Information geometric theory of neural information processing and disorder

信息处理被看似不同的非线性复杂动力学所共享。特别是，人们对信息几何越来越感兴趣，它指的是通过在统计流形中定义度量(距离)的概念，将微分几何应用于概率和统计。特别是，它为我们理解随机随机过程提供了一种强有力的方法，具有理论和实际意义。从概念上讲，将度量分配给概率密度函数(PDF)使我们能够量化不同PDF之间的差异，从而在随机过程、复杂性和几何之间建立漂亮的联系。本项目旨在开发一种新的神经信息处理的无模型信息几何理论，以通过克服以下各种当前的挑战来改进疾病诊断的实用目的。大脑是复杂的信息处理器官，其在不同部位的适当功能对于我们的最佳福祉是不可或缺的。许多关键问题，如理解神经信息处理和神经疾病的诊断，不仅需要识别区域激活，还需要识别大脑不同区域之间的因果联系，以及解释观察到的反应的最简单电路。特别是，因果关系(有效连通性)分析为一系列神经疾病提供了新的诊断机会。因此，经典结构连通性的研究得到了功能连通性的补充，更重要的是，通过对神经生理信号(如功能磁共振成像和脑电)的统计建模进行因果分析。神经信号分析的主要挑战来自于人脑不确定的时变非线性动力学。数据通常是非平稳和非高斯的，而平均值、方差或其他高阶矩可能会在时间上突然变化。在传统的基于平稳或高斯数据的传递熵和格兰杰因果关系公式中，这样的数据不能被充分量化。此外，潜在的数学模型并不总是可以用来拟合数据。另一方面，数据中降低的信噪比通常会阻碍准确的分析。因此，开发一种能够有效量化数据动态变化的无模型方法是至关重要的。面对这些挑战，我们将以信息几何的前沿研究为起点，进一步发展该方法，以最有效地量化非平稳时变效应、非线性和非高斯随机性。为此，我们提出了一个为期一年的协同计划，通过利用我们团队的互补技能，进行理论和计算研究以及数据分析。具体地说，我们将：i)将我们的理论扩展到非线性/多变量；ii)数值模拟简单的神经活动模型。同时，我们将：iii)应用我们的新方法分析来自健康对照组和某些神经疾病患者(例如癫痫、认知功能正常的帕金森病、阿尔茨海默病)的匿名脑电数据。特别是，我们将比较健康对照组和患者大脑关键区域的信息处理和大脑连接性，并确定它们的相似和不同之处。然后，我们将开发生物标记物来诊断神经疾病，如癫痫发作，并在探索临床意义的同时跟踪疾病进展。鉴于信息论在各学科中日益重要的作用，这个项目将成为未来提出解决其他实际挑战的垫脚石。

Information processing is shared among seemingly different nonlinear complex dynamics. In particular, there has been a growing interest in information geometry that refers to the application of differential geometry to probability and statistics by defining the notion of metric (distance) in statistical manifolds. In particular, it provides us with a powerful method for understanding random stochastic processes for theoretical and practical purposes. Conceptually, assigning a metric to probability density functions (PDFs) enables us to quantify the difference among different PDFs and thus to make a beautiful link between a stochastic process, complexity, and geometry. This project aims to develop a new model-free information geometric theory of neural information processing for the practical purpose of improved disorder diagnosis by overcoming various current challenges described below.Brains are complex information-processing organs whose proper function in different parts is indispensable for our optimal well-being. Many critical issues, such as understanding neural information processing and diagnosis of neurological disorders, require the identification of not only regional activation, but also the causal connectivity among different regions of the brain and the simplest possible circuit to explain observed responses. In particular, causality (effective connectivity) analysis offers new diagnostic opportunities for a whole range of neurological disorders. Therefore, the study of classical structural connectivity is complemented by functional connectivity and, crucially, causal analysis through statistical modelling of neurophysiological signals (e.g., such as functional magnetic resonance imaging and electroencephalography (EEG)).The main challenges in neurological signal analysis stem from the uncertain time-varying nonlinear dynamics of the human brain. Data are generally non-stationary and non-Gaussian, while the mean value, variance, or other higher moments can abruptly change in time. Such data cannot be adequately quantified in the traditional formulation of transfer entropy and Granger causality based on stationary or Gaussian data. Furthermore, underlying mathematical models are not always available to fit the data. On the other hand, the reduced signal-to-noise ratio in data often hampers an accurate analysis. It is thus critical to develop a model-free method that can effectively quantify dynamic changes in data.To face these challenges, we will take our leading-edge research on information geometry as our starting point and develop the method further to quantify non-stationary time-varying effects, nonlinearity, and non-Gaussian stochasticity most effectively. To this end, we propose a one-year, synergistic program on theoretical and computational studies and data analysis by harnessing the complementary skills of our team. Specifically, we will: i) extend our theory to nonlinear/multiple variables; ii) numerically simulate simple neural activity models. In parallel, we will: iii) apply our new methods to analyse the anonymised EEG data from healthy control groups and patients with certain neurological disorders (e.g., epilepsy, Parkinson's disease with normal cognitive function, Alzheimer's disease). In particular, we will compare information processing and brain connectivities among key regions of the brain in healthy control groups and patients and identify their similarities and differences. We will then develop biomarkers to diagnose neurological disorders, such as seizures, and track disease progression while exploring clinical implications. This project will be a stepping stone for future proposals to address other practical challenges given the increasingly important role of information theory across disciplines.