Related papers: Mutual information for the sparse stochastic block…
The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…
In network science, researchers often use mutual information to understand the difference between network partitions produced by community detection methods. Here we extend the use of mutual information to covers, that is, the cases where a…
Modeling relations between individuals is a classical question in social sciences and clustering individuals according to the observed patterns of interactions allows to uncover a latent structure in the data. Stochastic block model (SBM)…
Stochastic blockmodels provide a convenient representation of relations between communities of nodes in a network. However, they imply a notion of stochastic equivalence that is often unrealistic for real networks, and they comprise large…
The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow…
This paper considers the problem of community detection on multiple potentially correlated graphs from an information-theoretical perspective. We first put forth a random graph model, called the multi-view stochastic block model (MVSBM),…
Normalized mutual information is widely used as a similarity measure for evaluating the performance of clustering and classification algorithms. In this paper, we argue that results returned by the normalized mutual information are biased…
By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…
This paper investigates large-population stochastic control problems in which agents share their state information and cooperate to minimize a convex cost functional. The latter is decomposed into individual and coupling costs, with the…
In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with $k$ blocks, for any $k$ fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the…
In this paper a numerical method is presented, which finds a lower bound for the mutual information between a binary and an arbitrary finite random variable with joint distributions that have a variational distance not greater than a known…
In the standard stochastic block model for networks, the probability of a connection between two nodes, often referred to as the edge probability, depends on the unobserved communities each of these nodes belongs to. We consider a flexible…
Mutual information (MI) minimization has gained considerable interests in various machine learning tasks. However, estimating and minimizing MI in high-dimensional spaces remains a challenging problem, especially when only samples, rather…
The integrated information theory is thought to be a key clue towards the theoretical understanding of consciousness. In this study, we propose a simple numerical model comprising a set of coupled double quantum dots, where the…
This paper is motivated by the reconstruction problem on the sparse stochastic block model. Mossel, et. al. proved that a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The…
This paper addresses how to calculate and interpret the time-delayed mutual information for a complex, diversely and sparsely measured, possibly non-stationary population of time-series of unknown composition and origin. The primary vehicle…
Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…
Community detection is one of the most critical problems in modern network science. Its applications can be found in various fields, from protein modeling to social network analysis. Recently, many papers appeared studying the problem of…
We formulate and analyze the compound information bottleneck programming. In this problem, a Markov chain $ \mathsf{X} \rightarrow \mathsf{Y} \rightarrow \mathsf{Z} $ is assumed with fixed marginal distributions $\mathsf{P}_{\mathsf{X}}$…
The stochastic block model is widely used for detecting community structures in network data. However, the research interest of much literature focuses on the study of one sample of stochastic block models. How to detect the difference of…