arXiv：cs.LG· Ashraful Islam, Shuichi Nishino, Tomohiro Shiraishi, Ichiro Takeuchi·· 3 小时前
PSI-SINDy：面向非线性动力学稀疏辨识的选后推断方法
PSI-SINDy: Post-Selection Inference for Sparse Identification of Nonlinear Dynamics
AI 导读
研究者提出 PSI-SINDy，一种针对 SINDy 的选后推断方法，通过假设检验和置信区间量化所选动力学项的可靠性。该方法用 data thinning 将单条观测轨迹分解为四个相互独立的视图，分别承担选择与推断角色，从而同时处理选择偏差、测量误差以及响应与设计之间的共享噪声。研究给出了该方法在既定条件下的理论有效性证明，并在模拟与实验动力学系统数据上进行了数值实验评估。
正文
Abstract:Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for discovering governing dynamics from time-series data by identifying a sparse subset of candidate dynamical terms from a prespecified library. In this work, we develop a statistical inference framework for quantifying the reliability of dynamical terms selected by SINDy through hypothesis tests and confidence intervals. A key difficulty is that using the same noisy trajectory for both selecting dynamical terms and assessing their statistical significance can introduce selection bias. Post-selection inference provides a principled framework for addressing such bias, and we propose PSI-SINDy, a post-selection inference method tailored to SINDy. Direct application of existing post-selection inference techniques is challenging because SINDy involves measurement error in the candidate terms and shared noise between the response and design. To address these challenges, PSI-SINDy uses data thinning to decompose a single observed trajectory into four mutually independent views with distinct roles in selection and inference. This construction enables inference for selected dynamical terms while accounting not only for selection bias but also for measurement-error and shared noise effects. We establish the theoretical validity of PSI-SINDy under stated conditions and evaluate its performance through numerical experiments on simulated and experimental dynamical-system data.
| Comments: | 47 pages, 3 figures, 16 tables |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.11486 [stat.ML] |
| (or arXiv:2610.11486v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11486 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ashraful Islam [view email]
[v1]
Thu, 8 Oct 2026 08:29:21 UTC (138 KB)
来源：arXiv：cs.LG · arxiv.org