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金融中的高斯过程与贝叶斯优化

文章 arXiv papers · 作者: Joan Gonzalvez et al.
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总结

本文介绍高斯过程（GP）和贝叶斯优化，说明GP回归如何支持贝叶斯机器学习，以及如何选择其超参数。贝叶斯优化利用概率模型搜索黑箱函数的最优值，无需计算导数，尤其适用于参数数量较少的情况。

本文介绍两种金融应用：拟合利率期限结构，并将GP预测与随机游走模型进行比较；以及通过在线估计趋势窗口和协方差窗口构建趋势跟踪策略。文中所述比较说明了这些方法的评估对象，但摘录未提供绩效结果、数据细节或实现选择。因此，本文概述了相关工具及其应用，但证据不足以判断其预测价值、交易成本或稳健性。

核心观点

  • 高斯过程将高斯随机向量扩展到函数，并用于核方法。
  • 贝叶斯优化利用GP模型引导无导数搜索，以寻找黑箱函数的最优值。
  • GP回归是该方法的核心，且需要选择其超参数。
  • 本文将高斯过程用于利率期限结构拟合，并将预测与随机游走进行比较。
  • 本文还研究了如何在线选择趋势跟踪策略的趋势窗口和协方差窗口。

标签

机器学习统计学固定收益趋势跟踪
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# Financial Applications of Gaussian Processes and Bayesian Optimization


# Financial Applications of Gaussian Processes and Bayesian Optimization









In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a generalization of Gaussian random vectors and are associated with the development of kernel methods. Bayesian optimization is an approach for performing derivative-free global optimization in a small dimension, and uses Gaussian processes to locate the global maximum of a black-box function. The first part of the article reviews these two tools and shows how they are connected. In particular, we focus on the Gaussian process regression, which is the core of Bayesian machine learning, and the issue of hyperparameter selection. The second part is dedicated to two financial applications. We first consider the modeling of the term structure of interest rates. More precisely, we test the fitting method and compare the GP prediction and the random walk model. The second application is the construction of trend-following strategies, in particular the online estimation of trend and covariance windows.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。