Chernoff-Hoeffding Inequality and Applications

Material for ” Combinatorial multi - armed bandit : general framework , results and applications

We use the following two well known bounds in our proofs. Lemma 1 (Chernoff-Hoeffding bound). Let X1, · · · , Xn be random variables with common support [0, 1] and E[Xi] = μ. Let Sn = X1 + · · ·+Xn. Then for all t ≥ 0, Pr[Sn ≥ nμ+ t] ≤ e−2t /n and Pr[Sn ≤ nμ− t] ≤ e−2t /n Lemma 2 (Bernstein inequality). Let X1, . . . , Xn be independent zero-mean random variables. If for all 1 ≤ i ≤ n, |Xi| ≤ k...

Chernoff-Hoeffding Inequality

When dealing with modern big data sets, a very common theme is reducing the set through a random process. These generally work by making “many simple estimates” of the full data set, and then judging them as a whole. Perhaps magically, these “many simple estimates” can provide a very accurate and small representation of the large data set. The key tool in showing how many of these simple estima...

Chernoff-Hoeffding Inequality

When dealing with modern big data sets, a very common theme is reducing the set through a random process. These generally work by making “many simple estimates” of the full data set, and then judging them as a whole. Perhaps magically, these “many simple estimates” can provide a very accurate and small representation of the large data set. The key tool in showing how many of these simple estima...

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

Material for ” Combinatorial multi - armed bandit

We use the following two well known bounds in our proofs. Lemma 1 (Chernoff-Hoeffding bound). Let X1, · · · , Xn be random variables with common support [0, 1] and E[Xi] = μ. Let Sn = X1 + · · ·+Xn. Then for all t ≥ 0, Pr[Sn ≥ nμ+ t] ≤ e−2t /n and Pr[Sn ≤ nμ− t] ≤ e−2t /n Lemma 2 (Bernstein inequality). Let X1, . . . , Xn be independent zero-mean random variables. If for all 1 ≤ i ≤ n, |Xi| ≤ k...