Distributed majorization-minimization for Laplacian regularized problems

Distributed Majorization-Minimization for Laplacian Regularized Problems

We consider the problem of minimizing a block separable convex function (possibly nondifferentiable, and including constraints) plus Laplacian regularization, a problem that arises in applications including model fitting, regularizing stratified models, and multi-period portfolio optimization. We develop a distributed majorizationminimization method for this general problem, and derive a comple...

Majorization-Minimization for Manifold Embedding

Nonlinear dimensionality reduction by manifold embedding has become a popular and powerful approach both for visualization and as preprocessing for predictive tasks, but more efficient optimization algorithms are still crucially needed. MajorizationMinimization (MM) is a promising approach that monotonically decreases the cost function, but it remains unknown how to tightly majorize the manifol...

Majorization bounds for signless Laplacian eigenvalues

More inequalities for Laplacian indices by way of majorization

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...

Generalized Majorization-Minimization

Non-convex optimization is ubiquitous in machine learning. The MajorizationMinimization (MM) procedure systematically optimizes non-convex functions through an iterative construction and optimization of upper bounds on the objective function. The bound at each iteration is required to touch the objective function at the optimizer of the previous bound. We show that this touching constraint is u...