  Recently a majorization method for optimizing partition functions of
log-linear models was proposed alongside a novel quadratic variational
upper-bound. In the batch setting, it outperformed state-of-the-art first- and
second-order optimization methods on various learning tasks. We propose a
stochastic version of this bound majorization method as well as a low-rank
modification for high-dimensional data-sets. The resulting stochastic
second-order method outperforms stochastic gradient descent (across variations
and various tunings) both in terms of the number of iterations and computation
time till convergence while finding a better quality parameter setting. The
proposed method bridges first- and second-order stochastic optimization methods
by maintaining a computational complexity that is linear in the data dimension
and while exploiting second order information about the pseudo-global curvature
of the objective function (as opposed to the local curvature in the Hessian).
