Latent linear dynamical systems with Bernoulli observations provide a powerful modeling framework for identifying the temporal dynamics underlying binary time series data, which arise in a variety of contexts such as binary decision-making and discrete stochastic processes such as binned neural spike trains. Here, we develop a spectral learning method for fast, efficient fitting of Bernoulli latent linear dynamical system (LDS) models. Our approach extends traditional subspace identification methods to the Bernoulli setting via a transformation of the first and second sample moments. This results in a robust, fixed-cost estimator that avoids the hazards of local optima and the long computation time of iterative fitting procedures like the expectation-maximization (EM) algorithm. In regimes where data is limited or assumptions about the statistical structure of the data are not met, we demonstrate that the spectral estimate provides a good initialization for Laplace-EM fitting. Finally, we show that the estimator provides substantial benefits to real world settings by analyzing data from mice performing a sensory decision-making task.

翻译：伯努利观测下的潜在线性动态系统为识别二元时间序列数据中的时间动态提供了强大的建模框架，这类数据出现在多种场景中，例如二元决策过程以及离散随机过程（如分箱处理的神经脉冲序列）。本文提出了一种谱学习方法，用于快速高效地拟合伯努利潜在线性动态系统（LDS）模型。该方法通过变换一阶和二阶样本矩，将传统子空间辨识方法扩展到伯努利框架中，从而得到鲁棒且计算成本固定的估计器，避免了局部最优陷阱以及期望最大化（EM）算法等迭代拟合过程所需的长时间计算。在数据有限或数据的统计结构假设不成立的情况下，我们证明谱估计能为拉普拉斯-EM拟合提供良好的初始值。最后，通过分析小鼠执行感觉决策任务的数据，我们展示了该估计器在实际场景中的显著优势。