用神经网络学习粒子滤波中的状态与提议分布，提升非线性场景下隐藏状态恢复精度。
Learning state and proposal dynamics in state-space models using differentiable particle filters and neural networks
- 用双神经网络拟合粒子滤波的转移和提议分布，均以高斯混合模型表示。
- 在高度非线性场景中，隐藏状态恢复效果显著优于现有方法。
- 仅需观测序列即可训练，兼具状态空间模型可解释性与神经网络灵活性。
状态空间模型是分析序列数据的常用统计框架。在此框架中，粒子滤波常用于对非线性状态空间模型进行推断。本文提出新方法 StateMixNN，利用一对神经网络学习粒子滤波的提议分布和转移分布，两者均通过多变量高斯混合模型近似，其分量均值与协方差作为可学习函数的输出。该方法以最大化对数似然为目标进行训练，仅需观测序列，融合了状态空间模型的可解释性与人工神经网络的灵活性和逼近能力。相比现有最优方法，该方法显著提升了隐藏状态的恢复效果，尤其在高度非线性场景中表现更优。
原文摘要 · Abstract (English)
State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that uses a pair of neural networks to learn the proposal distribution and transition distribution of a particle filter. Both distributions are approximated using multivariate Gaussian mixtures. The component means and covariances of these mixtures are learnt as outputs of learned functions. Our method is trained targeting the log-likelihood, thereby requiring only the observation series, and combines the interpretability of state-space models with the flexibility and approximation power of artificial neural networks. The proposed method significantly improves recovery of the hidden state in comparison with the state-of-the-art, showing greater improvement in highly non-linear scenarios.
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