Unparameterised multi-modal data, high order signatures, and the mathematics of data science

我们的祖先通过在洞穴墙壁上抓挠来交流，通过观察星星来做出导航决定，通过倾听病人的声音来做出医疗诊断。这些简单的数据流中捕获了大量的信息;我们基于信息捕获、处理和决定行动的能力遍及人类生活的各个方面。今天，人们面临着同样的挑战，但信息量要大得多，对结果的期望也要高得多。当我们用手指在iPhone上写字时，当我们的声音被记录下来供医生评估我们的情绪时，当视频被分析为异常行为时，或者当望远镜深入星系寻找黑洞、恒星、行星时，技术复杂的系统将连续的数据流转换成可以处理和识别的模式。2我们相对较新的将数据分析卸载到大规模数字系统上的能力正在改变我们的世界。然而，巨大的挑战依然存在。突破性的数学创新正在迅速扩大我们在一个领域的理解深度。该项目旨在建立在成功的试点合作基础上，创建真正将这种新数学与现有数据科学融合的工具，然后将其应用于范例挑战，以产生更有效的“捕获，处理和决策”过程的抽象。现在的证据是压倒性的，降维和高阶方法可以非常有效地捕获序列数据。数学基础提供了关键的一步，导致牛顿的微积分超越伊藤理论的延伸到粗糙的道路;它的数学表达，水流的特征，显著增强了深度学习方法，以开发具有最先进水平的在线手写识别。这个项目的目标是开发和嵌入围绕粗糙路径和复杂流数据的抽象数学到一些最富有挑战性的是“捕获、处理和决定”任务。研究人员和世界领先的项目合作伙伴通过共同的挑战来改善这项任务，这些挑战涉及四种背景下的重要复杂数据集：* 健康 * 人类界面 * 人类行为 * 观察宇宙我们开始的具体基本挑战是：1）使用面部，语音数据，以及其他自我报告的情绪数据，以更好地检测支持精神疾病患者的干预措施是否有效。2)当一个人用手指在卫星导航设备或移动的电话上书写（中文）时，为了更好地将这个信号准确和经济地转录成数字字符，并识别是谁写的。3）通过观察视频数据中不断变化的图像，开发可以对人类行为进行分类的工具。4)开发测量仪器和天文数据的非线性处理技术，以提高瞬态探测灵敏度，并进行新的观测，例如对绕恒星运行的行星进行观测。这个项目是一个近乎独特的机会，将这些结合在一起，产生一个有效的共同方法，并创造大量的交叉施肥。最近的一个例子值得强调。2013年，本·格雷厄姆（当时的沃里克大学，现在的Facebook）使用该签名来简单有效地量化中国手写字符的笔画。捕获阶段非常微妙，大大提高了识别过程的准确性;该项目的中国合作伙伴随后创建了一个应用程序，该应用程序已被下载数百万次。虽然粗糙路径的手写上下文定义得非常好，而且很成功，但理解视频中的人的动作仍处于成功的早期阶段！这些背景显然是相关的，并通过面部与心理健康挑战联系起来，并通过天文学中的瞬变与遮挡联系起来。全都连在一起了！

Our ancestors communicated by scratching on the walls of caves, took navigational decisions by looking at the stars and made medical diagnoses simply by listening to patients. A great deal of information is captured in these simple data streams; our ability to capture, process, and decide actions based on information pervades all aspects of human life.Today, one has the same challenges but the information is much more voluminous and the expectations for the outcomes far higher. When we write using our finger on an iphone, as our voice is recorded for doctors to assess our mood, when video is analysed for abnormal actions, or as telescopes look deep into the galaxies for black holes, stars, planets,... technically sophisticated systems translate streams of sequential data into processed and recognised patterns that can be actioned.Our relatively new ability to offload data analysis onto massive digital systems is transforming our world. However huge challenges remain. Groundbreaking mathematical innovation is rapidly expanding our depth of understanding in one area. This project aims to build on successful pilot collaborations to create tools that really merge this new maths with the existing data science, and then apply them to exemplar challenges to produce a more effective abstraction of the "capture, process, and decide" process. The evidence is now overwhelming that dimension reduction and high order methods can capture sequential data very effectively. The maths underpinning this provided the crucial step that resulted in the extension of Newton's calculus beyond Itô's theory to rough paths; its mathematical articulation, the signature of a stream, has significantly enhanced deep learning methods to develop online handwriting recognition with state-of-the-art accuracy.This project has the goal of developing and embedding the abstract mathematics around rough paths and complex streamed data into a few of the richest challenges involved in the "capture, process, and decide" task. The investigators and the world-leading project partners are connected by the shared challenge of improving this task with complex datasets of importance in four contexts:* Health* Human interfaces* Human Actions* Observing the UniverseThe specific base challenges we start from are:1) Use face, speech data, with other self-reported mood data to better detect when an intervention to support someone with mental illness is or is not working. 2) When a person writes (in Chinese) with their finger on a sat-nav device or mobile phone, to better transcribe this signal into digital characters accurately and economically, and to recognise who wrote it. 3) By observing evolving images in video data, develop tools that can classify the human actions. 4) Develop measurement instruments, and nonlinear processing techniques for astronomical data that improve detection sensitivity for transients and make new observations, e.g. for planets orbiting stars.The technical challenges are deeply interconnected. This project is a near unique opportunity to bring these together to produce a validated common methodology, and to create substantial cross-fertilization. One recent example of how this can happen is worth highlighting. In 2013, Ben Graham (then University of Warwick, now Facebook) used the signature to quantify strokes from Chinese hand-written characters parsimoniously and efficiently. The capture stage is subtle and has appreciably improved the accuracy of the recognition process; the China-based partners on this project subsequently created an app which has been downloaded millions of times.While the handwriting context for rough paths is very well defined and successful, understanding motion of people in videos is at a successful but early stage! The contexts are clearly related, and link through faces with the mental health challenge, and through occlusion with transients in astronomy. It is all joined up!