Practical Time-Series Modelling for Scientific Data

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，复杂的计算模型、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，使时间序列的推理能够更有原则、更准确、更有效，并应用于现实世界的科学数据集。总体目标将是向研究界提供使用机器学习和(特别是)贝叶斯推理技术对物理和生物系统的数学模型进行参数化的实用指南，在这种情况下，对这些系统的实验询问将产生时间序列数据。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。下面将简要讨论其中的每一个。相关噪声。为简单起见，许多现有的时间序列模型没有考虑噪声的相关性。然而，人们越来越认识到，许多噪声过程是自相关的。尤其令人担忧的是，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。通过扩展以前使用的时间序列模型来捕捉噪声中的相关性，我们打算能够进行更准确的推断，并克服以前观察到的错误结果。型号说明错误。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。我们建议对时间序列的模型偏差检测进行研究，包括重点解释模型偏差对参数推断的影响。这一领域最初将通过使用模型问题的电子实验来探讨，以便在将开发的技术应用于现实世界问题之前，可以控制模型错误指定的程度，并将其影响量化。对可能性的模拟。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非常昂贵。仿真是一种计算策略，它用评估成本更低的函数来近似似然。虽然仿真器可以实现显著的加速，但其准确性仍然令人担忧。我们计划考虑在抽样策略中使用模拟器，通过接受/拒绝步骤纠正这种不准确性，潜在地允许对后验分布进行准确抽样。这种方法与现有复杂的马尔可夫链蒙特卡罗(MCMC)算法相结合所带来的加速比，可能是增加计算密集型科学问题的可处理性的关键。自动选择超参数。MCMC采样算法的行为通常由几个调谐参数(超参数)控制。这些超参数通常对MCMC算法的性能有很大影响，但理想值可能不明显，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，我们考虑了在MCMC超参数配置上最大化某些给定的采样器性能度量(例如，单位时间产生的有效样本)的问题。汇款。该项目属于EPSRC数学科学研究主题。该项目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我们的合作者提供的真实数据上进行测试，这些数据来自约克大学和莫纳什大学化学系以及巴塞尔的罗氏创新中心。

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.