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Graph neural networks (GNNs), which propagate the node features through the edges and learn how to transform the aggregated features under label supervision, have achieved great success in supervised feature extraction for both node-level…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
Cell formation is a critical step in the design of cellular manufacturing systems. Recently, it was tackled using a cut-based-graph-partitioning model. This model meets real-life production systems requirements as it uses the actual amount…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…
Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as real physical notion so as to…
This paper is the first in the series devoted to evaluation of the partition function in statistical models on graphs with loops in terms of the Berezin/fermion integrals. The paper focuses on a representation of the determinant of a square…
A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the…
For spin systems, such as the $q$-colorings and independent-set models, approximating the partition function in the so-called non-uniqueness region, where the model exhibits long-range correlations, is typically computationally hard for…
Graph representation learning is a ubiquitous task in machine learning where the goal is to embed each vertex into a low-dimensional vector space. We consider the bipartite graph and formalize its representation learning problem as a…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…
The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is…
We study the belief propagation algorithm for the graph bi-partitioning problem, i.e. the ground state of the ferromagnetic Ising model at a fixed magnetization. Application of a message passing scheme to a model with a fixed global…
Although Graph Convolutional Networks (GCNs) have demonstrated their power in various applications, the graph convolutional layers, as the most important component of GCN, are still using linear transformations and a simple pooling step. In…
In graph neural networks (GNNs), both node features and labels are examples of graph signals, a key notion in graph signal processing (GSP). While it is common in GSP to impose signal smoothness constraints in learning and estimation tasks,…
Factor graphs are a ubiquitous tool for multi-source inference in robotics and multi-sensor networks. They allow for heterogeneous measurements from many sources to be concurrently represented as factors in the state posterior distribution,…
The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a…
[...] In this thesis, we are interested in generalizing factor graphs and the relevant methods toward describing quantum systems. Two generalizations of classical graphical models are investigated, namely double-edge factor graphs (DeFGs)…
One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied…
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…