Exactly solvable statistical physics models for large neuronal populations

Area of Science:

• Computational Neuroscience
• Statistical Physics
• Systems Neuroscience

Background:

• Maximum-entropy methods link neural activity measurements to statistical physics models.
• Traditional methods are effective for small neural populations (N~100).
• Scaling to larger populations (N~1500) introduces an undersampled regime requiring careful observable selection.

Purpose of the Study:

• To develop a principled approach for constructing maximum-entropy models in the undersampled regime.
• To introduce and apply the "minimax entropy" principle for selecting optimal observables.
• To analyze large-scale neural activity in the mouse hippocampus.

Main Methods:

• Formulated a "minimax entropy" principle to select observables that maximally reduce entropy.
• Restricted model construction to tree-like correlations among neuron pairs for tractability.
• Developed an efficient algorithm to find the optimal tree structure.
• Applied the method to analyze neural recordings from ~1500 mouse hippocampal neurons.

Main Results:

• The minimax entropy principle provides an efficient method for model construction in large neural populations.
• The tree-based approach allows for exact solutions of the underlying statistical physics models.
• Analysis of mouse hippocampal data revealed that the resulting model captures key features of collective neural activity.

Conclusions:

• The minimax entropy approach offers a scalable and principled framework for analyzing large neural populations.
• This method effectively bridges neural recordings with statistical physics models.
• The findings demonstrate the utility of the minimax entropy principle in understanding complex neural network dynamics.