Information theory | Inequalities

Fano's inequality

In information theory, Fano's inequality (also known as the Fano converse and the Fano lemma) relates the average information lost in a noisy channel to the probability of the categorization error. It was derived by Robert Fano in the early 1950s while teaching a Ph.D. seminar in information theory at MIT, and later recorded in his 1961 textbook. It is used to find a lower bound on the error probability of any decoder as well as the lower bounds for in density estimation. Let the random variables and represent input and output messages with a joint probability . Let represent an occurrence of error; i.e., that , with being an approximate version of . Fano's inequality is where denotes the support of , is the conditional entropy, is the probability of the communication error, and is the corresponding binary entropy. (Wikipedia).

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Related pages

Kullback–Leibler divergence | Random variable | Expected value | Density estimation | Probability density function | Conditional entropy | Information theory | Probability | Binary entropy function