170 research outputs found
On sequential and parallel solution of initial value problems
AbstractWe deal with the solution of systems z′(x) = f(x, z(x)), x ϵ [0, 1], z(0) = η, where the function ƒ [0, 1] × Rs → Rs has r continuous bounded partial derivatives. We assume that available information about the problem consists of evaluations of n linear functionals at ƒ. If an adaptive choice of these functionals is allowed (which is suitable for sequential processing), then the minimal error of an algorithm is of order n−(r+1), for any dimension s. We show that if nonadaptive information (well-suited for parallel computation) is used, then the minimal error cannot be essentially less than n−(r+1)(s+1). Thus, adaption is significantly better, and the advantage of using it grows with s. This yields that the ε-complexity in sequential computation is smaller for adaptive information. For parallel computation, nonadaptive information is more efficient only if the number of processors is very large, depending exponentially on the dimension s. We conclude that using parallelism by computing the information nonadaptively is not feasible
Efficient Optimization of Performance Measures by Classifier Adaptation
In practical applications, machine learning algorithms are often needed to
learn classifiers that optimize domain specific performance measures.
Previously, the research has focused on learning the needed classifier in
isolation, yet learning nonlinear classifier for nonlinear and nonsmooth
performance measures is still hard. In this paper, rather than learning the
needed classifier by optimizing specific performance measure directly, we
circumvent this problem by proposing a novel two-step approach called as CAPO,
namely to first train nonlinear auxiliary classifiers with existing learning
methods, and then to adapt auxiliary classifiers for specific performance
measures. In the first step, auxiliary classifiers can be obtained efficiently
by taking off-the-shelf learning algorithms. For the second step, we show that
the classifier adaptation problem can be reduced to a quadratic program
problem, which is similar to linear SVMperf and can be efficiently solved. By
exploiting nonlinear auxiliary classifiers, CAPO can generate nonlinear
classifier which optimizes a large variety of performance measures including
all the performance measure based on the contingency table and AUC, whilst
keeping high computational efficiency. Empirical studies show that CAPO is
effective and of high computational efficiency, and even it is more efficient
than linear SVMperf.Comment: 30 pages, 5 figures, to appear in IEEE Transactions on Pattern
Analysis and Machine Intelligence, 201
A survey of information-based complexity
AbstractWe survey some recent results in information-based complexity. We focus on the worst case setting and also indicate some average case results
Heterogeneous thin films: Combining homogenization and dimension reduction with directors
We analyze the asymptotic behavior of a multiscale problem given by a
sequence of integral functionals subject to differential constraints conveyed
by a constant-rank operator with two characteristic length scales, namely the
film thickness and the period of oscillating microstructures, by means of
-convergence. On a technical level, this requires a subtile merging of
homogenization tools, such as multiscale convergence methods, with dimension
reduction techniques for functionals subject to differential constraints. One
observes that the results depend critically on the relative magnitude between
the two scales. Interestingly, this even regards the fundamental question of
locality of the limit model, and, in particular, leads to new findings also in
the gradient case.Comment: 28 page
RIACS
Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project
Multi-Carrier NOMA-Empowered Wireless Federated Learning with Optimal Power and Bandwidth Allocation
Wireless federated learning (WFL) undergoes a communication bottleneck in
uplink, limiting the number of users that can upload their local models in each
global aggregation round. This paper presents a new multi-carrier
non-orthogonal multiple-access (MC-NOMA)-empowered WFL system under an adaptive
learning setting of Flexible Aggregation. Since a WFL round accommodates both
local model training and uploading for each user, the use of Flexible
Aggregation allows the users to train different numbers of iterations per
round, adapting to their channel conditions and computing resources. The key
idea is to use MC-NOMA to concurrently upload the local models of the users,
thereby extending the local model training times of the users and increasing
participating users. A new metric, namely, Weighted Global Proportion of
Trained Mini-batches (WGPTM), is analytically established to measure the
convergence of the new system. Another important aspect is that we maximize the
WGPTM to harness the convergence of the new system by jointly optimizing the
transmit powers and subchannel bandwidths. This nonconvex problem is converted
equivalently to a tractable convex problem and solved efficiently using
variable substitution and Cauchy's inequality. As corroborated experimentally
using a convolutional neural network and an 18-layer residential network, the
proposed MC-NOMA WFL can efficiently reduce communication delay, increase local
model training times, and accelerate the convergence by over 40%, compared to
its existing alternative.Comment: 33 pages, 16 figure
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