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Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution

机译：具有高度信息量的观测值学习状态空间模型：缓和的顺序蒙特卡洛解决方案

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摘要

Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems. Some problems of this type that were previously intractable can now be solved on standard personal computers thanks to recent advances in Monte Carlo methods. In particular, for learning of unknown parameters in nonlinear state-space models, methods based on the particle filter (a Monte Carlo method) have proven very useful. A notoriously challenging problem, however, still occurs when the observations in the state-space model are highly informative, i.e. when there is very little or no measurement noise present, relative to the amount of process noise. The particle filter will then struggle in estimating one of the basic components for probabilistic learning, namely the likelihood p(data|parameters). To this end we suggest an algorithm which initially assumes that there is substantial amount of artificial measurement noise present. The variance of this noise is sequentially decreased in an adaptive fashion such that we, in the end, recover the original problem or possibly a very close approximation of it. The main component in our algorithm is a sequential Monte Carlo (SMC) sampler, which gives our proposed method a clear resemblance to the SMC2 method. Another natural link is also made to the ideas underlying the approximate Bayesian computation (ABC). We illustrate it with numerical examples, and in particular show promising results for a challenging Wiener-Hammerstein benchmark problem.
机译：概率（或贝叶斯）建模和学习为使用概率论系统地表示不确定性提供了有趣的可能性。但是，概率学习通常会导致计算难题。得益于蒙特卡洛方法的最新进展，以前可以解决的某些此类问题现在可以在标准个人计算机上解决。特别是，对于学习非线性状态空间模型中的未知参数，已证明基于粒子滤波器的方法（蒙特卡洛方法）非常有用。但是，当状态空间模型中的观测值具有很高的信息性时，即相对于过程噪声量而言，几乎没有测量噪声或没有测量噪声存在时，仍然会发生一个极具挑战性的问题。然后，粒子滤波器将努力估计概率学习的基本成分之一，即似然性p（data）。为此，我们建议一种算法，该算法最初假定存在大量的人工测量噪声。该噪声的方差以自适应方式依次减小，从而最终使我们恢复了原始问题或可能非常接近该问题。我们算法的主要组成部分是顺序蒙特卡罗（SMC）采样器，它使我们提出的方法与SMC2方法非常相似。另一个自然联系也与近似贝叶斯计算（ABC）的思想联系在一起。我们通过数值示例对其进行说明，尤其是对于有挑战性的Wiener-Hammerstein基准问题显示出令人鼓舞的结果。

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