Learning stable, regularised latent models of neural population dynamics.

Area of Science:

• Computational Neuroscience
• Systems Neuroscience
• Machine Learning for Neuroscience

Background:

• Simultaneous recordings of large neuronal populations are becoming common, necessitating advanced statistical models.
• Latent population models like linear dynamical systems (LDS) effectively capture neural data structure but face challenges with stability and temporal continuity.
• Existing LDS models often produce biologically implausible unstable dynamics when trained on realistic datasets, hindering applications like brain-machine interfaces (BMI).

Purpose of the Study:

• To propose a novel expectation-maximization-based method for learning stable LDS models from neural population recordings.
• To ensure learned LDS models reflect true temporal continuity and avoid unstable dynamics.
• To improve the statistical description and stability of LDS models, particularly when limited training data is available.

Main Methods:

• Developed an expectation-maximization (EM) algorithm for fitting LDS models.
• Incorporated parameter constraints to guarantee system stability.
• Utilized regularization techniques to promote the capture of temporal structure in the neural data.

Main Results:

• The proposed method yields LDS parameter estimates that guarantee stable dynamics.
• When trained on limited data, the method provides a substantially better statistical description of neural activity compared to alternatives.
• Demonstrated effectiveness using both synthetic datasets and real multi-electrode recordings from the motor cortex.

Conclusions:

• The novel EM-based method effectively learns stable and temporally accurate LDS models for neural population activity.
• This approach overcomes limitations of traditional LDS models, offering improved performance with limited data.
• The developed technique is a valuable tool for analyzing complex neural dynamics and advancing brain-machine interface algorithms.