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This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
Information Theory provides a fundamental basis for analysis, and for a variety of subsequent methodological approaches, in relation to uncertainty quantification. The transversal character of concepts and derived results justifies its…
This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition). It aims to provide students…
These lecture notes were written with the aim to provide an accessible though technically solid introduction to the logic of systematical analyses of statistical data to both undergraduate and postgraduate students, in particular in the…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
This paper examines the summarization of events that evolve through time. It discusses different types of evolution taking into account the time in which the incidents of an event are happening and the different sources reporting on the…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
This report concerns the information content of a graph, optionally conditional on one or more background, "common knowledge" graphs. It describes an algorithm to estimate this information content, and includes some examples based on…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as…
This monograph aims at providing an introduction to key concepts, algorithms, and theoretical results in machine learning. The treatment concentrates on probabilistic models for supervised and unsupervised learning problems. It introduces…
This document consists of lecture notes for a graduate course, which focuses on the relations between Information Theory and Statistical Physics. The course is aimed at EE graduate students in the area of Communications and Information…
The history of data analysis that is addressed here is underpinned by two themes, -- those of tabular data analysis, and the analysis of collected heterogeneous data. "Exploratory data analysis" is taken as the heuristic approach that…
This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet…
Primitive recursion, mu-recursion, universal object and universe theories, complexity controlled iteration, code evaluation, soundness, decidability, G\"odel incompleteness theorems, inconsistency provability for set theory, constructive…
Brief lecture notes for a course about random matrices given at the University of Cambridge.
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…