论文标题
非平稳在线回归
Non-stationary Online Regression
论文作者
论文摘要
在不断变化的环境下进行在线预测一直是许多现实世界应用中重要性提高的问题。在本文中，我们考虑\ citet {zhang2017dynamic}中介绍的元词素与不同的子例程相结合。我们表明，对于非平稳在线线性回归，可以获得可以获得$ \ tilde {o}（n^{1/3} c_n^{2/3}）$的预期累积误差，其中参数序列的总变化是由$ c_n $绑定的。我们的论文将在\ cite {baby2019online}中提议的一维时间序列的在线预测扩展到一般$ d $ d $维不是平稳的线性回归。我们提高了$ o（\ sqrt {n c_n}）$的利率。 2017年和Besbes等。 2015年。我们进一步将分析扩展到非平稳的在线内核回归。与非平稳的在线回归案例相似，我们使用了Zhang等人的元过程。 2017与内核-AWV（Jezequel etal。2020）相结合，以实现由RKHS的有效维度和序列的总变化的预期累积控制。据我们所知，这项工作是非平稳在线回归到非平稳内核回归的首次扩展。最后，我们通过几种现有基准对方法进行经验评估，并将其与本文获得的理论结合进行了比较。
Online forecasting under a changing environment has been a problem of increasing importance in many real-world applications. In this paper, we consider the meta-algorithm presented in \citet{zhang2017dynamic} combined with different subroutines. We show that an expected cumulative error of order $\tilde{O}(n^{1/3} C_n^{2/3})$ can be obtained for non-stationary online linear regression where the total variation of parameter sequence is bounded by $C_n$. Our paper extends the result of online forecasting of one-dimensional time-series as proposed in \cite{baby2019online} to general $d$-dimensional non-stationary linear regression. We improve the rate $O(\sqrt{n C_n})$ obtained by Zhang et al. 2017 and Besbes et al. 2015. We further extend our analysis to non-stationary online kernel regression. Similar to the non-stationary online regression case, we use the meta-procedure of Zhang et al. 2017 combined with Kernel-AWV (Jezequel et al. 2020) to achieve an expected cumulative controlled by the effective dimension of the RKHS and the total variation of the sequence. To the best of our knowledge, this work is the first extension of non-stationary online regression to non-stationary kernel regression. Lastly, we evaluate our method empirically with several existing benchmarks and also compare it with the theoretical bound obtained in this paper.
