{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01651",
  "author_total": 3,
  "authors": [
    {
      "name": "Kieran S. Owens"
    },
    {
      "name": "Masako Tamaki"
    },
    {
      "name": "Ben D. Fulcher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kjskfe4vkw80.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01651",
  "fulltext_url": null,
  "id": "6kjskfe4vkw80",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01651",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.data-an"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.01651",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kjskfe4vkw80.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.01651",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01651"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    }
  ],
  "title": "Parameter inference from a non-stationary unknown process using statistical feature-based slow feature analysis",
  "title_text": "Parameter inference from a non-stationary unknown process using statistical feature-based slow feature analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/6kjskfe4vkw80",
  "venue": "arXiv",
  "versions": []
}