# Heavy Hitters and Bernoulli Convolutions

## TL;DR

The paper introduces a simple, event-sensitive frequency approximation algorithm that models event distributions as biased Bernoulli convolutions, enabling analysis of their moments and self-similarity properties.

## Contribution

It presents a novel event frequency algorithm that links to biased Bernoulli convolutions, providing new insights into their moments and self-similarity.

## Key findings

- Algorithm effectively models event distributions as Bernoulli convolutions.
- Estimation of moments for biased Bernoulli convolutions is demonstrated.
- Self-similarity properties are identified under certain conditions.

## 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.