Outcomes of the equivalence of adaptive ridge with least absolute shrinkage
Proceedings of the 1998 conference on Advances in neural information processing systems II
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Grafting: fast, incremental feature selection by gradient descent in function space
The Journal of Machine Learning Research
Convex Optimization
Gradient LASSO for feature selection
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Feature selection, L1 vs. L2 regularization, and rotational invariance
ICML '04 Proceedings of the twenty-first international conference on Machine learning
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Statistics for High-Dimensional Data: Methods, Theory and Applications
Statistics for High-Dimensional Data: Methods, Theory and Applications
Foundations and Trends® in Machine Learning
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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In recent years, the problem of reconstructing the connectivity in large neural circuits ("connectomics") has re-emerged as one of the main objectives of neuroscience. Classically, reconstructions of neural connectivity have been approached anatomically, using electron or light microscopy and histological tracing methods. This paper describes a statistical approach for connectivity reconstruction that relies on relatively easy-to-obtain measurements using fluorescent probes such as synaptic markers, cytoplasmic dyes, transsynaptic tracers, or activity-dependent dyes. We describe the possible design of these experiments and develop a Bayesian framework for extracting synaptic neural connectivity from such data. We show that the statistical reconstruction problem can be formulated naturally as a tractable L 1-regularized quadratic optimization. As a concrete example, we consider a realistic hypothetical connectivity reconstruction experiment in C. elegans, a popular neuroscience model where a complete wiring diagram has been previously obtained based on long-term electron microscopy work. We show that the new statistical approach could lead to an orders of magnitude reduction in experimental effort in reconstructing the connectivity in this circuit. We further demonstrate that the spatial heterogeneity and biological variability in the connectivity matrix--not just the "average" connectivity--can also be estimated using the same method.