State Space Models with Dynamical and Sparse Variances, and Inference by EM Message Passing
State Space Models with Dynamical and Sparse Variances, and Inference by EM Message Passing
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具有动态和稀疏方差的状态空间模型以及通过 EM 消息传递进行的推理
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发表时间：
2019
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通讯作者：
Hans
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作者：
Federico Wadehn;Thilo Weber;Hans
稀疏贝叶斯学习（SBL）是一种概率估计方法，基于用方差未知的正态表示稀疏提升先验。这种表示与线性高斯状态空间模型（SSM）很好地融合在一起。然而，在经典的SBL中，未知方差是先验独立的，这不适合于建模组稀疏信号，或方差具有结构的信号。为了对信号进行建模，例如，指数衰减或piecewisconstant（特别是块稀疏）的方差，我们提出了SSM与动态和稀疏方差（SSM-DSV）。这些是两层SSM，其中底层模拟物理信号，顶层模拟受到突然变化的动态变化。在这些层次模型中的推理和学习是用期望最大化（EM）算法的消息传递版本来执行的，该算法是更一般的变分消息传递算法的特殊实例。我们验证了所提出的模型和估计算法与两个应用程序，使用模拟和真实的数据。首先，我们实现了一个块离群不敏感的卡尔曼平滑建模的干扰过程与SSM-DSV。其次，我们使用SSM-DSV来建模眼动系统，并采用EM消息传递来估计来自眼睛位置数据的神经控制器信号。
Sparse Bayesian learning (SBL) is a probabilistic approach to estimation problems based on representing sparsitypromoting priors by Normals with Unknown Variances. This representation blends well with linear Gaussian state space models (SSMs). However, in classical SBL the unknown variances are a priori independent, which is not suited for modeling group sparse signals, or signals whose variances have structure. To model signals with, e.g., exponentially decaying or piecewiseconstant (in particular block-sparse) variances, we propose SSMs with dynamical and sparse variances (SSM-DSV). These are two-layer SSMs, where the bottom layer models physical signals, and the top layer models dynamical variances that are subject to abrupt changes. Inference and learning in these hierarchical models is performed with a message passing version of the expectation maximization (EM) algorithm, which is a special instance of the more general class of variational message passing algorithms. We validated the proposed model and estimation algorithm with two applications, using both simulated and real data. First, we implemented a block-outlier insensitive Kalman smoother by modeling the disturbance process with a SSM-DSV. Second, we used SSM-DSV to model the oculomotor system and employed EM-message passing for estimating neural controller signals from eye position data.