论文标题
复发性神经网络和贝叶斯过滤器的通用近似
Recurrent Neural Networks and Universal Approximation of Bayesian Filters
论文作者
论文摘要
我们考虑贝叶斯最佳过滤问题：即，从观察序列估算潜在时间序列信号的某些条件统计。经典方法通常依赖于假定或估计的过渡和观察模型的使用。取而代之的是，我们制定了一个通用的经常性神经网络框架，并试图直接学习从观测输入到所需估计量统计数据的递归映射。本文的主要重点是该框架的近似功能。我们为在一般的非压缩域中过滤提供近似误差界。我们还考虑强大的时均匀近似误差界限，以确保长期表现良好。我们讨论并说明了这些结果的许多实际问题和含义。
We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and observation models. Instead, we formulate a generic recurrent neural network framework and seek to learn directly a recursive mapping from observational inputs to the desired estimator statistics. The main focus of this article is the approximation capabilities of this framework. We provide approximation error bounds for filtering in general non-compact domains. We also consider strong time-uniform approximation error bounds that guarantee good long-time performance. We discuss and illustrate a number of practical concerns and implications of these results.
