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，复杂的计算建模、贝叶斯技术和机器学习被用于分析时间序列。在这个项目中，我们考虑了几个研究方向，这些方向可以使时间序列的推理更有原则，更准确，更有效，并应用于现实世界的科学数据集。总体目标将是为研究界提供一个实用的指南，以使用机器学习和（特别是）贝叶斯推理技术在物理和生物系统的数学模型参数化中，这些系统的实验询问结果是时间序列数据。我们已经确定了一系列主题（来自我们小组以前的研究），这些主题将形成这个项目的初步方向。下面将简要讨论其中的每一个。相关噪声。为简便起见，许多现有的时间序列模型没有考虑噪声的相关性。然而，越来越多的人认识到许多噪声过程是自相关的。特别令人担忧的是，简化噪声中无相关性的假设可能导致参数推断中不确定性的低估。通过扩展以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以前观察到的错误结果。misspecification模型。用于时间序列数据的模型通常是错误指定的，通常是由于对系统的不完全理解。我们建议研究时间序列模型差异的检测，包括重点解释模型差异对参数推断的影响。在将开发的技术应用于现实世界问题之前，将首先通过使用模型问题的计算机实验来接近该领域，以便可以控制模型错误规格的程度，并对其影响进行量化。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，它用一个计算成本更低的函数来近似可能性。尽管仿真器可以实现显著的加速，但对其准确性的担忧仍然存在。我们计划考虑在采样策略中使用模拟器，该策略通过接受/拒绝步骤来纠正这种不准确性，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，结合现有的复杂的马尔可夫链蒙特卡罗（MCMC）算法，可能是提高计算密集型科学问题可追溯性的关键。自动选择超参数。MCMC采样算法的行为通常由几个调优参数（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，通过该方法可以设置调优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采样器性能的某些给定度量（例如每单位时间生成的有效样本）的问题。的职责。该项目属于EPSRC数学科学研究主题。该项目涵盖的特定研究领域包括人工智能技术、数学生物学、统计学和应用概率论。涉及的公司和合作者。我们在约克大学和莫纳什大学化学系以及巴塞尔罗氏创新中心的合作伙伴将对所有理论上开发的方法进行实际数据测试。

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.