Related papers: A Partial Information Decomposition Based on Causa…
Information causality (IC) was one of the first principles that have been invoked to bound the set of quantum correlations. For some families of correlations, this principle recovers exactly the boundary of the quantum set; for others,…
Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in…
Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…
We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles…
In many scientific contexts, different investigators experiment with or observe different variables with data from a domain in which the distinct variable sets might well be related. This sort of fragmentation sometimes occurs in molecular…
This paper considers the problem of defining a measure of redundant information that quantifies how much common information two or more random variables specify about a target random variable. We discussed desired properties of such a…
Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…
Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…
Built upon the concept of causal faithfulness, the so-called causal discovery algorithms propose the breakdown of mutual information (MI) and conditional mutual information (CMI) into sets of variables to reveal causal influences. These…
The standard approach to modeling the human brain as a complex system is with a network, where the basic unit of interaction is a pairwise link between two brain regions. While powerful, this approach is limited by the inability to assess…
Measurements can be viewed as interactions between a measured system and a pointer system that imprint information about the system on the pointer. For so-called unbiased interactions, the measurement statistics--the information…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
In modern communication systems such as the Internet, random losses of information can be mitigated by oversampling the source. This is equivalent to expanding the source using overcomplete systems of vectors (frames), as opposed to the…
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
Multivariate information decompositions hold promise to yield insight into complex systems, and stand out for their ability to identify synergistic phenomena. However, the adoption of these approaches has been hindered by there being…
We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…
We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel…
In the context of agent based modeling and network theory, we focus on the problem of recovering behavior-related choice information from origin-destination type data, a topic also known under the name of network tomography. As a basis for…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing…