Related papers: Universal Lossless Compression of Graphical Data

We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…

Conditional graph entropy is known to be the minimal rate for a natural functional compression problem with side information at the receiver. In this paper we show that it can be formulated as an alternating minimization problem, which…

In the last few decades, research techniques have improved lossless compression ratios by significantly increasing processing time. However, these techniques have not gained popularity in industry because production systems require high…

Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…

Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: $(i)$ Estimate latent variables…

The goal of lossy data compression is to reduce the storage cost of a data set $X$ while retaining as much information as possible about something ($Y$) that you care about. For example, what aspects of an image $X$ contain the most…

Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…

We study finite-sum nonlinear programs with localized variable coupling encoded by a (hyper)graph. We introduce a graph-compliant decomposition framework that brings message passing into continuous optimization in a rigorous, implementable,…

The burgeoning volume of graph data presents significant computational challenges in training graph neural networks (GNNs), critically impeding their efficiency in various applications. To tackle this challenge, graph condensation (GC) has…

This work presents a maximum entropy principle based algorithm for solving minimum multiway $k$-cut problem defined over static and dynamic {\em digraphs}. A multiway $k$-cut problem requires partitioning the set of nodes in a graph into…

It is known that modeling an information source via a symbolic dynamical system evolving over the unit interval, leads to a natural lossless compression scheme attaining the entropy rate of the source, under general conditions. We extend…

Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…

The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J.…

Parameter-free stochastic optimization aims to design algorithms that are agnostic to the underlying problem parameters while still achieving convergence rates competitive with optimally tuned methods. While some parameter-free methods do…

This study addresses the issue of balancing graph summarization and graph change detection. Graph summarization compresses large-scale graphs into a smaller scale. However, the question remains: To what extent should the original graph be…

The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural…

Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…

In recent deep image compression neural networks, the entropy model plays a critical role in estimating the prior distribution of deep image encodings. Existing methods combine hyperprior with local context in the entropy estimation…

Formation mechanisms are fundamental to the study of complex networks, but learning them from observations is challenging. In real-world domains, one often has access only to the final constructed graph, instead of the full construction…

Graph representation learning has many real-world applications, from super-resolution imaging, 3D computer vision to drug repurposing, protein classification, social networks analysis. An adequate representation of graph data is vital to…