31,718 research outputs found
Coding for Random Projections
The method of random projections has become very popular for large-scale
applications in statistical learning, information retrieval, bio-informatics
and other applications. Using a well-designed coding scheme for the projected
data, which determines the number of bits needed for each projected value and
how to allocate these bits, can significantly improve the effectiveness of the
algorithm, in storage cost as well as computational speed. In this paper, we
study a number of simple coding schemes, focusing on the task of similarity
estimation and on an application to training linear classifiers. We demonstrate
that uniform quantization outperforms the standard existing influential method
(Datar et. al. 2004). Indeed, we argue that in many cases coding with just a
small number of bits suffices. Furthermore, we also develop a non-uniform 2-bit
coding scheme that generally performs well in practice, as confirmed by our
experiments on training linear support vector machines (SVM)
Randomized Sketches of Convex Programs with Sharp Guarantees
Random projection (RP) is a classical technique for reducing storage and
computational costs. We analyze RP-based approximations of convex programs, in
which the original optimization problem is approximated by the solution of a
lower-dimensional problem. Such dimensionality reduction is essential in
computation-limited settings, since the complexity of general convex
programming can be quite high (e.g., cubic for quadratic programs, and
substantially higher for semidefinite programs). In addition to computational
savings, random projection is also useful for reducing memory usage, and has
useful properties for privacy-sensitive optimization. We prove that the
approximation ratio of this procedure can be bounded in terms of the geometry
of constraint set. For a broad class of random projections, including those
based on various sub-Gaussian distributions as well as randomized Hadamard and
Fourier transforms, the data matrix defining the cost function can be projected
down to the statistical dimension of the tangent cone of the constraints at the
original solution, which is often substantially smaller than the original
dimension. We illustrate consequences of our theory for various cases,
including unconstrained and -constrained least squares, support vector
machines, low-rank matrix estimation, and discuss implications on
privacy-sensitive optimization and some connections with de-noising and
compressed sensing
Compact Random Feature Maps
Kernel approximation using randomized feature maps has recently gained a lot
of interest. In this work, we identify that previous approaches for polynomial
kernel approximation create maps that are rank deficient, and therefore do not
utilize the capacity of the projected feature space effectively. To address
this challenge, we propose compact random feature maps (CRAFTMaps) to
approximate polynomial kernels more concisely and accurately. We prove the
error bounds of CRAFTMaps demonstrating their superior kernel reconstruction
performance compared to the previous approximation schemes. We show how
structured random matrices can be used to efficiently generate CRAFTMaps, and
present a single-pass algorithm using CRAFTMaps to learn non-linear multi-class
classifiers. We present experiments on multiple standard data-sets with
performance competitive with state-of-the-art results.Comment: 9 page
Random Feature Maps via a Layered Random Projection (LaRP) Framework for Object Classification
The approximation of nonlinear kernels via linear feature maps has recently
gained interest due to their applications in reducing the training and testing
time of kernel-based learning algorithms. Current random projection methods
avoid the curse of dimensionality by embedding the nonlinear feature space into
a low dimensional Euclidean space to create nonlinear kernels. We introduce a
Layered Random Projection (LaRP) framework, where we model the linear kernels
and nonlinearity separately for increased training efficiency. The proposed
LaRP framework was assessed using the MNIST hand-written digits database and
the COIL-100 object database, and showed notable improvement in object
classification performance relative to other state-of-the-art random projection
methods.Comment: 5 page
Feature Selection for Linear SVM with Provable Guarantees
We give two provably accurate feature-selection techniques for the linear
SVM. The algorithms run in deterministic and randomized time respectively. Our
algorithms can be used in an unsupervised or supervised setting. The supervised
approach is based on sampling features from support vectors. We prove that the
margin in the feature space is preserved to within -relative error of
the margin in the full feature space in the worst-case. In the unsupervised
setting, we also provide worst-case guarantees of the radius of the minimum
enclosing ball, thereby ensuring comparable generalization as in the full
feature space and resolving an open problem posed in Dasgupta et al. We present
extensive experiments on real-world datasets to support our theory and to
demonstrate that our method is competitive and often better than prior
state-of-the-art, for which there are no known provable guarantees.Comment: Appearing in Proceedings of 18th AISTATS, JMLR W&CP, vol 38, 201
On Lightweight Privacy-Preserving Collaborative Learning for IoT Objects
The Internet of Things (IoT) will be a main data generation infrastructure
for achieving better system intelligence. This paper considers the design and
implementation of a practical privacy-preserving collaborative learning scheme,
in which a curious learning coordinator trains a better machine learning model
based on the data samples contributed by a number of IoT objects, while the
confidentiality of the raw forms of the training data is protected against the
coordinator. Existing distributed machine learning and data encryption
approaches incur significant computation and communication overhead, rendering
them ill-suited for resource-constrained IoT objects. We study an approach that
applies independent Gaussian random projection at each IoT object to obfuscate
data and trains a deep neural network at the coordinator based on the projected
data from the IoT objects. This approach introduces light computation overhead
to the IoT objects and moves most workload to the coordinator that can have
sufficient computing resources. Although the independent projections performed
by the IoT objects address the potential collusion between the curious
coordinator and some compromised IoT objects, they significantly increase the
complexity of the projected data. In this paper, we leverage the superior
learning capability of deep learning in capturing sophisticated patterns to
maintain good learning performance. Extensive comparative evaluation shows that
this approach outperforms other lightweight approaches that apply additive
noisification for differential privacy and/or support vector machines for
learning in the applications with light data pattern complexities.Comment: 12 pages,IOTDI 201
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