Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve according to simple locally linear dynamics. However, existing methods for latent variable estimation are not robust to dynamical noise and system nonlinearity due to noise-sensitive inference procedures and limited model formulations. This can lead to inconsistent results on signals with similar dynamics, limiting the model's ability to provide scientific insight. In this work, we address these limitations and propose a probabilistic approach to latent variable estimation in decomposed models that improves robustness against dynamical noise. Additionally, we introduce an extended latent dynamics model to improve robustness against system nonlinearities. We evaluate our approach on several synthetic dynamical systems, including an empirically-derived brain-computer interface experiment, and demonstrate more accurate latent variable inference in nonlinear systems with diverse noise conditions. Furthermore, we apply our method to a real-world clinical neurophysiology dataset, illustrating the ability to identify interpretable and coherent structure where previous models cannot.

翻译：时变线性状态空间模型是获取神经信号数学可解释表示的强大工具。例如，切换模型和分解模型通过遵循简单局部线性动态演化的潜变量来描述复杂系统。然而，由于现有潜变量估计方法对噪声敏感的推断过程和有限的模型表达形式，其对于动态噪声和系统非线性缺乏鲁棒性。这可能导致对具有相似动态特性的信号产生不一致的结果，从而限制了模型提供科学洞察的能力。在本工作中，我们针对这些局限性提出了一种概率化方法，用于分解模型中的潜变量估计，以提升对动态噪声的鲁棒性。此外，我们引入了一种扩展的潜动态模型，以增强对系统非线性的稳健性。我们在多个合成动态系统（包括一个经验导出的脑机接口实验）上评估了所提出的方法，并证明了在具有不同噪声条件的非线性系统中能实现更准确的潜变量推断。进一步地，我们将该方法应用于真实世界的临床神经生理学数据集，展示了在先前模型无法识别的情况下发现可解释且连贯结构的能力。