基于变分推断的聚类回归及其在金融预测中的应用
Cluster-based Regression using Variational Inference and Applications in Financial Forecasting
AI总结：
本文提出一种基于变分推断同时识别聚类并估计特定聚类回归参数的方法，可输出预测的期望值与完整分布，在金融预测等具有不同状态的市场中表现出清晰可解释性与计算效率。
摘要：
本文描述了一种从给定数据中同时识别聚类并估计特定聚类回归参数的方法。当估计输出的回归参数在输入空间的不同区域有所不同时，这种方法在学习输入与输出之间的关系时非常有用。变分推断（VI）是一种使用优化技术获取后验概率密度的机器学习方法，本文使用它来识别解释变量的聚类以及每个聚类的回归参数。从这些结果中，可以获得预测输出的期望值和完整分布。该方法的其他优点包括优雅的理论解和结果的清晰可解释性。该方法非常适合金融预测，因为金融市场具有不同的状态（或聚类），且每个状态下的市场变化模式和相关性各不相同。在金融应用中，关于此类聚类的知识可以为投资组合表现提供有用的见解，并识别不同市场状态下变量的相对重要性。本文考虑了一个预测单日S&P变化的示例，以说明该方法并将所提方法与无聚类的标准回归的性能进行比较。由于该问题的广泛适用性、其优雅的理论解以及所提算法的计算效率，该方法可能在金融领域之外的许多领域中发挥作用。
英文摘要：
This paper describes an approach to simultaneously identify clusters and estimate cluster-specific regression parameters from the given data. Such an approach can be useful in learning the relationship between input and output when the regression parameters for estimating output are different in different regions of the input space. Variational Inference (VI), a machine learning approach to obtain posterior probability densities using optimization techniques, is used to identify clusters of explanatory variables and regression parameters for each cluster. From these results, one can obtain both the expected value and the full distribution of predicted output. Other advantages of the proposed approach include the elegant theoretical solution and clear interpretability of results. The proposed approach is well-suited for financial forecasting where markets have different regimes (or clusters) with different patterns and correlations of market changes in each regime. In financial applications, knowledge about such clusters can provide useful insights about portfolio performance and identify the relative importance of variables in different market regimes. An illustrative example of predicting one-day S&P change is considered to illustrate the approach and compare the performance of the proposed approach with standard regression without clusters. Due to the broad applicability of the problem, its elegant theoretical solution, and the computational efficiency of the proposed algorithm, the approach may be useful in a number of areas extending beyond the financial domain.
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