Decision Theoretic Bayesian Computation

无论是在商业、政策制定还是工程系统中，决策者都面临着在不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、在服务系统中做出投资决定或人员配备决定。现代决策者通常使用复杂的概率模型来捕捉不确定性，并在这种模型的框架内采取最优行动。一般来说，模型本身涉及未知参数，这些参数必须从数据中估计出来。虽然大数据集改善了参数的估计，导致了更准确的决策，但这些大数据设置也带来了计算挑战，需要在估计中进行近似。当前的方法通常分为两个步骤：(1)使用大量的统计和机器学习文献来近似估计模型参数，以及(2)使用所得到的近似来计算可能的最佳动作。由于第一阶段计算的近似不适合第二阶段的决策问题，这种两阶段程序可能导致行动的次最优。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临不确定性的情况下帮助在行动中做出决定。该项目将提供工具和理论，以准确地考虑统计准确性、决策理论效用和计算复杂性之间的权衡，并将把决策纳入推动现代数据科学的计算革命。这些工具和理论可能会对大量数据驱动的决策问题产生影响。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。研究集中在贝叶斯决策理论的近似计算带来的理论和方法论挑战。研究人员考虑了两个相辅相成的问题，(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领域发展的变分方法，以逼近难以处理的贝叶斯后验分布。研究人员将从理论上研究这类算法在决策方面的最佳性，而不是预测，并开发使用决策理论而不是推理标准来搜索近似的新的“损失校准”算法。任务(B)认识到，模型始终是现实的近似值，因此被错误地指定。因此，贝叶斯后验分布，即使精确计算，也可能不能实际描述未来观测的分布特征。研究人员探索与第一个任务的近似值之间的联系，并从特定模型下参数和变量的不确定性，转移到模型本身的选择的不确定性。他们开发和分析方法，使之能够在这种“奈特”不确定性面前做出稳健和原则性的决定。这一奖项反映了NSF的法定使命，并通过使用基金会的智力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.