The data processing inequality is an information theoretic concept that states that the information content of a signal cannot be increased via a local physical operation. This can be expressed concisely as 'post-processing cannot increase information'.[1]
^Beaudry, Normand (2012), "An intuitive proof of the data processing inequality", Quantum Information & Computation, 12 (5–6): 432–441, arXiv:1107.0740, Bibcode:2011arXiv1107.0740B, doi:10.26421/QIC12.5-6-4, S2CID 9531510
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The dataprocessinginequality is an information theoretic concept that states that the information content of a signal cannot be increased via a local...
}(x))} via the data-processinginequality. That is, we append a latent space to the observable space, paying the price of a weaker inequality for the sake...
operation on that system. In this form, it is better known as the dataprocessinginequality, and is equivalent to the monotonicity of relative entropy under...
break down of the inequalities in terms of basic Information measures. Dataprocessinginequality Cramér–Rao bound Entropy power inequality Entropic vector...
{\begin{aligned}I(X;Y,Z)&=I(X;Z)+I(X;Y|Z)\\&=I(X;Y)+I(X;Z|Y)\end{aligned}}} The dataprocessinginequality is closely related to conditional mutual information and can be...
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divergence on Γ n {\displaystyle \Gamma _{n}} that satisfies the dataprocessinginequality must be the Kullback–Leibler divergence. (In fact, a weaker assumption...
equals the mutual information between θ and X. In other words, the dataprocessinginequality becomes an equality: I ( θ ; T ( X ) ) = I ( θ ; X ) {\displaystyle...
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and Development. Brookings. World Inequality Database (WID.world) (2023) – processed by Our World in Data "Inequality in Brazil: A Regional Perspective"...
part of Spain Categorical data Categorical distribution Categorical variable Cauchy distribution Cauchy–Schwarz inequality Causal Markov condition CDF-based...
arXiv:1509.07127 Carlen, Eric A.; Vershynina, Anna (2017-10-06). "Recovery map stability for the DataProcessingInequality". arXiv:1710.02409 [math.OA]....
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Markov's inequality or Chebyshev's inequality. The Chernoff bound is related to the Bernstein inequalities. It is also used to prove Hoeffding's inequality, Bennett's...
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