State space models have been extensively applied to model and control dynamical systems in disciplines including neuroscience, target tracking, and audio processing. A common modeling assumption is that both the state and data noise are Gaussian because it simplifies the estimation of the system's state and model parameters. However, in many real-world scenarios where the noise is heavy-tailed or includes outliers, this assumption does not hold, and the performance of the model degrades. In this paper, we present a new approximate inference algorithm for state space models with Laplace-distributed multivariate data that is robust to a wide range of non-Gaussian noise. Exact inference is combined with an expectation propagation algorithm, leading to filtering and smoothing that outperforms existing approximate inference methods for Laplace-distributed data, while retaining a fast speed similar to the Kalman filter. Further, we present a maximum posterior expectation-maximization (EM) algorithm that learns the parameters of the model in an unsupervised way, automatically avoids over-fitting the data, and provides better model estimation than existing methods for the Gaussian model. The quality of the inference and learning algorithms are exemplified through a diverse set of experiments and an application to non-linear tracking of audio frequency.

中文翻译：

---

拉普拉斯噪声状态空间模型的近似推理与学习


状态空间模型已广泛应用于神经科学、目标跟踪和音频处理等学科的动态系统建模和控制。常见的建模假设是状态和数据噪声都是高斯分布，因为它简化了系统状态和模型参数的估计。然而，在许多现实场景中，噪声是重尾或包含异常值，这一假设不成立，并且模型的性能会下降。在本文中，我们提出了一种用于具有拉普拉斯分布多元数据的状态空间模型的新近似推理算法，该算法对各种非高斯噪声具有鲁棒性。精确推理与期望传播算法相结合，使得过滤和平滑效果优于拉普拉斯分布数据的现有近似推理方法，同时保持类似于卡尔曼滤波器的快速速度。此外，我们提出了一种最大后验期望最大化（EM）算法，该算法以无监督的方式学习模型的参数，自动避免过度拟合数据，并提供比现有高斯模型方法更好的模型估计。推理和学习算法的质量通过一系列不同的实验和音频非线性跟踪的应用得到了例证。