Heavy Hitters and Bernoulli Convolutions

Abstract

A very simple event frequency approximation algorithm that is sensitive to event timeliness is suggested. The algorithm iteratively updates categorical click-distribution, producing (path of) a random walk on a standard n-dimensional simplex. Under certain conditions, this random walk is self-similar and corresponds to a biased Bernoulli convolution. Algorithm evaluation naturally leads to estimation of moments of biased (finite and infinite) Bernoulli convolutions.

Improving Recommendation Relevance by simulating User Interest

“…This short section closely follows [10]. In general, arrival of recommendation clicks can be viewed as a stochastic processes (sequence) of discrete timedependent categorical distributions P (τ ) where time τ is measured in number of clicks per web page.…”

“…It is not hard to see (cf. [10]) that at the end of time period the expectation of a distribution computed by Algorithm 1 will be…”

“…Remark 7 It should be clear (cf. [10]), that in case of m incoming click distributions P 1 , P 2 , • • • , P m that are "switched over" at times 0 < t 1 < t 2 < • • • < t m < t the expectation of the distribution produced by Algorithm 1 will be…”

“…Dividing by the coefficient at P m , throwing away the first term (as α t 1 − α tm ) and applying the same approximation as in (10), one gets…”

“…For some intuitive "theoretical" considerations in favor of Algorithm 1 see [10] and Appendix 2. A simulation model for evaluation of this algorithm is described in Appendix 3.…”