WebOct 26, 2024 · We derive a dimension-free Hanson-Wright inequality for quadratic forms of independent sub-gaussian random variables in a separable Hilbert space. Our inequality is an infinite-dimensional generalization of the classical Hanson-Wright inequality for finite-dimensional Euclidean random vectors. WebThe Hanson-Wright inequality for arbitrary n × n matrix A, and X a random vector with subgaussian coordinates (of norm 1) is P r ( X T A X − E X T A X ≥ t) ≤ 2 exp ( − c min …
Hanson-Wright inequality and sub-gaussian concentration
WebThere are inequalities similar to (1.3) for multilinear chaos in Gaussian random variables proven in [22] (and in fact, a lower bound using the same quantities as well), and in [4] for polynomials in sub-Gaussian random variables. Moreover, extensions of the Hanson–Wright inequality to certain types of dependent random variables have been WebMay 6, 2024 · Hanson-Wright Inequality for Symmetric Matrices. for i.i.d. X, X ′. We then establish in the case where X, X ′ are gaussian the bound. Finally, one shows that we can replace arbitrary X, X ′ with normally distributed counterparts while only paying a constant cost (see page 140 of Vershynin High Dimensional Probability). In particular, for ... hugh bottoms
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WebToday, the Hanson–Wright inequality is an important probabilistic tool and can be found in various textbooks covering the basics of signal processing and probability theory, such … WebThe following proof of the Hanson-Wright was shared to me by Sjoerd Dirksen (personal commu-nication). See also a recent proof in [RV13]. Recall that by problem set 1, problem 1, the statement of the Hanson-Wright inequality below is equivalent to the statement that there exists a constant C>0 such that for all >0 P ˙ j˙TA˙ E˙TA˙j> . e C 2 ... WebOct 4, 2024 · The Hanson–Wright inequality is a concentration inequality for quadratic forms of random vectors—that is, expressions of the form where is a random vector. Many statements of this inequality in the literature have an unspecified constant ; our goal in this post will be to derive a fairly general version of the inequality with only explicit ... holiday inn albany ny western ave