具有最优前视偏差与方差权衡的贝叶斯插补
Bayesian Imputation with Optimal Look-Ahead-Bias and Variance Tradeoff
AI总结：
本文针对时间序列缺失数据插补中前视偏差与方差的权衡问题，提出一种融合多个后验的贝叶斯共识后验方法，并通过两步优化程序在投资组合配置中验证其有效性。
摘要：
缺失的时间序列数据是运营管理、医疗保健和金融领域许多规范性分析模型中普遍存在的问题。时间序列数据的插补方法通常应用于完整的面板数据，目的是为下游的样本外任务训练一个规范性模型。例如，缺失资产收益的插补可以在估计最优投资组合配置之前进行。然而，这种做法可能导致下游任务未来表现中的前视偏差，并且在使用整个数据集进行插补所带来的前视偏差与仅使用数据集的训练部分进行插补所带来的较大方差之间存在固有的权衡。通过连接随时间揭示的信息层，我们提出了一种贝叶斯共识后验，它融合任意数量的后验，以优化插补中的方差与前视偏差权衡。我们推导了易于处理的两步优化程序，用于寻找最优共识后验，其中使用Kullback-Leibler散度和Wasserstein距离作为后验分布之间的差异度量。我们在模拟和实证研究中展示了我们的插补机制在缺失收益的投资组合配置中的优势。
英文摘要：
Missing time-series data is a prevalent problem in many prescriptive analytics models in operations management, healthcare and finance. Imputation methods for time-series data are usually applied to the full panel data with the purpose of training a prescriptive model for a downstream out-of-sample task. For example, the imputation of missing asset returns may be applied before estimating an optimal portfolio allocation. However, this practice can result in a look-ahead-bias in the future performance of the downstream task, and there is an inherent trade-off between the look-ahead-bias of using the entire data set for imputation and the larger variance of using only the training portion of the data set for imputation. By connecting layers of information revealed in time, we propose a Bayesian consensus posterior that fuses an arbitrary number of posteriors to optimize the variance and look-ahead-bias trade-off in the imputation. We derive tractable two-step optimization procedures for finding the optimal consensus posterior, with Kullback-Leibler divergence and Wasserstein distance as the dissimilarity measure between posterior distributions. We demonstrate in simulations and in an empirical study the benefit of our imputation mechanism for portfolio allocation with missing returns.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
