# Generative Models for Periodicity Detection in Noisy Signals

## TL;DR

This paper introduces a new algorithm for detecting periodic patterns in event data, even when the data is noisy or complex.

## Contribution

The paper introduces two new generative models and a novel algorithm for detecting multiple periodicities in noisy binary time series.

## Key findings

- The GMPDA successfully detects single and multiple periodicities in synthetic data with varying noise levels.
- The algorithm performs well on real-world data from leg movements during sleep, identifying expected periodic patterns.
- The Clock and Random Walk Models provide a comprehensive framework for generating and detecting periodic event behavior.

## Abstract

We present the Gaussian Mixture Periodicity Detection Algorithm (GMPDA), a novel method for detecting periodicity in the binary time series of event onsets. The GMPDA addresses the periodicity detection problem by inferring parameters of a generative model. We introduce two models, the Clock Model and the Random Walk Model, which describe distinct periodic phenomena and provide a comprehensive generative framework. The GMPDA demonstrates robust performance in test cases involving single and multiple periodicities, as well as varying noise levels. Additionally, we evaluate the GMPDA on real-world data from recorded leg movements during sleep, where it successfully identifies expected periodicities despite high noise levels. The primary contributions of this paper include the development of two new models for generating periodic event behavior and the GMPDA, which exhibits high accuracy in detecting multiple periodicities even in noisy environments.