论文标题

超越OCCAM在系统识别中的剃须刀:建模动力学时双重发病

Beyond Occam's Razor in System Identification: Double-Descent when Modeling Dynamics

论文作者

Ribeiro, Antônio H., Hendriks, Johannes N., Wills, Adrian G., Schön, Thomas B.

论文摘要

系统标识旨在从数据中构建动力系统的模型。传统上,选择模型要求设计师在两个矛盾的自然目标之间取得平衡。该模型必须足够丰富以捕获系统动力学,但并不是那么灵活,以至于从数据集中学习虚假的随机效果。通常观察到,随着模型复杂性的增加,模型验证性能遵循U形曲线。然而,机器学习和统计数据的最新发展观察到了“双研究”曲线的情况,该曲线属于这一U形模型表现曲线。由于性能的第二次降低超出了模型达到插值能力的程度 - 即(接近)完美拟合的训练数据。据我们所知,这种现象尚未在动态系统的背景下进行研究。本文旨在回答以下问题:“在估计动态系统参数时也可以观察到这种现象吗?”我们表明答案是肯定的,对人为生成和现实世界数据集的实验验证此类行为。

System identification aims to build models of dynamical systems from data. Traditionally, choosing the model requires the designer to balance between two goals of conflicting nature; the model must be rich enough to capture the system dynamics, but not so flexible that it learns spurious random effects from the dataset. It is typically observed that the model validation performance follows a U-shaped curve as the model complexity increases. Recent developments in machine learning and statistics, however, have observed situations where a "double-descent" curve subsumes this U-shaped model-performance curve. With a second decrease in performance occurring beyond the point where the model has reached the capacity of interpolating - i.e., (near) perfectly fitting - the training data. To the best of our knowledge, such phenomena have not been studied within the context of dynamic systems. The present paper aims to answer the question: "Can such a phenomenon also be observed when estimating parameters of dynamic systems?" We show that the answer is yes, verifying such behavior experimentally both for artificially generated and real-world datasets.

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