综述深度学习在状态空间模型中的应用，涵盖离散与连续时间建模方法。
Deep Learning-based Approaches for State Space Models: A Selective Review
- 从经典最大似然到变分自编码器，统一梳理神经网络状态空间建模框架。
- 重点分析基于隐变量的深度模型，包括潜在神经微分方程等代表性方法。
- 适合对序列建模、动态系统分析感兴趣的研究人员参考。
状态空间模型（SSMs）为动态系统分析提供强大框架，假设系统的时间演化由潜变量状态决定，进而控制观测值。本文对基于深度神经网络的状态空间模型近期进展进行选择性综述，提出离散时间与连续时间模型（如潜在神经常微分方程和随机微分方程）的统一视角。首先回顾经典基于最大似然的学习方法，接着介绍变分自编码器作为含潜变量神经网络方法的一般学习范式，并详细讨论若干属于SSM框架的代表性深度学习模型。此外，还考察了将SSMs作为独立架构模块提升序列建模效率的最新发展。最后，通过混合频率及非规则间隔时间序列数据的例子，展示SSMs在此类场景中的优势。
原文摘要 · Abstract (English)
State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.
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