Post selection inference improves reliability of sparse nonlinear dynamics discovery
PSI-SINDy: Post-Selection Inference for Sparse Identification of Nonlinear Dynamics
Machine Learning
Summary
Discovering the underlying rules of how things change over time from noisy data is tricky, especially when you only want a few important rules. The authors worked on making sure that the rules chosen this way are truly reliable, not just lucky guesses from noisy measurements. They developed a method called PSI-SINDy that carefully checks these selected rules by cleverly splitting the data to remove bias and noise problems. This method was tested on simulated and real data and shown to be valid under certain conditions.
What this means in practice
- •For control systems engineers: Evaluate which model terms genuinely govern a system’s dynamics from noisy measurements to improve control strategy design.
- •For data analysts in finance: Statistically validate selected factors in dynamic financial models derived from time-series market data despite noisy observations.
Authors
Ashraful Islam, Shuichi Nishino, Tomohiro Shiraishi, Ichiro Takeuchi
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.