Model Reduction of High Dimensional Hidden Markov Models and Markov Decision Processes

知识价值：我们目前生活在一个数据是一种主要货币的时代，它有望为我们的社会带来变革性的变化。因此，在高维数据上使用机器学习（ML）算法产生非结构化随机模型的情况激增。这样的模型往往是非常高的维度，限制了它们在涉及优化或决策系统的各种应用中的效用。该提案的重点是发展一个基本的理论模型减少应用到类的随机模型，特别是隐马尔可夫模型（HALGORY），这些是随机模型，描述了底层有限维状态空间。更广泛的影响：最终，模型简化理论将影响与复杂随机模型相关的许多基本方面，包括模拟，预测，编码，鲁棒学习，决策设计和强化学习。这项研究将开发新的见解，以解决其他随机模型的类似问题，包括跳跃线性系统和具有潜变量的图形模型，并将对与人工智能和强化学习相关的问题产生直接影响。后者正在成为许多涉及社会行为的决策系统应用程序的流行方法-其中不存在简单的机械模型。这样的问题的例子是关键的基础设施和智能服务，其中高维非结构化数据是真实的时间。在这种方法中出现的模型往往具有非常高的维度。模型简化的基础理论将影响我们学习和利用复杂随机模型的方式。因此，这种发展将以类似于模型简化理论如何影响线性系统理论课程的方式进入我们在麻省理工学院的课程。发展应该会影响随机模型，机器学习，统计学习理论，强化学习和AI的课程。 我们还打算将模型简化和统计学习之间的联系纳入我们新的麻省理工学院统计和数据科学微硕士课程中。该奖项反映了NSF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。

Intellectual Merit: We currently live in an era where data is a major currency promising a transformative change to our society. Consequently, there has been a surge in the use of machine learning (ML) algorithms on high dimensional data producing unstructured stochastic models. Such models tend to be of very high dimensions limiting their utility in various applications involving optimization or decision systems. This proposal focuses on developing a foundational theory for model reduction applied to classes of stochastic models, in particular, Hidden Markov Models (HMMs); these are stochastic models that are described by underlying finite dimensional state space. Broader Impact: Ultimately, a model reduction theory will impact many fundamental aspects related to complex stochastic models including simulation, prediction, coding, robust learning, decision design and reinforcement learning. This research will develop new insights to address similar questions for other stochastic models including jump linear systems, and graphical models with latent variables and will have a direct impact on problems related to artificial intelligence and reinforcement learning. The latter is emerging as a popular approach for many decision-systems applications involving social behavior-- where simple mechanistic models do not exist. Examples of such problems are critical infrastructures and smart services where high dimensional unstructured data is available in real time. Models emerging in such approaches tend to have very high dimensions. A foundational theory for model reduction will affect the way we learn and utilize complex stochastic models. As a result, this development will enter our courses at MIT in a fashion similar to how model reduction theory impacted courses in linear system theory. The development should affect classes in stochastic models, machine learning, and statistical learning theory, reinforcement learning, and AI. We also intend to incorporate the connection between model reduction and statistical learning in our new MIT micromasters in statistics and data science.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.