Convex relaxation of mixture regression with efficient algorithms
Novi Quadrianto, Tiberio Caetano, John Lim and Dale Schuurmans
In: 23rd Annual Conference on Neural Information Processing Systems, 7-12 Dec 2009, Vancouver, B.C., Canada.
We develop a convex relaxation of maximum a posteriori estimation of
a mixture of regression models.
Although our relaxation involves a semidefinite matrix variable,
we reformulate the problem
to eliminate the need for general
In particular, we provide two reformulations that admit fast algorithms.
The first is a max-min spectral reformulation exploiting quasi-Newton descent.
The second is a min-min reformulation consisting of
fast alternating steps of closed-form updates.
We evaluate the methods against Expectation-Maximization
in a real problem of motion segmentation from video data.