Information theory

Information dimension

In information theory, information dimension is an information measure for random vectors in Euclidean space, based on the normalized entropy of finely quantized versions of the random vectors. This concept was first introduced by Alfréd Rényi in 1959. Simply speaking, it is a measure of the fractal dimension of a probability distribution. It characterizes the growth rate of the Shannon entropy given by successively finer discretizations of the space. In 2010, Wu and Verdú gave an operational characterization of Rényi information dimension as the fundamental limit of almost lossless data compression for analog sources under various regularity constraints of the encoder/decoder. (Wikipedia).

Information dimension
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(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

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Dimensions (1 of 3: The Traditional Definition - Directions)

More resources available at www.misterwootube.com

From playlist Exploring Mathematics: Fractals

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Dimensions Chapter 5

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From playlist Dimensions

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Dimensions Chapter 1

Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 2

Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 6

Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 4

Chapter 4 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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From playlist ITIL Training Videos [2022 Updated]

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RailsConf 2017: Reporting on Rails - ActiveRecord and ROLAP Working Together by Tony Drake

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Entropy-Based Bounds on Dimension Reduction in L_1 - Oded Regev

Oded Regev CNRS-ENS-Paris and Tel Aviv University November 28, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

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From playlist Papers Explained

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Entanglement entropy, quantum field theory, and holography by Matthew Headrick

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From playlist US-India Advanced Studies Institute: Classical and Quantum Information

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From playlist Fundamentals of Machine Learning

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From playlist Data Warehousing Tutorial Videos

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Exploring 3 Dimensions - Abigail Thompson

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From playlist Friends of the Institute

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The concept of “dimension” in measured signals

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From playlist Dimension reduction and source separation

Related pages

Correlation dimension | Differential entropy | Random variable | Rectified Gaussian distribution | Lebesgue's decomposition theorem | Alfréd Rényi | Exponential function | Mean value theorem | Euclidean vector | Real number | Probability distribution | Euclidean space | Entropy (information theory) | Infimum and supremum | Information theory | Probability measure | IEEE Transactions on Information Theory | Fractal dimension