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Information-theoretic derivations of the formalism of quantum theory have recently attracted much attention. We analyze the axioms underlying a few such derivations and propose a conceptual framework in which, by combining several…
Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…
In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of G\"odel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to…
This paper reviews the basic ideas behind a Bayesian unfolding published some years ago and improves their implementation. In particular, uncertainties are now treated at all levels by probability density functions and their propagation is…
We give a survey of the foundations of statistical queries and their many applications to other areas. We introduce the model, give the main definitions, and we explore the fundamental theory statistical queries and how how it connects to…
Despite the increasing popularity of metaheuristics, many crucially important questions remain unanswered. There are two important issues: theoretical framework and the gap between theory and applications. At the moment, the practice of…
This is a technical report, containing all the theorem proofs and additional evaluations in paper "Monitor Placement for Maximal Identifiability in Network Tomography" by Liang Ma, Ting He, Kin K. Leung, Ananthram Swami, Don Towsley,…
This is a typeset version of Alan Turing's declassified Second World War paper \textit{Paper on Statistics of Repetitions}. See the companion paper, \textit{The Applications of Probability to Cryptography}, also available from arXiv at…
Attribute exploration has been investigated in several studies, with particular emphasis on the algorithmic aspects of this knowledge acquisition method. In its basic version the method itself is rather simple and transparent. But when…
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate the several distinguishability measures and "entropies" in general probabilistic theories. As their applications,…
The concept of Probability of Causation (PC) is critically important in legal contexts and can help in many other domains. While it has been around since 1986, current operationalizations can obtain only the minimum and maximum values of…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
taking aside the review part, a finite-cardinality's set of new ideas concerning algorithmic information issues in Quantum Mechanics is introduced and analyzed
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
What makes a paper independently reproducible? Debates on reproducibility center around intuition or assumptions but lack empirical results. Our field focuses on releasing code, which is important, but is not sufficient for determining…
The definition of conditional probability in case of continuous distributions was an important step in the development of mathematical theory of probabilities. How can we define this notion in algorithmic probability theory? In this survey…