Five Proofs of Chernoff's Bound with Applications

We discuss five ways of proving Chernoff's bound and show how they lead to different extensions of the basic bound.

[1]  Aaron Roth,et al.  The Algorithmic Foundations of Differential Privacy , 2014, Found. Trends Theor. Comput. Sci..

[2]  Thomas Steinke,et al.  Subgaussian Tail Bounds via Stability Arguments , 2017, ArXiv.

[3]  Oded Goldreich,et al.  Computational complexity: a conceptual perspective , 2008, SIGA.

[4]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[5]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[6]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[7]  Xinjia Chen,et al.  A Likelihood Ratio Approach for Probabilistic Inequalities , 2013, ArXiv.

[8]  Fan Chung Graham,et al.  Concentration Inequalities and Martingale Inequalities: A Survey , 2006, Internet Math..

[9]  Pat Morin,et al.  Encoding Arguments , 2016, ACM Comput. Surv..

[10]  Éva Tardos,et al.  Algorithm design , 2005 .

[11]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[12]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[13]  C. McDiarmid.  Concentration , 1862, The Dental register.

[14]  Kazuoki Azuma.  WEIGHTED SUMS OF CERTAIN DEPENDENT RANDOM VARIABLES , 1967 .

[15]  Russ Bubley,et al.  Randomized algorithms , 2018, CSUR.

[16]  Torben Hagerup,et al.  A Guided Tour of Chernoff Bounds , 1990, Inf. Process. Lett..

[17]  Vasek Chvátal,et al.  The tail of the hypergeometric distribution , 1979, Discret. Math..

[18]  Kunal Talwar,et al.  Mechanism Design via Differential Privacy , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[19]  Alessandro Panconesi,et al.  Concentration of Measure for the Analysis of Randomized Algorithms , 2009 .

[20]  Russell Impagliazzo,et al.  Constructive Proofs of Concentration Bounds , 2010, APPROX-RANDOM.