McDiarmid's Inequality
McDiarmid's inequality is a core tool in probability theory and statistical learning theory for studying concentration phenomena of functions of independent random variables. It generalizes Hoeffding's inequality to multivariate functions and relies on the bounded differences assumption.
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The classical McDiarmid inequality has the form: if a function f changes by at most c_i when the i-th coordinate is altered, then the probability that f(X_1,...,X_n) deviates from its expectation is at most 2exp(-2t^2/Σc_i^2).
The new result replaces the bounded difference condition of the classical McDiarmid inequality with a conditional moment assumption, and replaces two-sided boundedness with a one-sided upper bound.
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The classical McDiarmid inequality has the form: if a function f changes by at most c_i when the i-th coordinate is altered, then the probability that f(X_1,...,X_n) deviates from its expectation is at most 2exp(-2t^2/Σc_i^2).
50%UnverifiedThe new result replaces the bounded difference condition of the classical McDiarmid inequality with a conditional moment assumption, and replaces two-sided boundedness with a one-sided upper bound.
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