Parameter inference from a nonstationary unknown process
Abstract
Nonstationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze nonstationary processes, and yet most timeseries analysis methods that are used in practice, on important problems across science and industry, make the simplifying assumption of stationarity. One important problem in the analysis of nonstationary systems is the problem class that we refer to as Parameter Inference from a Nonstationary Unknown Process (PINUP). Given an observed time series, this involves inferring the parameters that drive nonstationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here we review and unify a diverse literature of algorithms for PINUP. We formulate the problem, and categorize the various algorithmic contributions. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on  notably the nonstationary Lorenz process and logistic map  are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing nonstationary systems and suggest new directions for progress on the PINUP problem and the broader study of nonstationary phenomena.
 Publication:

arXiv eprints
 Pub Date:
 July 2024
 DOI:
 10.48550/arXiv.2407.08987
 arXiv:
 arXiv:2407.08987
 Bibcode:
 2024arXiv240708987O
 Keywords:

 Physics  Data Analysis;
 Statistics and Probability;
 Computer Science  Machine Learning;
 Nonlinear Sciences  Chaotic Dynamics;
 Statistics  Machine Learning