论文标题
使用流数据集的乘法回归的可再生学习
Renewable Learning for Multiplicative Regression with Streaming Datasets
论文作者
论文摘要
当大量数据连续到达流中时，在线更新是减少存储和计算负担的有效方法。在线更新的关键思想是，以前的估计器仅使用当前数据和一些历史原始数据的摘要统计信息进行顺序更新。在本文中，我们为带有流数据的乘法回归模型开发了可再生的学习方法，其中基于最小产品相对误差标准的参数估计器将在不重新审视任何历史原始数据的情况下续订。在某些规律性条件下，我们建立了可再生估计量的一致性和渐近正态性。此外，理论结果证实，所提出的可再生估计量与使用整个数据集的最小产品相对误差估计器相同的渐近分布。提供了数值研究和两个实际数据示例，以评估我们提出的方法的性能。
When large amounts of data continuously arrive in streams, online updating is an effective way to reduce storage and computational burden. The key idea of online updating is that the previous estimators are sequentially updated only using the current data and some summary statistics of historical raw data. In this article, we develop a renewable learning method for a multiplicative regression model with streaming data, where the parameter estimator based on a least product relative error criterion is renewed without revisiting any historical raw data. Under some regularity conditions, we establish the consistency and asymptotic normality of the renewable estimator. Moreover, the theoretical results confirm that the proposed renewable estimator achieves the same asymptotic distribution as the least product relative error estimator with the entire dataset. Numerical studies and two real data examples are provided to evaluate the performance of our proposed method.
