2,816 research outputs found
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
Stochastic Low-Rank Kernel Learning for Regression
We present a novel approach to learn a kernel-based regression function. It
is based on the useof conical combinations of data-based parameterized kernels
and on a new stochastic convex optimization procedure of which we establish
convergence guarantees. The overall learning procedure has the nice properties
that a) the learned conical combination is automatically designed to perform
the regression task at hand and b) the updates implicated by the optimization
procedure are quite inexpensive. In order to shed light on the appositeness of
our learning strategy, we present empirical results from experiments conducted
on various benchmark datasets.Comment: International Conference on Machine Learning (ICML'11), Bellevue
(Washington) : United States (2011
Learning Multiple Visual Tasks while Discovering their Structure
Multi-task learning is a natural approach for computer vision applications
that require the simultaneous solution of several distinct but related
problems, e.g. object detection, classification, tracking of multiple agents,
or denoising, to name a few. The key idea is that exploring task relatedness
(structure) can lead to improved performances.
In this paper, we propose and study a novel sparse, non-parametric approach
exploiting the theory of Reproducing Kernel Hilbert Spaces for vector-valued
functions. We develop a suitable regularization framework which can be
formulated as a convex optimization problem, and is provably solvable using an
alternating minimization approach. Empirical tests show that the proposed
method compares favorably to state of the art techniques and further allows to
recover interpretable structures, a problem of interest in its own right.Comment: 19 pages, 3 figures, 3 table
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