Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, October 02, 2012, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Jan Hazla

Concentration bounds limit the probability of a random variable deviating too much from a certain value (usually its expectation).

Let us have a look at a simple version of the so called Chernoff bound:

Let A1, A2, ... be independent events with Pr[A_i] = 1/2. Let k be a number between 0 and n/2 and let S(n, k) be the event that at least n/2 + k of the events A_1, ..., A_n occur. We would like to show that Pr[S(n,k)] \leq exp(-Omega(k^2/n)).

The standard proof optimizes certain exponential function of the number of events occurring and applies Markov's inequality.

We propose a different approach: one can use Bayes' rule to bound Pr[S(n,k)] with exp(-k/n) * Pr[S(n-1,k-1)] and apply the induction to finish the proof.

We will present some generalisations and applications of this technique. In particular, we will show how the independence assumption can be relaxed while still obtaining a good bound. We will also sketch how to apply the technique to the problem of counting occurences of a certain subgraph (e.g., a triangle) in a random graph.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login