Articles containing proofs | Theory of computation | Computability theory | Algorithmic information theory | Information theory
The chain rule for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states: That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X.This follows immediately from the definitions of conditional and joint entropy, and the fact from probability theory that the joint probability is the product of the marginal and conditional probability: The equivalent statement for Kolmogorov complexity does not hold exactly; it is true only up to a logarithmic term: (An exact version, KP(x, y) = KP(x) + KP(y|x*) + O(1),holds for the prefix complexity KP, where x* is a shortest program for x.) It states that the shortest program printing X and Y is obtained by concatenating a shortest program printing X with a program printing Y given X, plus at most a logarithmic factor. The results implies that algorithmic mutual information, an analogue of mutual information for Kolmogorov complexity is symmetric: I(x:y) = I(y:x) + O(log K(x,y)) for all x,y. (Wikipedia).
This is How You Use the Chain Rule in Calculus
This is How You Use the Chain Rule in Calculus
From playlist Random calculus problems:)
http://mathispower4u.wordpress.com/
From playlist Differentiation Using the Chain Rule
Chain rule for functions of two variables
Free ebook http://tinyurl.com/EngMathYT A example on the mathematics of the chain rule for functions of two variables.
From playlist A second course in university calculus.
Kolmogorov Complexity - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Chain Rule for Several Variable Functions
How to apply the chain rule for partial deriviatves. An example is discussed. Free ebook tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
Proof - The Chain Rule of Differentiation
This video proves the chain rule of differentiation. http://mathispower4u.com
From playlist Calculus Proofs
Nexus Trimester - Andrei Romashchenko (LIRMM)
On Parallels Between Shannon’s and Kolmogorov’s Information Theories (where the parallelism fails and why) Andrei Romashchenko (LIRMM) February 02, 2016 Abstract: Two versions of information theory - the theory of Shannon's entropy and the theory of Kolmgorov complexity - have manifest
From playlist Nexus Trimester - 2016 - Distributed Computation and Communication Theme
Gérard Letac: Quasi logistic distributions and Gaussian scale mixing
CIRM VIRTUAL EVENT Recorded during the meeting "Mathematical Methods of Modern Statistics 2" the June 02, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicia
From playlist Virtual Conference
Stéphane Jaffard - Conférence organisée par l'Institut Fourier et le Laboratoire Jean Kuntzmann
Conférence organisée par l'Institut Fourier et le Laboratoire Jean Kuntzmann Licence: CC BY NC-ND 4.0
From playlist Conférences grand public "MathEnVille"
Silke Glas: Symplectic model reduction of Hamiltonian systems on nonlinear manifolds
CONFERENCE Recorded during the meeting "Energy-Based Modeling, Simulation, and Control of Complex Constrained Multiphysical Systems" the April 19, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other
From playlist Numerical Analysis and Scientific Computing
Pierre Baudot (8/19/20): Cohomological characterization of information structures
Speaker: Pierre Baudot, Median Technologies. In collaboration in part with Daniel Bennequin, Monica Tapia, and Jean-Marc Goaillard Title: Cohomological characterization of information and higher order statistical structures - Machine learning and statistical physics aspects Abstract: We
From playlist AATRN 2020
Explanation of the Chain Rule In this video, I explain the chain rule, and illustrate it with a couple of examples. And at the end, I give an intuitive explanation of why the chain rule should be true. Who runs faster? Usain Bolt or a train? Watch this video to find out! Subscribe to my
From playlist Calculus
Spotlight Talks - Amir Asadi, Dimitris Kalimeris
Workshop on Theory of Deep Learning: Where next? Topic: Spotlight Talks Speaker: Amir Asadi, Dimitris Kalimeris Date: October 15, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Andreï Kolmogorov: un grand mathématicien au coeur d'un siècle tourmenté
Conférence grand public au CIRM Luminy Andreï Kolmogorov est un mathématicien russe (1903-1987) qui a apporté des contributions frappantes en théorie des probabilités, théorie ergodique, turbulence, mécanique classique, logique mathématique, topologie, théorie algorithmique de l'informati
From playlist OUTREACH - GRAND PUBLIC
Berry's Paradox - An Algorithm For Truth
Go to https://expressvpn.com/upandatom and find out how you can get 3 months free. Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collections/up-and-at
From playlist Math
Shannon 100 - 27/10/2016 - Jean Louis DESSALLES
Information, simplicité et pertinence Jean-Louis Dessalles (Télécom ParisTech) Claude Shannon fonda la notion d’information sur l’idée de surprise, mesurée comme l’inverse de la probabilité (en bits). Sa définition a permis la révolution des télécommunications numériques. En revanche, l’
From playlist Shannon 100
Chain Rule Chain Rule Chain Rule
A statement of the chain rule, plus examples
From playlist Exam 2 Fall 2013, MAT 241
Chain rule for functions of two variables
Free ebook http://tinyurl.com/EngMathYT A lecture on the mathematics of the chain rule for functions of two variables. Plenty of examples are presented to illustrate the ideas. These concepts are seen at university.
From playlist A second course in university calculus.
Asymptotic efficiency in high-dimensional covariance estimation – V. Koltchinskii – ICM2018
Probability and Statistics Invited Lecture 12.18 Asymptotic efficiency in high-dimensional covariance estimation Vladimir Koltchinskii Abstract: We discuss recent results on asymptotically efficient estimation of smooth functionals of covariance operator Σ of a mean zero Gaussian random
From playlist Probability and Statistics