Nonparametric Bayesian Estimation of Periodic Functions

TL;DR

This paper introduces a nonparametric Bayesian Gaussian Process model for estimating the period of periodic functions from noisy, irregular data, improving accuracy especially for non-sinusoidal signals, with a new optimization algorithm and domain knowledge integration.

Contribution

It presents a novel Gaussian Process-based Bayesian model for period estimation, a new hyper-parameter optimization algorithm, and a method to incorporate domain knowledge into the estimation process.

Findings

Significantly improved period estimation accuracy on astrophysics data.

Better performance for non-sinusoidal periodic signals.

Effective integration of domain knowledge enhances results.

Abstract

Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the problem of identifying the period: estimating the period of a periodic function based on noisy observations made at irregularly spaced time points. This problem is still a difficult challenge despite extensive study in different disciplines. The paper makes several contributions toward solving this problem. First, we present a nonparametric Bayesian model for period finding, based on Gaussian Processes (GP), that does not make strong assumptions on the shape of the periodic function. As our experiments demonstrate, the new model leads to significantly better results in period estimation when the target function is non-sinusoidal. Second, we develop a new algorithm for parameter optimization for GP which is useful when the likelihood function is very sensitive to the setting of the hyper-parameters with numerous local minima, as in the case of period estimation. The algorithm combines gradient optimization with grid search and incorporates several mechanisms to overcome the high complexity of inference with GP. Third, we develop a novel approach for using domain knowledge, in the form of a probabilistic generative model, and incorporate it into the period estimation algorithm. Experimental results on astrophysics data validate our approach showing significant improvement over the state of the art in this domain.