# Spectral learning of Bernoulli linear dynamical systems models

arXiv: https://arxiv.org/abs/2303.02060 · HTML: https://mlsanity.com/paper/2303.02060/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 64 references that are in the map.
- First posted on arXiv 3 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Learning Linear Dynamical Systems via Spectral Filtering](https://mlsanity.com/paper/1711.00946/) (2017)
- [Spectral Filtering for General Linear Dynamical Systems](https://mlsanity.com/paper/1802.03981/) (2018)
- [Tree-Structured Recurrent Switching Linear Dynamical Systems for Multi-Scale Modeling](https://mlsanity.com/paper/1811.12386/) (2018)
- [Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics](https://mlsanity.com/paper/2206.02972/) (2022)
- [Task-Optimal Exploration in Linear Dynamical Systems](https://mlsanity.com/paper/2102.05214/) (2021)
- [Experimental Design for Regret Minimization in Linear Bandits](https://mlsanity.com/paper/2011.00576/) (2020)
- [Poisson--Gamma Dynamical Systems](https://mlsanity.com/paper/1701.05573/) (2017)
- [A Linear Dynamical System Model for Text](https://mlsanity.com/paper/1502.04081/) (2015)
- [Extracting low-dimensional dynamics from multiple large-scale neural population recordings by learning to predict correlations](https://mlsanity.com/paper/1711.01847/) (2017)
- [Bayesian Inference in High-Dimensional Time-Serieswith the Orthogonal Stochastic Linear Mixing Model](https://mlsanity.com/paper/2106.13379/) (2021)

## Abstract (arXiv)

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.