The data processing inequality is an information theoretic concept that states that the information content of a signal cannot be increased via a local...

}(x))} via the data-processing inequality. 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 data processing inequality, and is equivalent to the monotonicity of relative entropy under...

mouse speed SystemVerilog DPI (Direct Programming Interface) Data processing inequality Digital public infrastructure Daytona Prototype International...

contributions to quantum information theory, including his proof of the data-processing inequality for quantum relative entropy, communicated in a series of three...

Algorithmic bias Auditory neuropathy spectrum disorder Computer says no Data processing inequality FINO No free lunch theorem Standard error Undefined behavior Demming...

( X ; Y ) {\displaystyle I(X;{\tilde {X}})\leq I(X;Y)} by the data processing inequality, and hence H ( X ∣ X ~ ) ≥ H ( X ∣ Y ) {\displaystyle H(X\mid...

method. Data processing inequality Cramér–Rao bound Entropy power inequality Entropic vector Fano's inequality Jensen's inequality Kraft inequality Pinsker's...

In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation...

Neumann entropy. For example, the smooth min-entropy satisfy a data-processing inequality: H min ϵ ( A | B ) ρ ≥ H min ϵ ( A | B C ) ρ   . {\displaystyle...

{\begin{aligned}I(X;Y,Z)&=I(X;Z)+I(X;Y|Z)\\&=I(X;Y)+I(X;Z|Y)\end{aligned}}} The data processing inequality is closely related to conditional mutual information and can be...

)}dQ\geq f{\bigg (}\int {\frac {dP}{dQ}}dQ{\bigg )}=f(1)=0.} Data-processing inequality: if κ is an arbitrary transition probability that transforms measures...

generalization of Rényi relative entropy and established its data processing inequality. He has written or coauthored several textbooks which have been...

information theory. This is closely related to what is known as the data processing inequality in quantum information theory. The Lieb-Ruskai proof of strong...

divergence on Γ n {\displaystyle \Gamma _{n}} that satisfies the data processing inequality must be the Kullback–Leibler divergence. (In fact, a weaker assumption...

dispersion intended to represent the income inequality, the wealth inequality, or the consumption inequality within a nation or a social group. It was developed...

Economic inequality is an umbrella term for three concepts: income inequality, how the total sum of money paid to people is distributed among them; wealth...

Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of income and economic inequality among...

Social inequality occurs when resources within a society are distributed unevenly, often as a result of inequitable allocation practices that create distinct...

equals the mutual information between θ and X. In other words, the data processing inequality becomes an equality: I ( θ ; T ( X ) ) = I ( θ ; X ) {\displaystyle...

Income inequality has fluctuated considerably in the United States since measurements began around 1915, moving in an arc between peaks in the 1920s and...

and Development. Brookings. World Inequality Database (WID.world) (2023) – processed by Our World in Data "Inequality in Brazil: A Regional Perspective"...

Gender inequality is the social phenomenon in which people are not treated equally on the basis of gender. This inequality can be caused by gender discrimination...

Effects of income inequality, researchers have found, include higher rates of health and social problems, and lower rates of social goods, a lower population-wide...

probability and statistics, the Dvoretzky–Kiefer–Wolfowitz–Massart inequality (DKW inequality) provides a bound on the worst case distance of an empirically...

A.; Vershynina, Anna (2020). "Recovery map stability for the Data Processing Inequality". J. Phys. A: Math. Theor. 53: 035204. arXiv:1710.02409. doi:10...

Orsay atomic-cascade experiment tests of Bell inequalities: a discussion and some new experimental data". Lettere al Nuovo Cimento. 43 (8): 345–348. doi:10...

Big data primarily refers to data sets that are too large or complex to be dealt with by traditional data-processing software. Data with many entries...

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...

Attention inequality is the inequality of distribution of attention across users on social networks, people in general, and for scientific papers. Yun...