CCF: Medium: Inference with dynamic deep probabilistic models

复杂系统的动力学研究通常是通过处理这些系统产生的多变量时间信号来进行的。从这类信号中更好地理解系统，关键在于使用系统的准确模型。所提出的从多变量时间信号进行推断的方法的基本原理基于三个重要原则：算法的可压缩性、局部性和深度概率建模。利用算法的可压缩性，人们可以在低得多的维度空间中解释看似复杂的高维数据。对于地方性，人们利用了这样一个事实，即本质上对一个事件最有影响力的事件是它的本地事件。对于深度概率建模，人们的目标是找到算法的可压缩性。这些原理被用来开发新的模型，而对观察到的系统的动力学几乎没有先验知识。对该项目感兴趣的另一个具有挑战性的问题是基于所采用的模型来发现因果关系。对从癫痫患者采集的多变量局部场电位进行了测试。基于这些信号，目标是找到大脑中导致患者癫痫发作的区域。找到这些区域并通过手术移除它们通常可以治愈患者。该项目概念化了一种使用深度概率建模来构建深层状态空间模型的原则性方法。这些研究包括发展估计这些模型的未知数的理论和方法，研究估计模型结构的方法，将新方法扩展到捕捉机制转换的模型，发展发现多变量时间信号之间的因果关系的理论和方法，以及识别导致癫痫患者癫痫发作的状态。这项研究基于对模型的最小假设，并在贝叶斯框架内进行。该方法并不需要大量的数据，所有产生的结果都是概率性质的。这种对深度概率模型和因果发现的研究极大地扩展了多变量时间信号的建模能力，这不仅有助于我们理解复杂系统，而且提供了新的范式，扩展了信号处理和机器学习的视野和范围。在医学和神经外科中的应用，例如识别癫痫患者大脑中导致癫痫发作的病理区，是他们应得的。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The dynamics of complex systems are often studied by processing multivariate time signals that are produced by these systems. Improved understanding of the systems from such signals hinges on working with accurate models of the systems. The rationale of the proposed methodology for making inference from multivariate time signals stands on three important principles: algorithmic compressibility, locality, and deep probabilistic modeling. With algorithmic compressibility, one interprets seemingly complex high-dimensional data in much lower dimensional spaces. With locality, one exploits the fact that in nature the most influential events to an event are its local events. With deep probabilistic modeling, one aims at finding algorithmic compressibilities. These principles are used for developing novel models with little prior knowledge about the dynamics of the observed system. Another challenging problem of interest in the project is discovering causes and effects based on the adopted models. The developed methods are tested on multivariate local field potentials acquired from patients with epilepsy. Based on these signals, the objective is to find the zones in the brain that cause seizures in the patients. Finding these zones and removing them by surgery often cures the patients. The project conceptualizes a principled approach to building deep state-space models with deep probabilistic modeling. The research includes the development of theory and methods for estimating the unknowns of these models, investigation of methods for estimating the structures of the models, extension of the new methods to models that capture regime switching, development of theory and methods for discovering causalities among multivariate time signals, and identification of states that cause seizures in patients with epilepsy. The research is based on minimal assumptions about the models and is carried out within the Bayesian framework. The methodology is not data hungry, and all the produced results are probabilistic in nature. This research on deep probabilistic models and causal discovery considerably extends the capabilities for modeling multivariate time signals, which not only facilitates our understanding of complex systems but also offers new paradigms that extend the horizons and scope of signal processing and machine learning. The applications in medicine and neurosurgery, such as identifying the pathological zones in the brain of epilepsy patients that cause seizures stand on their merit.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.