3,330,512 research outputs found
Barrier Frank-Wolfe for Marginal Inference
We introduce a globally-convergent algorithm for optimizing the
tree-reweighted (TRW) variational objective over the marginal polytope. The
algorithm is based on the conditional gradient method (Frank-Wolfe) and moves
pseudomarginals within the marginal polytope through repeated maximum a
posteriori (MAP) calls. This modular structure enables us to leverage black-box
MAP solvers (both exact and approximate) for variational inference, and obtains
more accurate results than tree-reweighted algorithms that optimize over the
local consistency relaxation. Theoretically, we bound the sub-optimality for
the proposed algorithm despite the TRW objective having unbounded gradients at
the boundary of the marginal polytope. Empirically, we demonstrate the
increased quality of results found by tightening the relaxation over the
marginal polytope as well as the spanning tree polytope on synthetic and
real-world instances.Comment: 25 pages, 12 figures, To appear in Neural Information Processing
Systems (NIPS) 2015, Corrected reference and cleaned up bibliograph
Variance Reduced Stochastic Gradient Descent with Neighbors
Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its
slow convergence can be a computational bottleneck. Variance reduction
techniques such as SAG, SVRG and SAGA have been proposed to overcome this
weakness, achieving linear convergence. However, these methods are either based
on computations of full gradients at pivot points, or on keeping per data point
corrections in memory. Therefore speed-ups relative to SGD may need a minimal
number of epochs in order to materialize. This paper investigates algorithms
that can exploit neighborhood structure in the training data to share and
re-use information about past stochastic gradients across data points, which
offers advantages in the transient optimization phase. As a side-product we
provide a unified convergence analysis for a family of variance reduction
algorithms, which we call memorization algorithms. We provide experimental
results supporting our theory.Comment: Appears in: Advances in Neural Information Processing Systems 28
(NIPS 2015). 13 page
Information, information processing and gravity
I discuss fundamental limits placed on information and information processing
by gravity. Such limits arise because both information and its processing
require energy, while gravitational collapse (formation of a horizon or black
hole) restricts the amount of energy allowed in a finite region. Specifically,
I use a criterion for gravitational collapse called the hoop conjecture. Once
the hoop conjecture is assumed a number of results can be obtained directly:
the existence of a fundamental uncertainty in spatial distance of order the
Planck length, bounds on information (entropy) in a finite region, and a bound
on the rate of information processing in a finite region. In the final section
I discuss some cosmological issues related to the total amount of information
in the universe, and note that almost all detailed aspects of the late universe
are determined by the randomness of quantum outcomes. This paper is based on a
talk presented at a 2007 Bellairs Research Institute (McGill University)
workshop on black holes and quantum information.Comment: 7 pages, 5 figures, revte
- …