16,427 research outputs found
Second-Order Kernel Online Convex Optimization with Adaptive Sketching
Kernel online convex optimization (KOCO) is a framework combining the
expressiveness of non-parametric kernel models with the regret guarantees of
online learning. First-order KOCO methods such as functional gradient descent
require only time and space per iteration, and, when the only
information on the losses is their convexity, achieve a minimax optimal
regret. Nonetheless, many common losses in kernel
problems, such as squared loss, logistic loss, and squared hinge loss posses
stronger curvature that can be exploited. In this case, second-order KOCO
methods achieve regret, which
we show scales as , where
is the effective dimension of the problem and is usually much smaller than
. The main drawback of second-order methods is their
much higher space and time complexity. In this paper, we
introduce kernel online Newton step (KONS), a new second-order KOCO method that
also achieves regret. To address the
computational complexity of second-order methods, we introduce a new matrix
sketching algorithm for the kernel matrix , and show that for
a chosen parameter our Sketched-KONS reduces the space and time
complexity by a factor of to space and
time per iteration, while incurring only times more regret
Fast and Guaranteed Tensor Decomposition via Sketching
Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in
statistical learning of latent variable models and in data mining. In this
paper, we propose fast and randomized tensor CP decomposition algorithms based
on sketching. We build on the idea of count sketches, but introduce many novel
ideas which are unique to tensors. We develop novel methods for randomized
computation of tensor contractions via FFTs, without explicitly forming the
tensors. Such tensor contractions are encountered in decomposition methods such
as tensor power iterations and alternating least squares. We also design novel
colliding hashes for symmetric tensors to further save time in computing the
sketches. We then combine these sketching ideas with existing whitening and
tensor power iterative techniques to obtain the fastest algorithm on both
sparse and dense tensors. The quality of approximation under our method does
not depend on properties such as sparsity, uniformity of elements, etc. We
apply the method for topic modeling and obtain competitive results.Comment: 29 pages. Appeared in Proceedings of Advances in Neural Information
Processing Systems (NIPS), held at Montreal, Canada in 201
Network Sketching: Exploiting Binary Structure in Deep CNNs
Convolutional neural networks (CNNs) with deep architectures have
substantially advanced the state-of-the-art in computer vision tasks. However,
deep networks are typically resource-intensive and thus difficult to be
deployed on mobile devices. Recently, CNNs with binary weights have shown
compelling efficiency to the community, whereas the accuracy of such models is
usually unsatisfactory in practice. In this paper, we introduce network
sketching as a novel technique of pursuing binary-weight CNNs, targeting at
more faithful inference and better trade-off for practical applications. Our
basic idea is to exploit binary structure directly in pre-trained filter banks
and produce binary-weight models via tensor expansion. The whole process can be
treated as a coarse-to-fine model approximation, akin to the pencil drawing
steps of outlining and shading. To further speedup the generated models, namely
the sketches, we also propose an associative implementation of binary tensor
convolutions. Experimental results demonstrate that a proper sketch of AlexNet
(or ResNet) outperforms the existing binary-weight models by large margins on
the ImageNet large scale classification task, while the committed memory for
network parameters only exceeds a little.Comment: To appear in CVPR201
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