Intro to generalization; Chernoff method

Lecture 03 : Chernoff Bounds and Intro to Spectral Graph Theory 3 1 . 1 Hoeffding ’ s Inequality

Chernoff type bounds for sum of dependent random variables and applications in additive number theory

We present generalizations of Chernoff’s large deviation bound for sum of dependent random variables. These generalizations seem to be very useful for the Erdős probabilistic method. As an illustrating application, we sketch the solution of an old problem of Nathanson [14] concerning thin Waring bases.

Improving Chernoff criterion for classification by using the filled function

Linear discriminant analysis is a well-known matrix-based dimensionality reduction method. It is a supervised feature extraction method used in two-class classification problems. However, it is incapable of dealing with data in which classes have unequal covariance matrices. Taking this issue, the Chernoff distance is an appropriate criterion to measure distances between distributions. In the p...

Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications

Ahlswede and Winter [IEEE Trans. Inf. Th. 2002] introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables. We present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan [JCSS 1988]). As a consequence, we derandomize an efficient construction ...

Derandomizing the AW matrix-valued Chernoff bound using pessimistic estimators and applications

Ahlswede and Winter [AW02] introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables. We present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan [Rag88]). As a consequence, we derandomize a construction of Alon and Roichman [AR94] (see als...