Computational Information Geometry/Neuroinformatics

计算信息几何/神经信息学

• 批准号: RGPIN-2020-04015
• 负责人: Marriott, Paul
• 金额: $ 1.97万
• 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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765778
• 关键词: Computational; Information; Geometry; Neuroinformatics

This research is motivated by the conviction that geometry, uniquely, gives us appropriate tools to understand: statistical model choice, the interplay between the statistical and scientific methods, and, especially, the limits to empirical information - all in the context of a given scientific problem. We aim to implement Box's view, where he states 'since all models are wrong the scientist must be alert to what is importantly wrong'. For a given scientific context, we define a 'space of all models' with an appropriate geometric structure. For any working statistical model we search for all small modelling changes which have big effects on the inferential question of interest. Here big and small are calibrated by a combination of data, geometry and scientific context. To understand this, in its full generality, is a highly challenging task, and so we focus on a particular area of Neuroscience where we already have both theoretical and practical expertise. Neurons are cells in the brain, connected in a huge network, which act in a basically binary way, being active or quiet, with the very short timescale activity periods being called spikes. Recent developments in experimental tools enable us to record these spikes across large numbers of neurons and long periods of time. This is a good example of a modern Big Data problem.  For any given scientific problem of interest, the statistician has to make modelling choices during the analysis of such data, and our research is focused on fully understanding the consequences of these choices. Our recent work has shown proof-of-concept of our geometric approach in simple examples, and this research will extend our breakthroughs to real, complex scientific contexts.  It may seem surprising that we use geometry in this statistical context but this use is, in fact, very common.  Euclidean geometry underlies linear regression, much of time series analysis, and many approximation methods used in applied statistics. Classical Information Geometry has generalised this Euclidean geometry to much richer classes of models and in our recent work we have further extended the theory to give a geometry of 'the space of all models' including important boundary and singular points. This gives us all the geometric tools that we need to study model building, sensitivity and uncertainty. Students involved in this research will be exposed to the foundations of statistical thought and its practical application in the context of real and complex scientific problems. They will also gain computational and data-analytic skills and, further, get invaluable experience working with practitioners. This training will fully prepare them for either an academic career or to help fill the, currently huge, demand in Canada for Data Scientists. Furthermore, since this is foundational work, our results will, in the long term, inform the whole discipline of applied statistics in areas far removed from neuroscience.

这项研究的动机是这样一种信念，即几何学独特地给了我们适当的工具来理解：统计模型的选择，统计方法和科学方法之间的相互作用，特别是经验信息的限制--所有这些都是在给定的科学问题的背景下进行的。我们的目标是实现Box的观点，他在其中表示，由于所有模型都是错误的，科学家必须警惕哪些是重要的错误。对于给定的科学背景，我们定义了一个具有适当几何结构的“所有模型的空间”。对于任何有效的统计模型，我们都会搜索对感兴趣的推理问题有重大影响的所有微小的建模变化。在这里，大小是通过数据、几何和科学背景的组合来校准的。要全面理解这一点，是一项极具挑战性的任务，因此我们专注于神经科学的一个特定领域，我们已经拥有理论和实践专业知识。神经元是大脑中的细胞，连接在一个巨大的网络中，它们的行为基本上是二元的，要么活跃，要么安静，非常短的时间尺度活动周期被称为尖峰。实验工具的最新发展使我们能够记录大量神经元和长时间的这些尖峰。这是现代大数据问题的一个很好的例子。对于任何给定的感兴趣的科学问题，统计学家在分析此类数据时必须做出建模选择，而我们的研究重点是充分了解这些选择的后果。我们最近的工作已经用简单的例子证明了我们的几何方法的概念，这项研究将把我们的突破扩展到真实的、复杂的科学背景。我们在这种统计背景下使用几何可能看起来很令人惊讶，但这种使用实际上是非常常见的。欧几里德几何是线性回归、大部分时间序列分析和应用统计学中使用的许多近似方法的基础。经典信息几何将这种欧几里德几何推广到更丰富的模型类别，在我们最近的工作中，我们进一步扩展了这一理论，给出了包括重要边界和奇点在内的“所有模型的空间”的几何。这为我们提供了研究模型构建、敏感性和不确定性所需的所有几何工具。参与这项研究的学生将接触到统计思想的基础及其在真实和复杂的科学问题中的实际应用。他们还将获得计算和数据分析技能，并进一步获得与从业者合作的宝贵经验。这一培训将为他们的学术生涯做好充分准备，或者帮助满足加拿大目前对数据科学家的巨大需求。此外，由于这是基础性的工作，从长远来看，我们的结果将为远离神经科学的领域的应用统计学的整个学科提供信息。