Related papers: Graphical Models as Block-Tree Graphs
General graphs are difficult for learning due to their irregular structures. Existing works employ message passing along graph edges to extract local patterns using customized graph kernels, but few of them are effective for the integration…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
Subgraph counting aims to count the occurrences of a subgraph template T in a given network G. The basic problem of computing structural properties such as counting triangles and other subgraphs has found applications in diverse domains.…
In this article, we propose the approach to structural optimization of neural networks, based on the braid theory. The paper describes the basics of braid theory as applied to the description of graph structures of neural networks. It is…
In recent years, various deep learning architectures have been proposed to solve complex challenges (e.g. spatial dependency, temporal dependency) in traffic domain, which have achieved satisfactory performance. These architectures are…
Traditional scene graph generation methods are trained using cross-entropy losses that treat objects and relationships as independent entities. Such a formulation, however, ignores the structure in the output space, in an inherently…
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…
The boxicity of a graph $G$ is the minimum dimension $d$ that admits a representation of $G$ as the intersection graph of a family of axis-parallel boxes in $\mathbb{R}^d$. Computing boxicity is an NP-hard problem, and there are few known…
The paper proposes the combination of stochastic blockmodels with smooth graphon models. The first allow for partitioning the set of individuals in a network into blocks which represent groups of nodes that presumably connect stochastically…
Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…
Advanced graph neural networks have shown great potentials in graph classification tasks recently. Different from node classification where node embeddings aggregated from local neighbors can be directly used to learn node labels, graph…
A BC-tree (block-cutpoint-tree) is a tree (with at least two vertices) where the distance between any two leaves is even. Motivated from the study of the "core" of a graph, BC-trees provide an interesting class of trees. We consider…
Graphs and various graph-like combinatorial structures, such as preorders and hypergraphs, are ubiquitous in programming. This paper focuses on representing graphs in a purely functional programming language like Haskell. There are several…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
With the need of fast retrieval speed and small memory footprint, document hashing has been playing a crucial role in large-scale information retrieval. To generate high-quality hashing code, both semantics and neighborhood information are…
High-dimensional graphical models are often estimated using regularization that is aimed at reducing the number of edges in a network. In this work, we show how even simpler networks can be produced by aggregating the nodes of the graphical…
Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…