Recovering Sparse Neural Connectivity from Partial Measurements: A Covariance-Based Approach with Granger-Causality Refinement

TL;DR

This paper introduces a covariance-based method combined with Granger-causality refinement to accurately recover neural network connectivity from partial, non-simultaneous measurements, revealing a fundamental tradeoff and implicit regularization effects.

Contribution

It proposes a novel covariance-based approach with Granger-causality refinement for neural connectivity inference from partial data, including theoretical analysis and experimental validation.

Findings

Stimulation improves identifiability but can disrupt dynamics.

Implicit regularization from linear approximation outperforms the oracle estimator.

Characterization of the control-estimation tradeoff and regularization effects.

Abstract

Inferring the connectivity of neural circuits from incomplete observations is a fundamental challenge in neuroscience. We present a covariance-based method for estimating the weight matrix of a recurrent neural network from sparse, partial measurements across multiple recording sessions. By accumulating pairwise covariance estimates across sessions where different subsets of neurons are observed, we reconstruct the full connectivity matrix without requiring simultaneous recording of all neurons. A Granger-causality refinement step enforces biological constraints via projected gradient descent. Through systematic experiments on synthetic networks modeling small brain circuits, we characterize a fundamental control-estimation tradeoff: stimulation aids identifiability but disrupts intrinsic dynamics, with the optimal level depending on measurement density. We discover that the ``incorrect'' linear approximation acts as implicit regularization -- outperforming the oracle estimator with known nonlinearity at all operating regimes -- and provide an exact characterization via the Stein--Price identity.