Computational Sensitivity Analysis for Decision-Making under Data Uncertainty

用于做出复杂决策的定量模型需要在得出决策之前指定各种参数。这些参数通常是数据中的不确定估计。由于导出的决策是依赖于参数，它是决策的一个重要组成部分，以分析如何改变时，估计参数扰动的决策。该研究旨在开发新的方法来分析通过复杂模型获得的决策的敏感性。即使随着计算能力的现代进步，分析包含大量可同时扰动的参数的高维模型的灵敏度仍然是一项具有挑战性的任务。拟议的研究将开发计算上实用的算法来执行高维模型的敏感性分析。本研究将分别针对两类决策问题达成目标，一类是一次做出复杂决策，另一类是需要在多个阶段做出一系列决策，即顺序决策。 该提案还旨在研究如何使用来自异构系统的数据影响顺序决策。一系列决策是基于从历史数据中获得的关于系统如何随时间演变的知识做出的。最近，从大人口的连续数据已经变得更容易获得，这样的数据很可能包含异质性的过渡模式。例如，在患有某种疾病的大人群中，某些患者的疾病状态可能比其他患者进展得更快。如果是这种情况，则单独地对每个过渡模式进行建模并应用对于特定过渡模式最佳的治疗计划可以产生更好的结果。本研究将正式研究以下一般性问题：在什么条件下，它是有益的模型异构模式，并分配决策量身定制的每一个模式？ 对于使用分析方法做出复杂决策的人来说，拟议的研究将提供计算上易于处理的方法来理解决策的敏感性。该提案的两个长期目标，分析参数不确定性下的最佳决策的敏感性，并研究建模不同的过渡趋势的好处，与个性化的决策，这是越来越多的关注，特别是在医疗保健应用。拟议的研究将提供方法来分析数据不确定性下的治疗计划的敏感性，并为异质患者类型找到最佳的护理计划。此外，该提案重点关注基于大规模数据集的决策中出现的问题，因此随着我们面临基于更大数据集做出更复杂的决策，对所提出的方法的需求将不断增加。

Quantitative models for making complex decisions require various parameters to be specified before a decision is derived. Those parameters are often uncertain estimates from data. Since a derived decision is dependent on the parameters, it is an essential part of decision-making to analyze how the decision changes when the estimated parameters are perturbed. The proposed research aims to develop novel methods to analyze the sensitivity of decisions obtained through complex models. Even with the modern advancement of computing power, it is still a challenging task to analyze the sensitivity of high-dimensional models that contain a large number of parameters that can be simultaneously perturbed. The proposed research will develop computationally practical algorithms to perform sensitivity analysis for high-dimensional models. This research will achieve the goal for two types of decision-making problems separately, the one where a complex decision is made once and the other where a series of decisions need to be made over multiple stages, that is, sequential decision-making. This proposal also aims to study how the use of data from heterogeneous systems affects sequential decision-making. A series of decisions are made based on knowledge obtained from historical data about how the system evolves over time. Recently, sequential data from large populations have become more readily available and such data are likely to contain heterogeneous transition patterns. For example, in a large population with a certain disease, the disease status of some patients might progress faster than for other patients. If this is the case, then modeling each transition pattern separately and applying a treatment plan that is optimal for the specific transition pattern can result in better outcomes. This research will formally study the following general question: under what conditions is it beneficial to model heterogeneous patterns and to assign decisions tailored to each pattern? To people who use analytical methods to make complex decisions, the proposed research will provide computationally tractable methods to understand the sensitivity of decisions. The two long-term objectives of this proposal, analyzing the sensitivity of optimal decisions under parameter uncertainty and studying the benefit of modeling distinct transition trends, align with personalized decision-making, which is gaining a lot of attention particularly in health care applications. The proposed research will provide methods to analyze the sensitivity of treatment plans under data uncertainty and to find optimal care plans for heterogeneous patient types. Furthermore, this proposal focuses on issues arising in decision-making based on large-scale data sets, so the need for the proposed methods will keep rising as we face more complex decisions to be made based on larger data sets.