18,879 research outputs found
Random Feature-based Online Multi-kernel Learning in Environments with Unknown Dynamics
Kernel-based methods exhibit well-documented performance in various nonlinear
learning tasks. Most of them rely on a preselected kernel, whose prudent choice
presumes task-specific prior information. Especially when the latter is not
available, multi-kernel learning has gained popularity thanks to its
flexibility in choosing kernels from a prescribed kernel dictionary. Leveraging
the random feature approximation and its recent orthogonality-promoting
variant, the present contribution develops a scalable multi-kernel learning
scheme (termed Raker) to obtain the sought nonlinear learning function `on the
fly,' first for static environments. To further boost performance in dynamic
environments, an adaptive multi-kernel learning scheme (termed AdaRaker) is
developed. AdaRaker accounts not only for data-driven learning of kernel
combination, but also for the unknown dynamics. Performance is analyzed in
terms of both static and dynamic regrets. AdaRaker is uniquely capable of
tracking nonlinear learning functions in environments with unknown dynamics,
and with with analytic performance guarantees. Tests with synthetic and real
datasets are carried out to showcase the effectiveness of the novel algorithms.Comment: 36 page
Learning with SGD and Random Features
Sketching and stochastic gradient methods are arguably the most common
techniques to derive efficient large scale learning algorithms. In this paper,
we investigate their application in the context of nonparametric statistical
learning. More precisely, we study the estimator defined by stochastic gradient
with mini batches and random features. The latter can be seen as form of
nonlinear sketching and used to define approximate kernel methods. The
considered estimator is not explicitly penalized/constrained and regularization
is implicit. Indeed, our study highlights how different parameters, such as
number of features, iterations, step-size and mini-batch size control the
learning properties of the solutions. We do this by deriving optimal finite
sample bounds, under standard assumptions. The obtained results are
corroborated and illustrated by numerical experiments
A Distributed Frank-Wolfe Algorithm for Communication-Efficient Sparse Learning
Learning sparse combinations is a frequent theme in machine learning. In this
paper, we study its associated optimization problem in the distributed setting
where the elements to be combined are not centrally located but spread over a
network. We address the key challenges of balancing communication costs and
optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW)
algorithm. We obtain theoretical guarantees on the optimization error
and communication cost that do not depend on the total number of
combining elements. We further show that the communication cost of dFW is
optimal by deriving a lower-bound on the communication cost required to
construct an -approximate solution. We validate our theoretical
analysis with empirical studies on synthetic and real-world data, which
demonstrate that dFW outperforms both baselines and competing methods. We also
study the performance of dFW when the conditions of our analysis are relaxed,
and show that dFW is fairly robust.Comment: Extended version of the SIAM Data Mining 2015 pape
Hashing for Similarity Search: A Survey
Similarity search (nearest neighbor search) is a problem of pursuing the data
items whose distances to a query item are the smallest from a large database.
Various methods have been developed to address this problem, and recently a lot
of efforts have been devoted to approximate search. In this paper, we present a
survey on one of the main solutions, hashing, which has been widely studied
since the pioneering work locality sensitive hashing. We divide the hashing
algorithms two main categories: locality sensitive hashing, which designs hash
functions without exploring the data distribution and learning to hash, which
learns hash functions according the data distribution, and review them from
various aspects, including hash function design and distance measure and search
scheme in the hash coding space
Stochastic Optimization for Deep CCA via Nonlinear Orthogonal Iterations
Deep CCA is a recently proposed deep neural network extension to the
traditional canonical correlation analysis (CCA), and has been successful for
multi-view representation learning in several domains. However, stochastic
optimization of the deep CCA objective is not straightforward, because it does
not decouple over training examples. Previous optimizers for deep CCA are
either batch-based algorithms or stochastic optimization using large
minibatches, which can have high memory consumption. In this paper, we tackle
the problem of stochastic optimization for deep CCA with small minibatches,
based on an iterative solution to the CCA objective, and show that we can
achieve as good performance as previous optimizers and thus alleviate the
memory requirement.Comment: in 2015 Annual Allerton Conference on Communication, Control and
Computin
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