Computational Information Geometry and Model Uncertainty/Neuro-informatics

计算信息几何和模型不确定性/神经信息学

• 批准号: RGPIN-2014-05424
• 负责人: Marriott, Paul
• 金额: $ 1.68万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635877
• 关键词: Computational; Information; Geometry; Model; Uncertainty

My research program is comprised of two streams: Computational Information Geometry (CIG) and Neuroinformatics (NI).Information Geometry (IG) is the application of geometry (differential, convex, affine, algebraic and the infinite dimensional geometries of Hilbert and Banach spaces), to the advancement of statistical theory. The term Computational Information Geometry means the focus is on producing computational tools for users of statistics. Stream I: The methodology to be developed in CIG has, in the long term, the potential to change statistical practice. The sub-project (CIG:1) tackles a ubiquitous problem of the development of assessment of statistical models, i.e., model building, sensitivity and uncertainty. It gives a computational and practical way of implementing Box's view of science, put forward in his landmark 1976 paper 'Science and Statistics'. In these papers, scientific knowledge is seen as advancing by 'a motivated iteration between theory and practice', 'efficient scientific iteration evidently requiring unhampered feedback', adding that: 'since all models are wrong the scientist must be alert to what is importantly wrong.' We are therefore developing operational, computation tools to implement these powerful ideas. These tools all have an underlying geometric background. The sub-project (CIG:2) combines advances in IG and some very exciting new work in Markov chain Monte Carlo (MCMC) theory. This will allow inference in very complex real world problems, in particular ones which are fundamentally high dimensional and/or have strong non-linear constraints. Stream II: Neuroinformatics involves the use of statistical methods to data from neuroscience and in this application we focus on so-called spike train data. The human brain consists of billions of cells, called neurons, which communicate with each other through electrochemical waves called action potentials. These are also known as spikes as they tend to be very localized in time, with a time scale typically around a few milliseconds. A sequence of these neural spikes generated by an individual neuron is called a spike train. The mechanism(s) that spike trains use to code information is of great interest and the complete characterization of this mechanism is still far from settled. This project is aimed using statistical methods to address precisely this question. In addition to addressing pure neuroscience questions, understanding spike trains is also has important applications such as the control of prosthetic limbs. The project, (NI: Neuroinformatics), is comprised of a number of smaller, largely independent, sub-projects and consisting of: (NI:1 Visualisation) - developing data visualisation tools for multiple spike train data. Modern spike train data can include recordings from large numbers of interrelated neurons, showing structure over many different time scales. Data visualisation tools will be extremely useful for practitioners working with this data. (NI:2 Robustness) - the analysis of the effect of measurement and classification errors which are typically found in spike train data. (NI:3 Dispersion) - understanding the underlying variability of spike trains is also a critical part of modelling this data and new methodology will be developed to do this. (NI:4 Phase) - the firing times of spikes relative to a periodic signal is called phased coding. We look at the analysis and modelling of time varying phases for multiple spike trains.Both streams will advance statistical methodology in two important, but distinct, areas: foundational theory and applications to neuroscience. They will provide high quality training for HQP in areas where there is a strong demand, both in academia and much more widely.

我的研究项目由两个方向组成：计算信息几何 (CIG) 和神经信息学 (NI)。信息几何 (IG) 是几何学（微分几何、凸几何、仿射几何、代数几何以及希尔伯特和巴拿赫空间的无限维几何）在统计理论发展中的应用。计算信息几何一词意味着重点是为统计用户提供计算工具。第一组：从长远来看，CIG 开发的方法有可能改变统计实践。该子项目 (CIG:1) 解决了统计模型评估开发中普遍存在的问题，即模型构建、敏感性和不确定性。它提供了一种计算和实用的方法来实现博克斯在 1976 年具有里程碑意义的论文“科学与统计”中提出的科学观。在这些论文中，科学知识被视为通过“理论与实践之间有动力的迭代”来推进，“有效的科学迭代显然需要不受阻碍的反馈”，并补充说：“由于所有模型都是错误的，科学家必须警惕什么是重要的错误。”因此，我们正在开发可操作的计算工具来实现这些强大的想法。这些工具都有一个基本的几何背景。该子项目 (CIG:2) 结合了 IG 的进步和马尔可夫链蒙特卡罗 (MCMC) 理论中一些非常令人兴奋的新工作。这将允许推理非常复杂的现实世界问题，特别是那些基本上是高维和/或具有强非线性约束的问题。第二组：神经信息学涉及对神经科学数据使用统计方法，在此应用中，我们重点关注所谓的尖峰序列数据。人脑由数十亿个称为神经元的细胞组成，它们通过称为动作电位的电化学波相互通信。这些也被称为尖峰，因为它们往往在时间上非常局部化，时间尺度通常约为几毫秒。由单个神经元生成的这些神经尖峰序列称为尖峰序列。脉冲序列用于编码信息的机制引起了人们的极大兴趣，但该机制的完整特征仍远未确定。该项目旨在利用统计方法来准确解决这个问题。除了解决纯粹的神经科学问题之外，理解尖峰序列也有重要的应用，例如假肢的控制。该项目（NI：神经信息学）由许多较小的、很大程度上独立的子项目组成，其中包括：（NI：1 可视化）- 为多个尖峰序列数据开发数据可视化工具。现代尖峰序列数据可以包括大量相互关联的神经元的记录，显示许多不同时间尺度的结构。数据可视化工具对于处理这些数据的从业者来说非常有用。 (NI:2 鲁棒性) - 对尖峰序列数据中常见的测量和分类误差的影响进行分析。 (NI:3 分散) - 了解尖峰序列的潜在变异性也是对该数据进行建模的关键部分，并且将开发新的方法来做到这一点。 （NI：4 相位）- 相对于周期信号的尖峰触发时间称为相控编码。我们着眼于多个尖峰序列的时变阶段的分析和建模。这两个流将在两个重要但不同的领域推进统计方法：基础理论和神经科学的应用。他们将在学术界和更广泛领域有强烈需求的领域为总部提供高质量的培训。