Whole-brain neural connectivity data are now available from viral tracing experiments, which reveal the connections between a source injection site and elsewhere in the brain. To achieve this goal, we seek to fit a weighted, nonnegative adjacency matrix among 100 μm brain "voxels" using viral tracer data. Despite a multi-year experimental effort, injections provide incomplete coverage, and the number of voxels in our data is orders of magnitude larger than the number of injections, making the problem severely underdetermined. Furthermore, projection data are missing within the injection site because local connections there are not separable from the injection signal. We use a novel machine-learning algorithm to meet these challenges and develop a spatially explicit, voxel-scale connectivity map of the mouse visual system.

The underlying model is a non-negative linear regression, y Wx \eta, where \eta is drawn from a spherical Gaussian model. The weight matrix, W, is assumed to be nonnegative and, in probabilistic terms, drawn from a spatially smooth prior. Optionally, a low-rank assumption may be incorporated into the weight model, which can dramatically improve memory efficiency for large-scale problems. While the individual components of this model (nonnegative regression, Laplacian regularized least squares, low-rank constraints) are well-studied, I think this is a nice combination and application of these techniques to a real-world, scientific problem. The presentation of the model, the synthetic examples, and the real world applications (and supplementary movies) are particularly clear. While it is certainly valid to directly construct a objective function that captures both the reconstruction error and the domain-specific constraints and inductive biases, I think a probabilistic perspective could elucidate a number of potential extensions and connections to existing work.

Whole-brain neural connectivity data are now available from viral tracing experiments, which reveal the connections between a source injection site and elsewhere in the brain. To achieve this goal, we seek to fit a weighted, nonnegative adjacency matrix among 100 μm brain "voxels" using viral tracer data. Despite a multi-year experimental effort, injections provide incomplete coverage, and the number of voxels in our data is orders of magnitude larger than the number of injections, making the problem severely underdetermined. Furthermore, projection data are missing within the injection site because local connections there are not separable from the injection signal. We use a novel machine-learning algorithm to meet these challenges and develop a spatially explicit, voxel-scale connectivity map of the mouse visual system.