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

A Feature Selection Method for Multivariate Performance Measures

Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for classification error. In this paper, we propose a generalized sparse regularizer. Based on the proposed regularizer, we present a unified feature selection framework for general loss functions. In particular, we study the novel feature selection paradigm by optimizing multivariate performance measures. The resultant formulation is a challenging problem for high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed to solve this problem, and the convergence is presented. In addition, we adapt the proposed method to optimize multivariate measures for multiple instance learning problems. The analyses by comparing with the state-of-the-art feature selection methods show that the proposed method is superior to others. Extensive experiments on large-scale and high-dimensional real world datasets show that the proposed method outperforms $l_1$-SVM and SVM-RFE when choosing a small subset of features, and achieves significantly improved performances over SVM$^{perf}$ in terms of $F_1$-score

Active Transfer Learning with Zero-Shot Priors: Reusing Past Datasets for Future Tasks

How can we reuse existing knowledge, in the form of available datasets, when solving a new and apparently unrelated target task from a set of unlabeled data? In this work we make a first contribution to answer this question in the context of image classification. We frame this quest as an active learning problem and use zero-shot classifiers to guide the learning process by linking the new task to the existing classifiers. By revisiting the dual formulation of adaptive SVM, we reveal two basic conditions to choose greedily only the most relevant samples to be annotated. On this basis we propose an effective active learning algorithm which learns the best possible target classification model with minimum human labeling effort. Extensive experiments on two challenging datasets show the value of our approach compared to the state-of-the-art active learning methodologies, as well as its potential to reuse past datasets with minimal effort for future tasks