11,339 research outputs found
Stochastic Optimization of PCA with Capped MSG
We study PCA as a stochastic optimization problem and propose a novel
stochastic approximation algorithm which we refer to as "Matrix Stochastic
Gradient" (MSG), as well as a practical variant, Capped MSG. We study the
method both theoretically and empirically
Permutation and Grouping Methods for Sharpening Gaussian Process Approximations
Vecchia's approximate likelihood for Gaussian process parameters depends on
how the observations are ordered, which can be viewed as a deficiency because
the exact likelihood is permutation-invariant. This article takes the
alternative standpoint that the ordering of the observations can be tuned to
sharpen the approximations. Advantageously chosen orderings can drastically
improve the approximations, and in fact, completely random orderings often
produce far more accurate approximations than default coordinate-based
orderings do. In addition to the permutation results, automatic methods for
grouping calculations of components of the approximation are introduced, having
the result of simultaneously improving the quality of the approximation and
reducing its computational burden. In common settings, reordering combined with
grouping reduces Kullback-Leibler divergence from the target model by a factor
of 80 and computation time by a factor of 2 compared to ungrouped
approximations with default ordering. The claims are supported by theory and
numerical results with comparisons to other approximations, including tapered
covariances and stochastic partial differential equation approximations.
Computational details are provided, including efficiently finding the orderings
and ordered nearest neighbors, and profiling out linear mean parameters and
using the approximations for prediction and conditional simulation. An
application to space-time satellite data is presented
On Longest Repeat Queries Using GPU
Repeat finding in strings has important applications in subfields such as
computational biology. The challenge of finding the longest repeats covering
particular string positions was recently proposed and solved by \.{I}leri et
al., using a total of the optimal time and space, where is the
string size. However, their solution can only find the \emph{leftmost} longest
repeat for each of the string position. It is also not known how to
parallelize their solution. In this paper, we propose a new solution for
longest repeat finding, which although is theoretically suboptimal in time but
is conceptually simpler and works faster and uses less memory space in practice
than the optimal solution. Further, our solution can find \emph{all} longest
repeats of every string position, while still maintaining a faster processing
speed and less memory space usage. Moreover, our solution is
\emph{parallelizable} in the shared memory architecture (SMA), enabling it to
take advantage of the modern multi-processor computing platforms such as the
general-purpose graphics processing units (GPU). We have implemented both the
sequential and parallel versions of our solution. Experiments with both
biological and non-biological data show that our sequential and parallel
solutions are faster than the optimal solution by a factor of 2--3.5 and 6--14,
respectively, and use less memory space.Comment: 14 page
Resource Allocation for Delay Differentiated Traffic in Multiuser OFDM Systems
Most existing work on adaptive allocation of subcarriers and power in
multiuser orthogonal frequency division multiplexing (OFDM) systems has focused
on homogeneous traffic consisting solely of either delay-constrained data
(guaranteed service) or non-delay-constrained data (best-effort service). In
this paper, we investigate the resource allocation problem in a heterogeneous
multiuser OFDM system with both delay-constrained (DC) and
non-delay-constrained (NDC) traffic. The objective is to maximize the sum-rate
of all the users with NDC traffic while maintaining guaranteed rates for the
users with DC traffic under a total transmit power constraint. Through our
analysis we show that the optimal power allocation over subcarriers follows a
multi-level water-filling principle; moreover, the valid candidates competing
for each subcarrier include only one NDC user but all DC users. By converting
this combinatorial problem with exponential complexity into a convex problem or
showing that it can be solved in the dual domain, efficient iterative
algorithms are proposed to find the optimal solutions. To further reduce the
computational cost, a low-complexity suboptimal algorithm is also developed.
Numerical studies are conducted to evaluate the performance the proposed
algorithms in terms of service outage probability, achievable transmission rate
pairs for DC and NDC traffic, and multiuser diversity.Comment: 29 pages, 8 figures, submitted to IEEE Transactions on Wireless
Communication
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