CCF: Medium: Inference with dynamic deep probabilistic models

复杂系统的动力学通常是通过处理这些系统产生的多变量时间信号来研究的。从这些信号中提高对系统的理解取决于对系统的精确模型的研究。所提出的从多元时间信号进行推理的方法的基本原理基于三个重要原则：算法可压缩性、局域性和深度概率建模。通过算法可压缩性，我们可以在低维空间中解释看似复杂的高维数据。关于局部性，人们利用这样一个事实：在自然界中，对一个事件最有影响的事件是它的局部性事件。通过深度概率建模，我们的目标是找到算法的可压缩性。这些原理用于开发新的模型，很少有关于观察系统动力学的先验知识。项目中另一个具有挑战性的问题是基于所采用的模型发现因果关系。所开发的方法在癫痫患者的多变量局部场电位上进行了测试。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切除它们通常可以治愈病人。该项目概念化了一种有原则的方法，通过深度概率建模来构建深度状态空间模型。该研究包括开发用于估计这些模型的未知因素的理论和方法，研究用于估计模型结构的方法，将新方法扩展到捕获状态切换的模型，开发用于发现多变量时间信号之间因果关系的理论和方法，以及识别导致癫痫患者发作的状态。该研究基于对模型的最小假设，并在贝叶斯框架内进行。该方法不需要大量数据，所有产生的结果本质上都是概率性的。这项关于深度概率模型和因果发现的研究大大扩展了建模多元时间信号的能力，这不仅有助于我们对复杂系统的理解，而且还提供了扩展信号处理和机器学习的视野和范围的新范式。在医学和神经外科方面的应用，如确定癫痫患者大脑中引起癫痫发作的病理区域，都有其优点。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。

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.