Multi-study inference of regulatory networks for more accurate models of gene regulation
Fig 2
Representation of the weights matrix for one gene in the multitask setting.
We represent model coefficients as a matrix W (predictors by datasets) where nonzero rows represent predictors relevant for all datasets. We decompose the weights into two components, and regularize them differently, using a sparse penalty (l1/l1 to S component) to encode a dataset-specific component and a block-sparse penalty (l1/l∞ to B component) to encode a conserved one. To illustrate, in this example, non-zero weights are shown on the right side. Note that, in this schematic example, regulators w3 and w7 are shared between all datasets. We also show the objective function minimized to estimate S and B on the bottom (for details, see Methods).