutations in to $m$ transpositions of some symmetric group $\mathcal{S}_n$ is naturally in bijection with the set of graphs of order $n$ and size $m$ with both edges and vertices labeled. We define a notion of duality (the \emph{mind-body duality}) for factorizations and such labeled gra…

Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise naturally when working with factor graphs. Belief propagation is a widely deplo…

We present a general theoretical analysis of structured prediction with a series of new results. We give new data-dependent margin guarantees for structured prediction for a very wide family of loss functions and a general family of hypotheses, with an arbitrary factor graph decomposition. These are the tightest margin…

Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and belief propagation take advantage of constraints embedded in this factorization …

This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that the regular Gaussian distributions that factorize with respect to a chain graph $G$ with $d$ parameters have positive Lebesgue measure with respect to $\mathbb{R}^d$, whereas those that factorize with respect…

Paper proposes AI for stock market forecasting using external knowledge.

We prove that the marginal densities of a global probability mass function in a primal normal factor graph and the corresponding marginal densities in the dual normal factor graph are related via local mappings. The mapping depends on the Fourier transform of the local factors of the models. Details of the mapping, inc…

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of nonnegative data. Recently, Graph regula…

New principle controls graph-informed adversarial discrepancies.

We address some computational issues that may hinder the use of AMP chain graphs in practice. Specifically, we show how a discrete probability distribution that satisfies all the independencies represented by an AMP chain graph factorizes according to it. We show how this factorization makes it possible to perform infe…

We address the problem of disentangled representation learning with independent latent factors in graph convolutional networks (GCNs). The current methods usually learn node representation by describing its neighborhood as a perceptual whole in a holistic manner while ignoring the entanglement of the latent factors. Ho…

The paper studies graph Laplace operator behavior near isolated singularities.

Time series of graphs are increasingly prevalent in modern data and pose unique challenges to visual exploration and pattern extraction. This paper describes the development and application of matrix factorizations for exploration and time-varying community detection in time-evolving graph sequences. The matrix factori…

The study examines the stretch factors of outer automorphisms and their latent symmetry.

In matrix factorization, available graph side-information may not be well suited for the matrix completion problem, having edges that disagree with the latent-feature relations learnt from the incomplete data matrix. We show that removing these $\textit{contested}$ edges improves prediction accuracy and scalability. We…

Automates model comparison in probabilistic programming.

New distribution simplifies covariance matrix inference.