Practical Time-Series Modelling for Scientific Data

科学数据的实用时间序列建模

• 批准号: 2285274
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2285274
• 关键词: Practical; Time; Series; Modelling; Scientific

The analysis of time-series data is central to many scientific domains, such as electrochemistry, cardiac electrophysiology, and pharmacokinetics. In these and other fields, sophisticated computational modelling, Bayesian techniques, and machine learning are employed for the analysis of time-series. In this project, we consider several research directions which enable more principled, accurate, and efficient inference for time-series, with application to real-world scientific datasets. The overarching goal will be to provide to the research community a practical guide to the use of machine learning and (particularly) Bayesian Inference techniques in the parameterization of mathematical models of physical and biological systems, where the experimental interrogation of those systems results in time series data. We have identified a range of topics (arising from previous research in our group) that will form the initial directions of this project. Each of these is discussed briefly below.Correlated noise. For simplicity, many existing time-series models do not consider correlation of noise. However, it is increasingly recognised that many noise processes are autocorrelated. Particularly worrying is that the simplifying assumption of no correlation in the noise can lead to underestimation of uncertainty in parameter inference. By extending previously used time-series models to capture correlation in the noise, we intend to enable more accurate inference and overcome previously observed erroneous results. Model misspecification. Models used for time-series data are often misspecified, usually due to an incomplete understanding of the system. We propose to investigate the detection of model discrepancy for time-series, including a focus on explaining the effects of model discrepancy on parameter inference. This area will be approached initially through in silico experiments using model problems so that the degree of model misspecification can be controlled, and its effects quantified, before applying the techniques developed to real-world problems. Emulation of the likelihood. In many scientific applications, computational cost is a major bottleneck - in particular, evaluation of the likelihood can be highly costly. Emulation is a computational strategy which approximates the likelihood with a function that is cheaper to evaluate. Although emulators can enable significant speedups, concerns remain over their accuracy. We plan to consider using emulators within a sampling strategy that corrects for this inaccuracy via an accept/reject step potentially allowing exact sampling of a posterior distribution. The speedup enabled by this approach, combined with existing sophisticated Markov Chain Monte Carlo (MCMC) algorithms, could be key to increasing the tractability of computationally intensive scientific problems.Automated selection of hyperparameters. The behaviour of MCMC sampling algorithms is typically governed by several tuning parameters (hyperparameters). These hyperparameters typically have a drastic effect on the performance of MCMC algorithms, but the ideal values may not be obvious and may vary from problem to problem. We propose to develop machine learning methods by which tuning parameters can be set to obtain optimal performance. For example, we consider the problem of maximizing some given metric of sampler performance (such as effective samples generated per unit of time) over MCMC hyperparameter configurations. Remit. This project falls within the EPSRC Mathematical Sciences research theme. The particular research areas covered by this project include Artificial Intelligence Technologies, Mathematical Biology, and Statistics and Applied Probability.Companies and collaborators involved. All theoretically developed approaches will be tested on real-world data provided by our collaborators at in the Chemistry Departments at York and Monash University, and at the Roche Innovation Center in Basel.

时间序列数据的分析是许多科学领域的核心，如电化学，心脏电生理学和药代动力学。在这些和其他领域，复杂的计算建模，贝叶斯技术和机器学习被用于时间序列的分析。在这个项目中，我们考虑了几个研究方向，这些方向可以为时间序列提供更有原则，更准确和更有效的推理，并应用于现实世界的科学数据集。总体目标是为研究界提供一个实用指南，指导在物理和生物系统的数学模型参数化中使用机器学习和（特别是）贝叶斯推理技术，其中对这些系统的实验询问导致时间序列数据。我们已经确定了一系列主题（来自我们小组以前的研究），这些主题将构成本项目的初始方向。下面将对每一种噪声进行简要讨论。为了简单起见，许多现有的时间序列模型不考虑噪声的相关性。然而，人们越来越认识到，许多噪声过程是自相关的。特别令人担忧的是，噪声中没有相关性的简化假设可能会导致低估参数推断中的不确定性。通过扩展先前使用的时间序列模型来捕获噪声中的相关性，我们打算实现更准确的推断并克服先前观察到的错误结果。模型规格错误。用于时间序列数据的模型经常被错误指定，通常是由于对系统的不完全理解。我们建议调查的检测模型差异的时间序列，包括专注于解释模型差异对参数推断的影响。这一领域将首先通过使用模型问题的计算机实验来处理，以便在将开发的技术应用于现实世界的问题之前，可以控制模型错误指定的程度，并量化其影响。模拟可能性。在许多科学应用中，计算成本是一个主要的瓶颈-特别是，可能性的评估可能是非常昂贵的。仿真是一种计算策略，它用一个更便宜的函数来近似可能性。虽然仿真器可以显著提高速度，但人们仍然担心它们的准确性。我们计划考虑在采样策略中使用仿真器，通过接受/拒绝步骤纠正这种不准确性，从而可能允许对后验分布进行精确采样。通过这种方法实现的加速，与现有的复杂的马尔可夫链蒙特卡罗（MCMC）算法相结合，可能是提高计算密集型科学问题的易处理性的关键。MCMC采样算法的行为通常由几个调整参数（超参数）控制。这些超参数通常会对MCMC算法的性能产生巨大影响，但理想值可能并不明显，并且可能因问题而异。我们建议开发机器学习方法，通过这些方法可以设置调整参数以获得最佳性能。例如，我们考虑在MCMC超参数配置上最大化一些给定的采样器性能度量（例如每单位时间生成的有效样本）的问题。汇款该项目属于EPSRC数学科学研究主题的福尔斯。该项目所涉及的具体研究领域包括人工智能技术、数学生物学、统计学和应用概率。所有理论上开发的方法都将在约克和莫纳什大学化学系以及巴塞尔罗氏创新中心的合作者提供的真实数据上进行测试。