1,103 research outputs found
Optimal Rates for Random Fourier Features
Kernel methods represent one of the most powerful tools in machine learning
to tackle problems expressed in terms of function values and derivatives due to
their capability to represent and model complex relations. While these methods
show good versatility, they are computationally intensive and have poor
scalability to large data as they require operations on Gram matrices. In order
to mitigate this serious computational limitation, recently randomized
constructions have been proposed in the literature, which allow the application
of fast linear algorithms. Random Fourier features (RFF) are among the most
popular and widely applied constructions: they provide an easily computable,
low-dimensional feature representation for shift-invariant kernels. Despite the
popularity of RFFs, very little is understood theoretically about their
approximation quality. In this paper, we provide a detailed finite-sample
theoretical analysis about the approximation quality of RFFs by (i)
establishing optimal (in terms of the RFF dimension, and growing set size)
performance guarantees in uniform norm, and (ii) presenting guarantees in
() norms. We also propose an RFF approximation to derivatives of
a kernel with a theoretical study on its approximation quality.Comment: To appear at NIPS-201
Improving Sampling from Generative Autoencoders with Markov Chains
We focus on generative autoencoders, such as variational or adversarial autoencoders, which jointly learn a generative model alongside an inference model. We define generative autoencoders as autoencoders which are trained to softly enforce a prior on the latent distribution learned by the model. However, the model does not necessarily learn to match the prior. We formulate a Markov chain Monte Carlo (MCMC) sampling process, equivalent to iteratively encoding and decoding, which allows us to sample from the learned latent distribution. Using this we can improve the quality of samples drawn from the model, especially when the learned distribution is far from the prior. Using MCMC sampling, we also reveal previously unseen differences between generative autoencoders trained either with or without the denoising criterion
Caching with Unknown Popularity Profiles in Small Cell Networks
A heterogenous network is considered where the base stations (BSs), small
base stations (SBSs) and users are distributed according to independent Poisson
point processes (PPPs). We let the SBS nodes to posses high storage capacity
and are assumed to form a distributed caching network. Popular data files are
stored in the local cache of SBS, so that users can download the desired files
from one of the SBS in the vicinity subject to availability. The
offloading-loss is captured via a cost function that depends on a random
caching strategy proposed in this paper. The cost function depends on the
popularity profile, which is, in general, unknown. In this work, the popularity
profile is estimated at the BS using the available instantaneous demands from
the users in a time interval . This is then used to find an estimate
of the cost function from which the optimal random caching strategy is devised.
The main results of this work are the following: First it is shown that the
waiting time to achieve an difference between the achieved
and optimal costs is finite, provided the user density is greater than a
predefined threshold. In this case, is shown to scale as , where
is the support of the popularity profile. Secondly, a transfer
learning-based approach is proposed to obtain an estimate of the popularity
profile used to compute the empirical cost function. A condition is derived
under which the proposed transfer learning-based approach performs better than
the random caching strategy.Comment: 6 pages, Proceedings of IEEE Global Communications Conference, 201
Asymptotics of a Clustering Criterion for Smooth Distributions
We develop a clustering framework for observations from a population with a
smooth probability distribution function and derive its asymptotic properties.
A clustering criterion based on a linear combination of order statistics is
proposed. The asymptotic behavior of the point at which the observations are
split into two clusters is examined. The results obtained can then be utilized
to construct an interval estimate of the point which splits the data and
develop tests for bimodality and presence of clusters
k-Nearest Neighbor Classification over Semantically Secure Encrypted Relational Data
Data Mining has wide applications in many areas such as banking, medicine,
scientific research and among government agencies. Classification is one of the
commonly used tasks in data mining applications. For the past decade, due to
the rise of various privacy issues, many theoretical and practical solutions to
the classification problem have been proposed under different security models.
However, with the recent popularity of cloud computing, users now have the
opportunity to outsource their data, in encrypted form, as well as the data
mining tasks to the cloud. Since the data on the cloud is in encrypted form,
existing privacy preserving classification techniques are not applicable. In
this paper, we focus on solving the classification problem over encrypted data.
In particular, we propose a secure k-NN classifier over encrypted data in the
cloud. The proposed k-NN protocol protects the confidentiality of the data,
user's input query, and data access patterns. To the best of our knowledge, our
work is the first to develop a secure k-NN classifier over encrypted data under
the semi-honest model. Also, we empirically analyze the efficiency of our
solution through various experiments.Comment: 29 pages, 2 figures, 3 tables arXiv admin note: substantial text
overlap with arXiv:1307.482
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