发表机构
The University of Sydney; RIKEN Center for Brain Science; RIKEN Pioneering Research Institute（悉尼大学; 理化学研究所脑科学中心; 理化学研究所先锋研究本部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对非平稳未知过程的参数推断问题，提出f-SFA方法，其性能优于四种基准方法，可用于量化时间序列非平稳性，还能推断睡眠深度相关时变参数。
AI 中文摘要
非平稳现象无处不在，例如气候测量、大脑活动以及金融市场行为等。针对非平稳过程产生的时间序列，一个关键挑战是在无需学习动力学生成模型的前提下，推断构成这些系统非平稳性的时变参数，该问题被称为非平稳未知过程的参数推断（PINUP）。本文提出一种名为基于特征的慢特征分析（f-SFA）的PINUP方法，该方法包含对滑动窗口内时间序列特征的计算，随后通过慢特征分析（SFA）进行降维。这使得我们能够在由窗口长度决定的时间尺度上，检测被测动力学的潜在广泛统计特性中的缓慢变化。至关重要的是，使用全面的时间序列特征集可避免特征选择的主观性，而SFA的慢度约束克服了基于方差的降维方法中存在的对无关相关特征的偏差。在多种非平稳混沌过程中，f-SFA的性能优于四种基准PINUP方法，我们还探究了各类参数对性能的影响，包括观测噪声、参数时间尺度、参数振幅以及未见过的参数值。此外，将f-SFA应用于睡眠多导睡眠图数据，我们表明其能够推断非平稳睡眠记录背后的时变参数，该参数与睡眠深度密切相关。据我们所知，本研究首次开展了PINUP方法的比较研究，证明f-SFA是一种简单、有效且抗噪的方法，可用于量化时间序列的非平稳性，适用于多个领域。
英文摘要
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.
