Related papers: Information-theoretic thresholds from the cavity m…
Information theory, rooted in computer science, and many-body physics, have traditionally been studied as (almost) independent fields. Only recently has this paradigm started to shift, with many-body physics being studied and characterized…
The mutual and tripartite information between pairs and triples of disjoint regions in a quantum field theory are sensitive probes of the spread of correlations in an equilibrating system. We compute these quantities in strongly coupled…
Factorizing low-rank matrices is a problem with many applications in machine learning and statistics, ranging from sparse PCA to community detection and sub-matrix localization. For probabilistic models in the Bayes optimal setting, general…
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…
Recent advances in Neural Variational Inference allowed for a renaissance in latent variable models in a variety of domains involving high-dimensional data. While traditional variational methods derive an analytical approximation for the…
The goal of this chapter is to review the main ideas that underlie the cavity method for disordered models defined on random graphs, as well as present some of its outcomes, focusing on the random constraint satisfaction problems for which…
The ability to understand and solve high-dimensional inference problems is essential for modern data science. This article examines high-dimensional inference problems through the lens of information theory and focuses on the standard…
Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…
The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…
In the standard picture of structure formation, initially random-phase fluctuations are amplified by non-linear gravitational instability to produce a final distribution of mass which is highly non-Gaussian and has highly coupled Fourier…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
We present a fluctuation theorem for quantum bipartite systems in which the subsystems exchange information with each other. Our information fluctuation theorem includes correlations by introducing a quantum mechanical mutual information…
The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…
We provide matching upper and lower bounds on the mutual information in noisy reconstruction of parity check codes and thereby prove a long-standing conjecture by Montanari [IEEE Transactions on Information Theory 2005]. Besides extending a…
Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…
In this paper and a companion paper, we attempt to systematically investigate the possibility that the concept of information may enable a derivation of the quantum formalism from a set of physically comprehensible postulates. To do so, we…
We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower…
Due to their conceptual and mathematical simplicity, Erd\"os-R\'enyi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely…
The definitions of delayed mutual information and multi-information are recalled. It is shown how the delayed mutual information may be used to reconstruct the interaction topology resulting from some unknown scale-free graph with its…