Bayesian Meta-Prior Learning Using Empirical Bayes
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利用经验贝叶斯学习贝叶斯元先验
- 研究问题
- 缺少信息性先验且不同参数组学习速度不同时，如何从数据中学习层级先验，并改善稀疏数据下的学习表现？
- 方法与思路
- 作者提出层级经验贝叶斯方法，用观测数据估计元先验，并在广义线性模型中按特征组调节参数学习速度。
- 材料陈述的贡献
- 摘要报告元先验方差估计量的无偏性、强一致性和最优频率学派累积遗憾性质，以及模拟和生产实验中的改善。
- 阅读关注点
- 应核对特征分组和先验方差更新方式、同一数据参与学习的处理，以及理论结论和小流量实验的适用条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收未核实；摘要未列出理论假设和实验数值，声称可推广不代表所有贝叶斯模型均获保证。
原文摘要
Adding domain knowledge to a learning system is known to improve results. In multi-parameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, various model parameters can have different learning rates in real-world problems, especially with skewed data. Two often-faced challenges in Operation Management and Management Science applications are the absence of informative priors, and the inability to control parameter learning rates. In this study, we propose a hierarchical Empirical Bayes approach that addresses both challenges, and that can generalize to any Bayesian framework. Our method learns empirical meta-priors from the data itself and uses them to decouple the learning rates of first-order and second-order features (or any other given feature grouping) in a Generalized Linear Model. As the first-order features are likely to have a more pronounced effect on the outcome, focusing on learning first-order weights first is likely to improve performance and convergence time. Our Empirical Bayes method clamps features in each group together and uses the deployed model's observed data to empirically compute a hierarchical prior in hindsight. We report theoretical results for the unbiasedness, strong consistency, and optimal frequentist cumulative regret properties of our meta-prior variance estimator. We apply our method to a standard supervised learning optimization problem, as well as an online combinatorial optimization problem in a contextual bandit setting implemented in an Amazon production system. Both during simulations and live experiments, our method shows marked improvements, especially in cases of small traffic. Our findings are promising, as optimizing over sparse data is often a challenge.