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