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Sequential Monte Carlo: Towards Degeneracy-Free Methods

顺序蒙特卡罗：迈向无简并方法

基本信息

批准号：
EP/I017984/1
负责人：
Adam Johansen
金额：
$ 12.33万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2011
资助国家：
英国
起止时间：
2011 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FI017984%2F1
关键词：
Sequential Monte Carlo Towards Degeneracy

项目摘要

Imperfectly observed evolving systems arise throughout the human world. Weather forecasting, modelling stock prices, transcribing music or interpreting human speech automatically are just a few of the situations in which imperfect observations of a system which evolves in time are all that is available whilst the underlying system is the thing in which we are interested: Given satellite observations and sparse localised measurements, we'd like to accurately characterise the weather now and predict future weather; given measurements of pitch at discrete times we'd like a computer to be able to produce a meaningful description of what was being said at the time.Surprisingly, it's possible to model a great number of these problems using a common framework, known as a state space model (or hidden Markov model). Inferring the likely value of the unobserved process based upon a sequence of observations, as those observations become available is in principle reasonably straightforward but it requires the evaluation of integrals which cannot be solved by analytical mathematics and which are too complex to deal with accurately via simple numerical methods. Simulation-based techniques have been developed to address these problems and are now the most powerful collection of tools for estimating the current state of the unobserved process given all of the observations received so far. Much effort has been dedicated in recent years to designing algorithms to efficiently describe the likely path of the unobserved process from the beginning of the observation sequence up to the current time in a similar way. This problem is much harder as each observation we receive tells us a little more about the likely history of the process and continually updating this ever-longer list of locations in an efficient way is far from simple.The methods proposed here will attempt to extend simulation-based statistical techniques in a new direction which is particularly well suited to characterisation of the whole path of the unobserved process and not just its terminal value. Two different strategies based around the same premise - that sometimes several smaller simulations can in a particular sense outperform a single larger simulation for the same computational cost - will be investigated. The techniques developed will be investigated both theoretically and empirically.In addition to developing and analysing new computational techniques, the project will provide software libraries which simplify the use of these methods in real problems (hopefully to the extent that scientists who are expert in particular application domains will be able to apply the techniques directly to their own problems).The research could be considered successful if:1/ It leads to new methods for performing inference in state space models.2/ These methods can be implemented with less application-specific tuning that existing methods require or these methods provide more efficient use of computational resources.3/ These methods are sufficiently powerful to allow the use of more complex models than are currently practical.4/ The methods are adopted by practitioners in at least some of the many areas in which these techniques might be usefully employed.The long term benefits could include more realistic assessment of risk in financial systems, more reliable tracking and prediction of meteorological phenomena and improved technological products wherever there is a need to dynamically incorporate knowledge arising from measurements as they become available. There will be particular advantages in settings in which the full path of the imperfectly observed underlying process is of interest but there is scope for improvement even when this is not the case.

不完全观察的进化系统出现在整个人类世界。天气预报、模拟股票价格、转录音乐或自动翻译人类语言只是其中的几种情况，在这种情况下，对一个随时间演变的系统的不完美观测是所有可用的，而底层系统是我们感兴趣的东西：给定卫星观测和稀疏的局部测量，我们希望准确地预测现在的天气并预测未来的天气;我们希望计算机能够对当时所说的话进行有意义的描述。令人惊讶的是，可以使用一个通用的框架来建模大量的这些问题，称为状态空间模型（或隐马尔可夫模型）。根据一系列观测结果推断未观测到的过程的可能值，因为这些观测结果变得可用，原则上相当简单，但它需要评估积分，这些积分无法通过分析数学解决，并且过于复杂，无法通过简单的数值方法准确处理。基于模拟的技术已经开发出来，以解决这些问题，现在是最强大的工具，估计目前的状态，未观察到的过程中所收到的所有意见，到目前为止。近年来，许多努力致力于设计算法，以有效地描述未观察到的过程的可能路径，从观察序列的开始到当前时间以类似的方式。这个问题要困难得多，因为我们收到的每一个观察都告诉我们更多关于这个过程的可能历史，并且以有效的方式不断更新这个越来越长的位置列表远非简单。在一个新的方向，这是特别适合于未观察到的过程，而不仅仅是其终端的整个路径的特征统计技术值两种不同的策略基于相同的前提-有时几个较小的模拟可以在特定意义上优于一个单一的较大的模拟相同的计算成本-将进行调查。将从理论和经验两方面研究所开发的技术，除了开发和分析新的计算技术外，该项目还将提供软件库，简化这些方法在真实的问题中的使用（希望在特定应用领域的专家能够将这些技术直接应用于他们自己的问题）。如果符合以下条件，研究可以被认为是成功的：1/它导致了在状态空间模型中执行推理的新方法。2/这些方法可以通过现有方法所需的更少的特定于应用程序的调优来实现，或者这些方法提供了对计算资源的更有效的使用。3/这些方法足够强大，可以使用比当前实际更复杂的模型。4/这些方法至少在一些领域被从业者采用，这些技术可能会被有效地使用。长期的好处可能包括对金融系统的风险进行更现实的评估，更可靠地跟踪和预测气象现象，并改进技术产品，只要有必要动态地纳入从测量中获得的知识，变得可用。在不完全观察的基础过程的完整路径是感兴趣的但即使不是这种情况也有改进的余地的设置中，将有特别的优势。