Parameter inference from a non-stationary unknown process using statistical feature-based slow feature analysis
Abstract
Non-stationary phenomena are ubiquitous, with examples to be found in climatological measurements, brain activity, and the behavior of financial markets. Starting with a time series from a non-stationary process, a key challenge is to infer the time-varying parameters that underlie the non-stationarity in these systems, without requiring a generative model of the dynamics to be learned. This problem is referred to as Parameter Inference from a Non-stationary Unknown Process (PINUP). Here we introduce a PINUP method called feature-based Slow Feature Analysis (f -SFA) comprising the computation of time-series features across sliding windows, followed by dimension reduction using slow feature analysis (SFA). This allows us to detect slow variation in a potentially wide range of statistical properties of the measured dynamics on a timescale determined by the window length. Crucially, using a comprehensive time-series feature set avoids the subjectivity of feature selection, while the SFA slowness constraint overcomes the bias towards irrelevant correlated features seen with variance-based dimension reduction. The performance of f -SFA surpasses that of four benchmark PINUP methods across a diverse range of non-stationary chaotic processes, and we explore the impact of various parameters on performance, including observation noise, parameter timescales, parameter amplitudes, and unseen parameter values. Further, applying f -SFA to sleep polysomnography data, we show that it is able to infer a time-varying parameter underlying the non-stationary sleep recordings that closely tracks depth of sleep. To our knowledge, this work presents the first comparative study of PINUP methods, and we demonstrate that f -SFA is a simple, effective, and noise-robust approach for quantifying non-stationarity from time series, that can be applied in a range of fields.
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BibTeX
@misc{owens2026parameter,
title = {{Parameter inference from a non-stationary unknown process using statistical feature-based slow feature analysis}},
author = {Kieran S. Owens and Masako Tamaki and Ben D. Fulcher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01651},
eprint = {2609.01651},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01651},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Parameter inference from a non-stationary unknown process using statistical feature-based slow feature analysis
AU - Kieran S. Owens
AU - Masako Tamaki
AU - Ben D. Fulcher
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01651
UR - https://arxiv.org/abs/2609.01651
AB - Non-stationary phenomena are ubiquitous, with examples to be found in climatological measurements, brain activity, and the behavior of financial markets. Starting with a time series from a non-stationary process, a key challenge is to infer the time-varying parameters that underlie the non-stationarity in these systems, without requiring a generative model of the dynamics to be learned. This problem is referred to as Parameter Inference from a Non-stationary Unknown Process (PINUP). Here we introduce a PINUP method called feature-based Slow Feature Analysis (f -SFA) comprising the computation of time-series features across sliding windows, followed by dimension reduction using slow feature analysis (SFA). This allows us to detect slow variation in a potentially wide range of statistical properties of the measured dynamics on a timescale determined by the window length. Crucially, using a comprehensive time-series feature set avoids the subjectivity of feature selection, while the SFA slowness constraint overcomes the bias towards irrelevant correlated features seen with variance-based dimension reduction. The performance of f -SFA surpasses that of four benchmark PINUP methods across a diverse range of non-stationary chaotic processes, and we explore the impact of various parameters on performance, including observation noise, parameter timescales, parameter amplitudes, and unseen parameter values. Further, applying f -SFA to sleep polysomnography data, we show that it is able to infer a time-varying parameter underlying the non-stationary sleep recordings that closely tracks depth of sleep. To our knowledge, this work presents the first comparative study of PINUP methods, and we demonstrate that f -SFA is a simple, effective, and noise-robust approach for quantifying non-stationarity from time series, that can be applied in a range of fields.
ER -