Bayesian compressed sensing approach to reconstructing neural connectivity from subsampled anatomical data

Yuriy Mishchenko and Liam Paninski

In preparation
In recent years, the problem of reconstructing complete neural connectivity in large neural circuits (connectomics) has re-emerged as one of the main objectives of the neuroscience community. Classically, reconstructions of neural connectivity are approached anatomically, using extremely labor-intensive microscopy and histological approaches.
In this paper, we describe a new statistical paradigm for connectomics reconstructions that relies on collecting large samples of measurements using relatively easy-to-obtain anatomical probes (e.g., fluorescent synaptic markers, fluorescent cytoplasmic dyes, or transsynaptic tracers). We describe the principles of such an experiment's design, and develop a theoretical Bayesian framework for analysis of the resulting data. We show that the reconstruction of neural connectivity from certain types of such measurements can be formulated most naturally as an $L_1$-regularized quadratic optimization.
We demonstrate the utility of this approach by simulating a hypothetical neural connectivity reconstruction experiment in C. elegans, a popular neuroscience model where the complete wiring diagram is known from heroic long-term electron microscopy work. We show that physical connectivity in this neural circuit can in principle be inferred successfully and with an orders-of-magnitude reduction in experimental effort. We also demonstrate that biological variability in the connectivity matrix along with the "average" connectivity matrix can be estimated to a degree which has not previously been possible.
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