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 (e.g., binned neural spike trains). Here we develop a spectral learning method for fast, efficient fitting of probit-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：带有伯努利观测的潜在线性动态系统为识别二元时间序列数据背后的时间动态提供了强大的建模框架，这类数据出现在多种情境中，例如二元决策和离散随机过程（如分箱的神经脉冲序列）。本文开发了一种谱学习方法，用于快速、高效地拟合计分-伯努利潜在线性动态系统（LDS）模型。我们的方法通过一阶和二阶样本矩的变换，将传统的子空间识别方法扩展到伯努利设定下。这产生了一种鲁棒、固定成本的估计器，避免了局部最优的陷阱，也避免了期望最大化（EM）算法等迭代拟合过程的长时间计算。在数据有限或关于数据统计结构的假设不满足的情况下，我们证明谱估计为拉普拉斯-EM拟合提供了良好的初始化。最后，通过分析小鼠执行感觉决策任务的数据，我们展示该估计器为现实世界场景带来了显著益处。