Spectral learning of Bernoulli linear dynamical systems models.

Area of Science:

• Computational neuroscience
• Machine learning
• Time series analysis

Background:

• Latent linear dynamical systems (LDS) are crucial for modeling temporal dynamics in binary time series data.
• Binary data is prevalent in decision-making and neural activity (e.g., binned spike trains).
• Existing methods like Expectation-Maximization (EM) can be computationally intensive and prone to local optima.

Purpose of the Study:

• To develop a fast and efficient spectral learning method for probit-Bernoulli LDS models.
• To provide a robust, fixed-cost estimation technique for binary time series.
• To offer an alternative to iterative fitting procedures.

Main Methods:

• Extended traditional subspace identification methods to the Bernoulli setting.
• Utilized a transformation of the first and second sample moments.
• Developed a spectral learning approach for probit-Bernoulli LDS model fitting.

Main Results:

• The spectral learning method provides fast and efficient fitting of probit-Bernoulli LDS models.
• The method is robust, has a fixed computational cost, and avoids local optima.
• Spectral estimates serve as effective initializations for Laplace-EM fitting, especially with limited data.
• Demonstrated practical benefits using data from a mouse sensory decision-making task.

Conclusions:

• The proposed spectral learning method offers a significant advancement for analyzing binary time series data.
• This approach provides a computationally efficient and robust alternative to existing methods.
• The technique has broad applicability in neuroscience and other fields dealing with binary temporal data.