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Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo

机译：使用顺序蒙特卡洛法的非线性动力学系统的概率学习

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摘要

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data. Specifically, we consider learning of probabilistic nonlinear state-space models. There is no closed-form solution available for this problem, implying that we are forced to use approximations. In this tutorial we will provide a self-contained introduction to one of the state-of-the-art methods-the particle Metropolis-Hastings algorithm-which has proven to offer a practical approximation. This is a Monte Carlo based method, where the particle filter is used to guide a Markov chain Monte Carlo method through the parameter space. One of the key merits of the particle Metropolis-Hastings algorithm is that it is guaranteed to converge to the "true solution" under mild assumptions, despite being based on a particle filter with only a finite number of particles. We will also provide a motivating numerical example illustrating the method using a modeling language tailored for sequential Monte Carlo methods. The intention of modeling languages of this kind is to open up the power of sophisticated Monte Carlo methods-including particle Metropolis-Hastings-to a large group of users without requiring them to know all the underlying mathematical details.
机译：概率建模提供了表示和处理数据，模型，预测和决策中的不确定性的能力。我们关注从测量数据中学习动力系统的概率模型的问题。具体来说，我们考虑学习概率非线性状态空间模型。没有针对此问题的封闭式解决方案，这意味着我们被迫使用近似值。在本教程中，我们将对最先进的方法之一（粒子Metropolis-Hastings算法）进行自我介绍，事实证明该算法可以提供实用的近似值。这是基于蒙特卡洛的方法，其中使用了粒子过滤器来引导马尔可夫链蒙特卡洛方法通过参数空间。粒子Metropolis-Hastings算法的主要优点之一是，尽管它是基于仅包含有限数量粒子的粒子过滤器，但在温和的假设下仍可以保证收敛到“真实解”。我们还将提供一个激励性的数值示例，说明使用为顺序蒙特卡洛方法定制的建模语言的方法。对此类语言进行建模的目的是向大量用户开放复杂的蒙特卡洛方法（包括粒子Metropolis-Hastings）的功能，而无需他们知道所有基本的数学细节。

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