This paper presents ``randomized SINDy", a sequential machine learning algorithm designed for dynamic data that has a time-dependent structure. It employs a probabilistic approach, with its PAC learning property rigorously proven through the mathematical theory of functional analysis. The algorithm dynamically predicts using a learned probability distribution of predictors, updating weights via gradient descent and a proximal algorithm to maintain a valid probability density. Inspired by SINDy (Brunton et al. 2016), it incorporates feature augmentation and Tikhonov regularization. For multivariate normal weights, the proximal step is omitted to focus on parameter estimation. The algorithm's effectiveness is demonstrated through experimental results in regression and binary classification using real-world data.

翻译：本文提出了一种名为“随机SINDy”的顺序机器学习算法，专为具有时间依赖结构的动态数据设计。该算法采用概率方法，并通过泛函分析的数学理论严格证明了其PAC学习性质。算法利用学习得到的预测变量概率分布进行动态预测，通过梯度下降和近端算法更新权重以维持有效的概率密度。受SINDy算法（Brunton等人，2016）启发，该方法融合了特征增广和Tikhonov正则化。对于多元正态权重，算法省略近端步骤以专注于参数估计。基于真实数据的回归与二分类实验结果表明了该算法的有效性。