22,268 research outputs found
A Fast Stochastic Plug-and-Play ADMM for Imaging Inverse Problems
In this work we propose an efficient stochastic plug-and-play (PnP) algorithm
for imaging inverse problems. The PnP stochastic gradient descent methods have
been recently proposed and shown improved performance in some imaging
applications over standard deterministic PnP methods. However, current
stochastic PnP methods need to frequently compute the image denoisers which can
be computationally expensive. To overcome this limitation, we propose a new
stochastic PnP-ADMM method which is based on introducing stochastic gradient
descent inner-loops within an inexact ADMM framework. We provide the
theoretical guarantee on the fixed-point convergence for our algorithm under
standard assumptions. Our numerical results demonstrate the effectiveness of
our approach compared with state-of-the-art PnP methods
Scalable Peaceman-Rachford Splitting Method with Proximal Terms
Along with developing of Peaceman-Rachford Splittling Method (PRSM), many
batch algorithms based on it have been studied very deeply. But almost no
algorithm focused on the performance of stochastic version of PRSM. In this
paper, we propose a new stochastic algorithm based on PRSM, prove its
convergence rate in ergodic sense, and test its performance on both artificial
and real data. We show that our proposed algorithm, Stochastic Scalable PRSM
(SS-PRSM), enjoys the convergence rate, which is the same as those
newest stochastic algorithms that based on ADMM but faster than general
Stochastic ADMM (which is ). Our algorithm also owns wide
flexibility, outperforms many state-of-the-art stochastic algorithms coming
from ADMM, and has low memory cost in large-scale splitting optimization
problems
Bayesian Dark Knowledge
We consider the problem of Bayesian parameter estimation for deep neural
networks, which is important in problem settings where we may have little data,
and/ or where we need accurate posterior predictive densities, e.g., for
applications involving bandits or active learning. One simple approach to this
is to use online Monte Carlo methods, such as SGLD (stochastic gradient
Langevin dynamics). Unfortunately, such a method needs to store many copies of
the parameters (which wastes memory), and needs to make predictions using many
versions of the model (which wastes time).
We describe a method for "distilling" a Monte Carlo approximation to the
posterior predictive density into a more compact form, namely a single deep
neural network. We compare to two very recent approaches to Bayesian neural
networks, namely an approach based on expectation propagation [Hernandez-Lobato
and Adams, 2015] and an approach based on variational Bayes [Blundell et al.,
2015]. Our method performs better than both of these, is much simpler to
implement, and uses less computation at test time.Comment: final version submitted to NIPS 201
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