随机化算法实现动态数据的序列回归预测，理论严谨且高效。
Sequential Regression Learning with Randomized Algorithms
- 基于概率框架，用梯度下降与近端算法更新权重
- 在真实数据上实现回归与二分类任务，性能稳定
- 适合处理时间依赖型动态数据，理论保障强
本文提出「随机化SINDy」，一种针对具有时序结构的动态数据设计的序列机器学习算法。该算法采用概率方法，其泛化能力通过函数分析理论严格证明。它通过学习预测因子的概率分布进行动态预测，利用梯度下降和近端算法更新权重，确保概率密度的有效性。受SINDy（Brunton et al. 2016）启发，引入特征增强与Tikhonov正则化。对于多元正态权重情形，省略近端步骤以聚焦参数估计。实验结果表明，该算法在真实世界数据上的回归与二分类任务中表现有效。
原文摘要 · Abstract (English)
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.
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