Decision Theoretic Bayesian Computation

无论是在商业、政策制定还是工程系统中，决策者都面临着在没有完全了解世界状况的情况下采取行动的问题。这种情况的例子包括控制工业工厂、操纵自动驾驶汽车、开发新药、做出投资决策或服务系统中的人员配置决策。现代决策者通常使用复杂的概率模型来捕捉不确定性，并在这些模型的框架内采取最佳行动。通常，模型本身包含未知参数，这些参数必须从数据中估计出来。虽然大型数据集改善了对参数的估计，从而导致更准确的决策，但这些大数据设置也提出了计算挑战，需要在估计中进行近似值。目前的方法通常分两步进行：(1)使用大量的统计和机器学习文献来近似估计模型参数，(2)使用得到的近似来计算最佳可能的行动。这个两阶段的过程可能导致行动的次最优性，因为在第一阶段计算的近似值不适合第二阶段的决策问题。该项目的目标是开发和研究一种以决策为中心的近似计算方法框架，认识到大多数大数据分析的最终目标是在面对不确定性时帮助在行动中做出决定。该项目将提供工具和理论，以准确地解释统计准确性、决策理论效用和计算复杂性之间的权衡，并将决策整合到驱动现代数据科学的计算革命中。这些工具和理论可能会影响大量数据驱动的决策问题。该项目在贝叶斯统计的总体框架下工作，其中主要感兴趣的对象是未知参数和变量的后验分布。研究的重点是贝叶斯决策理论的近似计算所带来的理论和方法上的挑战。研究人员考虑两个互补的问题，(a)决策理论变分贝叶斯和(b)稳健决策。前一项任务从决策理论的角度分析和扩展了机器学习社区开发的变分方法，以近似难处理的贝叶斯后验分布。研究人员将从理论上研究这些算法在决策方面的最优性，而不是预测，并开发新的“损失校准”算法，使用决策理论而不是推理标准来搜索近似值。任务(b)认识到模型总是接近现实，因此是错误的。因此，贝叶斯后验分布，即使计算得很精确，也可能不能真正表征未来观测的分布。研究人员从第一个任务开始探索与近似的联系，并从指定模型下参数和变量的不确定性转移到模型本身选择的不确定性。他们开发和分析方法，允许在面对这种“骑士式”不确定性时做出稳健和有原则的决策。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Decision-makers, whether in business, policy-making, or engineering systems, face the problem of taking action without complete knowledge of the state of the world. Examples of such situations include controlling industrial plants, maneuvering autonomous vehicles, developing new drugs, making investment decisions or staffing decisions in service systems. Modern decision-makers typically use sophisticated probabilistic models to capture uncertainty, and take optimal actions within the framework of such models. In general, the models themselves involve unknown parameters which must be estimated from data. While large datasets improve the estimation of the parameters, leading to more accurate decisions, these big-data settings also raise computational challenges that call for approximations in the estimation. Current methodology typically proceeds in two steps: (1) use the vast statistical and machine learning literature to approximately estimate model parameters, and (2) use the resulting approximations to compute the best possible action. This two-stage procedure can result in sub-optimality of actions, as the approximations computed in the first stage are not tailored to the decision-making problem in the second stage. The objective of this project is to develop and study a methodological framework for approximate computation that puts decision-making at its center, recognizing that the ultimate goal of most big-data analyses is to help decide among actions in the face of uncertainty. The project will provide tools and theory to accurately account for trade-offs between statistical accuracy, decision-theoretic utility and computational complexity, and will integrate decision-making into the computational revolution that has driven much of modern data-science. The tools and theory potentially impact a large range of data-driven decision-making problems. This project works in the overarching framework of Bayesian statistics, where the primary object of interest is the posterior distribution over the unknown parameters and variables. The research focuses on theoretical and methodological challenges arising from approximate computation for Bayesian decision theory. The investigators consider two complementary problems, (a) Decision-theoretic variational Bayes, and (b) Robust decision-making. The former task analyzes and extends variational methods, developed in the machine learning community to approximate intractable Bayesian posterior distributions, from a decision-theoretic viewpoint. The investigators will theoretically study the optimality of such algorithms with respect to decision-making rather than prediction, and develop novel `loss-calibrated' algorithms that search for approximations using decision-theoretic, rather than inferential criteria. Task (b) recognizes that a model is always an approximation to reality, and is therefore misspecified. As a consequence, a Bayesian posterior distribution, even if calculated exactly, might not actually characterize the distribution over future observations. The investigators explore connections with approximations from the first task, and move from uncertainty about parameters and variables under a specified model, to uncertainty about the choice of model itself. They develop and analyze methodology that allows robust and principled decisions in the face of such `Knightian' uncertainty.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.