Recently it has become popular to learn sparse Gaussian graphical models
(GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision
matrix. Thispenalized likelihood approach results in a tractable convex
optimization problem. In this paper, we reinterpret these results as performing
MAP estimation under a novel prior which we call the group l1 and l1,2
positivedefinite matrix distributions.
We outline a representation for discrete multivariate distributions in terms
of interventional potential functions that are globally normalized. This
representation can be used to model the effects of interventions, and the
independence properties encoded in this model can be represented as a directed
graph that allows cycles.
We consider the problem of optimizing the sum of a smooth convex function and
a non-smooth convex function using proximal-gradient methods, where an error is
present in the calculation of the gradient of the smooth term or in the
proximity operator with respect to the non-smooth term.
Many structured data-fitting applications require the solution of an
optimization problem involving a sum over a potentially large number of
measurements. Incremental gradient algorithms (both deterministic and
randomized) offer inexpensive iterations by sampling only subsets of the terms
in the sum. These methods can make great progress initially, but often slow as
they approach a solution. In contrast, full gradient methods achieve steady
convergence at the expense of evaluating the full objective and gradient on
each iteration.