10,462 research outputs found
Fast learning rate of multiple kernel learning: Trade-off between sparsity and smoothness
We investigate the learning rate of multiple kernel learning (MKL) with
and elastic-net regularizations. The elastic-net regularization is a
composition of an -regularizer for inducing the sparsity and an
-regularizer for controlling the smoothness. We focus on a sparse
setting where the total number of kernels is large, but the number of nonzero
components of the ground truth is relatively small, and show sharper
convergence rates than the learning rates have ever shown for both and
elastic-net regularizations. Our analysis reveals some relations between the
choice of a regularization function and the performance. If the ground truth is
smooth, we show a faster convergence rate for the elastic-net regularization
with less conditions than -regularization; otherwise, a faster
convergence rate for the -regularization is shown.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1095 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org). arXiv admin note: text overlap with
arXiv:1103.043
Elastic Net Regularization Paths for All Generalized Linear Models
The lasso and elastic net are popular regularized regression models for supervised learning. Friedman, Hastie, and Tibshirani (2010) introduced a computationally efficient algorithm for computing the elastic net regularization path for ordinary least squares regression, logistic regression and multinomial logistic regression, while Simon, Friedman, Hastie, and Tibshirani (2011) extended this work to Cox models for right-censored data. We further extend the reach of the elastic net-regularized regression to all generalized linear model families, Cox models with (start, stop] data and strata, and a simplified version of the relaxed lasso. We also discuss convenient utility functions for measuring the performance of these fitted models
CoCoA: A General Framework for Communication-Efficient Distributed Optimization
The scale of modern datasets necessitates the development of efficient
distributed optimization methods for machine learning. We present a
general-purpose framework for distributed computing environments, CoCoA, that
has an efficient communication scheme and is applicable to a wide variety of
problems in machine learning and signal processing. We extend the framework to
cover general non-strongly-convex regularizers, including L1-regularized
problems like lasso, sparse logistic regression, and elastic net
regularization, and show how earlier work can be derived as a special case. We
provide convergence guarantees for the class of convex regularized loss
minimization objectives, leveraging a novel approach in handling
non-strongly-convex regularizers and non-smooth loss functions. The resulting
framework has markedly improved performance over state-of-the-art methods, as
we illustrate with an extensive set of experiments on real distributed
datasets
Pathway-Based Genomics Prediction using Generalized Elastic Net.
We present a novel regularization scheme called The Generalized Elastic Net (GELnet) that incorporates gene pathway information into feature selection. The proposed formulation is applicable to a wide variety of problems in which the interpretation of predictive features using known molecular interactions is desired. The method naturally steers solutions toward sets of mechanistically interlinked genes. Using experiments on synthetic data, we demonstrate that pathway-guided results maintain, and often improve, the accuracy of predictors even in cases where the full gene network is unknown. We apply the method to predict the drug response of breast cancer cell lines. GELnet is able to reveal genetic determinants of sensitivity and resistance for several compounds. In particular, for an EGFR/HER2 inhibitor, it finds a possible trans-differentiation resistance mechanism missed by the corresponding pathway agnostic approach
A Reduction of the Elastic Net to Support Vector Machines with an Application to GPU Computing
The past years have witnessed many dedicated open-source projects that built
and maintain implementations of Support Vector Machines (SVM), parallelized for
GPU, multi-core CPUs and distributed systems. Up to this point, no comparable
effort has been made to parallelize the Elastic Net, despite its popularity in
many high impact applications, including genetics, neuroscience and systems
biology. The first contribution in this paper is of theoretical nature. We
establish a tight link between two seemingly different algorithms and prove
that Elastic Net regression can be reduced to SVM with squared hinge loss
classification. Our second contribution is to derive a practical algorithm
based on this reduction. The reduction enables us to utilize prior efforts in
speeding up and parallelizing SVMs to obtain a highly optimized and parallel
solver for the Elastic Net and Lasso. With a simple wrapper, consisting of only
11 lines of MATLAB code, we obtain an Elastic Net implementation that naturally
utilizes GPU and multi-core CPUs. We demonstrate on twelve real world data
sets, that our algorithm yields identical results as the popular (and highly
optimized) glmnet implementation but is one or several orders of magnitude
faster.Comment: 10 page
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