Learning Mixtures of Linear Dynamical Systems via Hybrid Tensor-EM Method.

Area of Science:

• Computational Neuroscience
• Machine Learning
• Time-Series Analysis

Background:

• Mixtures of Linear Dynamical Systems (MoLDS) model diverse temporal dynamics but struggle with noisy, complex neural data.
• Existing tensor methods offer identifiability but degrade under noise, while Expectation-Maximization (EM) methods are sensitive to initialization.

Purpose of the Study:

• To develop a robust and identifiable method for learning MoLDS from complex, noisy time-series data, specifically for neural data analysis.
• To combine the global identifiability of tensor methods with the flexibility of EM algorithms for improved MoLDS learning.

Main Methods:

• Proposed a novel tensor-based method (Tensor-EM) for MoLDS learning, constructing moment tensors from input-output data for consistent parameter estimation.
• Integrated tensor-based identifiability with a Kalman EM algorithm featuring closed-form updates for refined parameter estimation.
• Validated the framework on synthetic datasets and real-world neural recordings from primate somatosensory cortex during reaching tasks.

Main Results:

• Tensor-EM demonstrated superior reliability and robustness in parameter recovery on synthetic data compared to pure tensor or randomly initialized EM methods.
• The method successfully modeled and clustered distinct experimental conditions in neural data as separate subsystems.
• Applied to sequential reaching tasks, MoLDS effectively modeled complex neural dynamics, showcasing Tensor-EM's reliability for neural data analysis.

Conclusions:

• MoLDS offers an effective framework for modeling complex neural data with diverse dynamics.
• Tensor-EM provides a reliable and robust approach to MoLDS learning, overcoming limitations of existing methods for neural data applications.