Information theory | Algorithmic information theory | Randomized algorithms
Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects (as opposed to stochastically generated), such as strings or any other data structure. In other words, it is shown within algorithmic information theory that computational incompressibility "mimics" (except for a constant that only depends on the chosen universal programming language) the relations or inequalities found in information theory. According to Gregory Chaitin, it is "the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously." Besides the formalization of a universal measure for irreducible information content of computably generated objects, some main achievements of AIT were to show that: in fact algorithmic complexity follows (in the self-delimited case) the same inequalities (except for a constant) that entropy does, as in classical information theory; randomness is incompressibility; and, within the realm of randomly generated software, the probability of occurrence of any data structure is of the order of the shortest program that generates it when running on a universal machine. AIT principally studies measures of irreducible information content of strings (or other data structures). Because most mathematical objects can be described in terms of strings, or as the limit of a sequence of strings, it can be used to study a wide variety of mathematical objects, including integers. One of the main motivations behind AIT is the very study of the information carried by mathematical objects as in the field of metamathematics, e.g., as shown by the incompleteness results mentioned below. Other main motivations came from surpassing the limitations of classical information theory for single and fixed objects, formalizing the concept of randomness, and finding a meaningful probabilistic inference without prior knowledge of the probability distribution (e.g., whether it is independent and identically distributed, Markovian, or even stationary). In this way, AIT is known to be basically founded upon three main mathematical concepts and the relations between them: algorithmic complexity, algorithmic randomness, and algorithmic probability. (Wikipedia).
(IC 1.6) A different notion of "information"
An informal discussion of the distinctions between our everyday usage of the word "information" and the information-theoretic notion of "information". A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F Attribution for image of TV static:
From playlist Information theory and Coding
(IC 1.1) Information theory and Coding - Outline of topics
A playlist of these videos is available at: http://www.youtube.com/playlist?list=PLE125425EC837021F Overview of central topics in Information theory and Coding. Compression (source coding) theory: Source coding theorem, Kraft-McMillan inequality, Rate-distortion theorem Error-correctio
From playlist Information theory and Coding
From information theory to learning via Statistical Physics: Introduction: by Florent Krzakala
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
From information theory to learning via Statistical Physics by Florent Krzakala
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
Thermodynamics of Information by Juan MR Parrondo (Lecture 4)
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
Thermodynamics of Information by Juan MR Parrondo (Lecture 2)
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
Thermodynamics of Information by Juan MR Parrondo (Lecture 1)
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
Computational Differential Geometry, Optimization Algorithms by Mark Transtrum
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
Shannon 100 - 27/10/2016 - Anne AUGER
How information theory sheds new light on black-box optimization Anne Auger (INRIA) Black-box optimization problems occur frequently in many domains ranging from engineering to biology or medicine. In black-box optimization, no information on the function to be optimized besides current
From playlist Shannon 100
Huffman Codes: An Information Theory Perspective
Huffman Codes are one of the most important discoveries in the field of data compression. When you first see them, they almost feel obvious in hindsight, mainly due to how simple and elegant the algorithm ends up being. But there's an underlying story of how they were discovered by Huffman
From playlist Data Compression
David McAllester - Dependent Type Theory from the Perspective of Mathematics, Physics, and (...)
Dependent type theory imposes a type system on Zemelo-Fraenkel set theory (ZFC). From a mathematics and physics perspective dependent type theory naturally generalizes the Bourbaki notion of structure and provides a universal notion of isomorphism and symmetry. This comes with a universal
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Tightening information-theoretic generalization bounds with data-dependent estimate... - Daniel Roy
Workshop on Theory of Deep Learning: Where next? Topic: Tightening information-theoretic generalization bounds with data-dependent estimates with an application to SGLD Speaker: Daniel Roy Affiliation: University of Toronto Date: October 15, 2019 For more video please visit http://video
From playlist Mathematics
IMS Public Lecture: Are Quantum Computers The Next Generation Of Supercomputers?
Reinhard Werner, Technische Universität Braunschweig, Germany
From playlist Public Lectures
Information Theory Meets Quantum Physics: The magic of wave dynamics by Apoorva Patel
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
The Abel Prize announcement 2021 - Avi Wigderson and László Lovász
0:49 The Abel Prize announced by Hans Petter Graver, President of The Norwegian Academy of Science and Letters 1:38 Citation by Hans Munthe-Kaas, Chair of the Abel committee 10:22 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 17:43
From playlist The Abel Prize announcements
Unit 3 Debate: Tomer Ullman and Laura Schulz
MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015 View the complete course: https://ocw.mit.edu/RES-9-003SU15 Instructor: Tomer Ullman, Laura Schulz Speakers debate what makes a good theory of the world, the potential role of stochastic search in theory formation, goal-o
From playlist MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015
Ximena Fernández 7/20/22: Morse theory for group presentations and the persistent fundamental group
Discrete Morse theory is a combinatorial tool to simplify the structure of a given (regular) CW-complex up to homotopy equivalence, in terms of the critical cells of discrete Morse functions. In this talk, I will present a refinement of this theory that guarantees not only a homotopy equiv
From playlist AATRN 2022
Universality in numerical computations with random data. Analytical results. - Percy Deift
Analysis Math-Physics Seminar Topic: Universality in numerical computations with random data. Analytical results. Speaker: Percy Deift Affiliation: New York University Date: October 19, 2016 For more video, please visit http://video.ias.edu
From playlist Mathematics
From information theory to learning via Statistical Physics: From statistical by Florent Krzakala
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information