Related papers: Algorithmic Data Analytics, Small Data Matters and…
The continuous increase of data generated provides enormous possibilities of both public and private companies. The management of this mass of data or big data will play a crucial role in the society of the future, as it finds applications…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
This paper establishes a theoretical foundation for understanding the fundamental limits of AI explainability through algorithmic information theory. We formalize explainability as the approximation of complex models by simpler ones,…
We show why the amount of information communicated between the past and future--the excess entropy--is not in general the amount of information stored in the present--the statistical complexity. This is a puzzle, and a long-standing one,…
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…
The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional…
Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…
We give an operational definition of information-theoretic resources within a given multipartite classical or quantum correlation. We present our causal model that serves as the source coding side of this correlation and introduce a novel…
Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple sub-fields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation…
An algorithm effects a causal representation of relations between features and labels in the human's perception. Such a representation might conflict with the human's prior belief. Explanations can direct the human's attention to the…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
Extensions to various information theoretic quantities used for nonlinear time series analysis are discussed, as well as their relationship to the generalized correlation integral. It is shown that calculating redundancies from the…
We address the problem of inferring the causal direction between two variables by comparing the least-squares errors of the predictions in both possible directions. Under the assumption of an independence between the function relating cause…
Causal discovery, the task of inferring causal structure from data, has the potential to uncover mechanistic insights from biological experiments, especially those involving perturbations. However, causal discovery algorithms over larger…
There is an abundance of complex dynamic systems that are critical to our daily lives and our society but that are hardly understood, and even with today's possibilities to sense and collect large amounts of experimental data, they are so…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
We explored the challenge of predicting and explaining the occurrence of events within sequences of data points. Our focus was particularly on scenarios in which unknown triggers causing the occurrence of events may consist of…
We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts…