Learning Sums of Independent Random Variables with Sparse ...
In this paper we investigate how this result generalizes if standard bit mutation is replaced by an arbitrary unbiased mutation operator. This ...
UC Berkeley - eScholarshipNote that lower tail bounds P(h(x(t)) ? c) can be rewritten as P ... However, Chernoff inequality yields a bound 0.95 whereas Bernstein inequality ... The Fast Johnson-Lindenstrauss Transform is Even Fasterlatter expression can be bounded by Chernoff bounds for the lower tail of independent random variables. Page 74. 64. Benjamin Doerr. 1.10.2.2 ... Lecture 7 1 Dimensionality Reduction - UBC Computer Science1.10.1.2 Multiplicative Chernoff Bounds for the Lower Tail. In principle, of course, there is no difference between bounds for the upper and lower tails. If ... Curvature, concentration and error estimates for Markov chain ...We already proved the Chernoff lower bound. We here prove an asymptotically matching upper bound. 21.1 The cumulant generating function. Recall that the ... Concentration Colin McDiarmidThe traditional Chernoff bounds concern the sum of independent, nonnegative, and uni- formly bounded random variables. In this work, we will try to extend such ... Theory of Evolutionary Computation ? Recent Developments in ...This book explores some of the (many) connections relating information theory, statistics, computa- tion, and learning. LECTURE NOTES ON PROBABILITY - Omer Tamuz- When A is the collection of lower-left quadrants, we establish in Theorem 1 a functional central limit theorem for random fields satisfying a Lp criterion for ... Statistics and Information Theory - Stanford UniversityThe proof is divided in three steps. The first is to obtain moment bounds for the single observables. ?u?(x). With the help of Theorem 2.7 and ... Exponential inequalities and functional central limit theorems for ...We show two nearly optimal hyperbolic Chernoff bounds: one for Rademacher sum of arbitrary vectors and another for random vectors in the hyperbolic cone. We ... a fluctuation result for the displacement in the optimal matching ...We use the Chernoff-Cramér method to derive a few standard bounds. Poisson variables We start with the Poisson case. Let Z ? Poi(?) be ... Hyperbolic Concentration, Anti-Concentration, and DiscrepancyTherefore, for t ? 0, the equality holds. ??. X(t) = sup ??0. {t? ? ?(?)}. We arrive at the Chernoff bound that ... [Sub-exponential tail bound] ... Moments and tailsWe leverage our inequalities to prove several new agreement testing theorems on high dimensional expanders, including a new 99%-regime test for ...
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