5,795 research outputs found
Scalable Kernel Methods via Doubly Stochastic Gradients
The general perception is that kernel methods are not scalable, and neural
nets are the methods of choice for nonlinear learning problems. Or have we
simply not tried hard enough for kernel methods? Here we propose an approach
that scales up kernel methods using a novel concept called "doubly stochastic
functional gradients". Our approach relies on the fact that many kernel methods
can be expressed as convex optimization problems, and we solve the problems by
making two unbiased stochastic approximations to the functional gradient, one
using random training points and another using random functions associated with
the kernel, and then descending using this noisy functional gradient. We show
that a function produced by this procedure after iterations converges to
the optimal function in the reproducing kernel Hilbert space in rate ,
and achieves a generalization performance of . This doubly
stochasticity also allows us to avoid keeping the support vectors and to
implement the algorithm in a small memory footprint, which is linear in number
of iterations and independent of data dimension. Our approach can readily scale
kernel methods up to the regimes which are dominated by neural nets. We show
that our method can achieve competitive performance to neural nets in datasets
such as 8 million handwritten digits from MNIST, 2.3 million energy materials
from MolecularSpace, and 1 million photos from ImageNet.Comment: 32 pages, 22 figure
Preserving Differential Privacy in Convolutional Deep Belief Networks
The remarkable development of deep learning in medicine and healthcare domain
presents obvious privacy issues, when deep neural networks are built on users'
personal and highly sensitive data, e.g., clinical records, user profiles,
biomedical images, etc. However, only a few scientific studies on preserving
privacy in deep learning have been conducted. In this paper, we focus on
developing a private convolutional deep belief network (pCDBN), which
essentially is a convolutional deep belief network (CDBN) under differential
privacy. Our main idea of enforcing epsilon-differential privacy is to leverage
the functional mechanism to perturb the energy-based objective functions of
traditional CDBNs, rather than their results. One key contribution of this work
is that we propose the use of Chebyshev expansion to derive the approximate
polynomial representation of objective functions. Our theoretical analysis
shows that we can further derive the sensitivity and error bounds of the
approximate polynomial representation. As a result, preserving differential
privacy in CDBNs is feasible. We applied our model in a health social network,
i.e., YesiWell data, and in a handwriting digit dataset, i.e., MNIST data, for
human behavior prediction, human behavior classification, and handwriting digit
recognition tasks. Theoretical analysis and rigorous experimental evaluations
show that the pCDBN is highly effective. It significantly outperforms existing
solutions
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