Related papers: Structural Entropy of the Stochastic Block Models
We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…
Data partitioning that maximizes/minimizes the Shannon entropy, or more generally the R\'enyi entropy is a crucial subroutine in data compression, columnar storage, and cardinality estimation algorithms. These partition algorithms can be…
Motivated by the prevalent data science applications of processing large-scale graph data such as social networks and biological networks, this paper investigates lossless compression of data in the form of a labeled graph. Particularly, we…
Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we…
Probabilistic embeddings have several advantages over deterministic embeddings as they map each data point to a distribution, which better describes the uncertainty and complexity of data. Many works focus on adjusting the distribution…
The traditional approach of statistical physics to supervised learning routinely assumes unrealistic generative models for the data: usually inputs are independent random variables, uncorrelated with their labels. Only recently, statistical…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Sample selection improves the efficiency and effectiveness of machine learning models by providing informative and representative samples. Typically, samples can be modeled as a sample graph, where nodes are samples and edges represent…
For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
The structure of a network is an unlabeled graph, yet graphs in most models of complex networks are labeled by meaningless random integers. Is the associated labeling noise always negligible, or can it overpower the network-structural…
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…
The stochastic block model is a classical cluster-exhibiting random graph model that has been widely studied in statistics, physics and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with…
In this paper, we study the problem of graph compression with side information at the decoder. The focus is on the situation when an unlabelled graph (which is also referred to as a structure) is to be compressed or is available as side…
In structured prediction, the goal is to jointly predict many output variables that together encode a structured object -- a path in a graph, an entity-relation triple, or an ordering of objects. Such a large output space makes learning…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving…