Lecture Notes on statistics and information Theory
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Lecture Notes on statistics and information Theory
Lecture Notes on statistics and information Theory
This
lecture note navigates through information theory, statistics and measure theory. It
covers fundamental concepts such as definitions, chain rules, data processing
inequalities, and divergences and extends to optimal procedures, LeCam’s and
Fano’s inequalities, and operational results like entropy and source coding. It
also focus on exponential families and statistical modeling, fitting procedures,
and lower bounds on testing parameters, sub-Gaussian and sub-exponential random
variables, martingale methods, uniformity covering topics such as
Kullback-Leibler divergence, PAC-Bayes bounds, interactive data analysis, and
error bounds.
This
lecture note navigates through information theory, statistics and measure theory. It
covers fundamental concepts such as definitions, chain rules, data processing
inequalities, and divergences and extends to optimal procedures, LeCam’s and
Fano’s inequalities, and operational results like entropy and source coding. It
also focus on exponential families and statistical modeling, fitting procedures,
and lower bounds on testing parameters, sub-Gaussian and sub-exponential random
variables, martingale methods, uniformity covering topics such as
Kullback-Leibler divergence, PAC-Bayes bounds, interactive data analysis, and
error bounds.
This book explains basics of thermodynamics, including thermodynamic
potentials, microcanonical and canonical distributions, and evolution in the
phase space, The inevitability of irreversibility, basics of information theory,
applications of information theory, new second law of thermodynamics and quantum
information.
This PDF covers the following
topics related to Information Theory : Information measures, Lossless data
compression, Binary hypothesis testing, Channel coding, Lossy data compression,
Advanced topics.
This note explains the
following topics: Shearer's Lemma, Entropy, Relative Entropy, Hypothesis
testing, total variation distance and Pinsker's lemma, Stability in Shearer's
Lemma, Communication Complexity, Set Disjointness, Direct Sum in Communication
Complexity and Internal Information Complexity, Data Structure Lower Bounds via
Communication Complexity, Algorithmic Lovasz Local Lemma, Parallel Repetition
Theorem, Graph Entropy and Sorting.
This is a graduate-level
introduction to mathematics of information theory. This note will cover both
classical and modern topics, including information entropy, lossless data
compression, binary hypothesis testing, channel coding, and lossy data
compression.