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

Generalized Second Price Auction with Probabilistic Broad Match

Generalized Second Price (GSP) auctions are widely used by search engines today to sell their ad slots. Most search engines have supported broad match between queries and bid keywords when executing GSP auctions, however, it has been revealed that GSP auction with the standard broad-match mechanism they are currently using (denoted as SBM-GSP) has several theoretical drawbacks (e.g., its theoretical properties are known only for the single-slot case and full-information setting, and even in this simple setting, the corresponding worst-case social welfare can be rather bad). To address this issue, we propose a novel broad-match mechanism, which we call the Probabilistic Broad-Match (PBM) mechanism. Different from SBM that puts together the ads bidding on all the keywords matched to a given query for the GSP auction, the GSP with PBM (denoted as PBM-GSP) randomly samples a keyword according to a predefined probability distribution and only runs the GSP auction for the ads bidding on this sampled keyword. We perform a comprehensive study on the theoretical properties of the PBM-GSP. Specifically, we study its social welfare in the worst equilibrium, in both full-information and Bayesian settings. The results show that PBM-GSP can generate larger welfare than SBM-GSP under mild conditions. Furthermore, we also study the revenue guarantee for PBM-GSP in Bayesian setting. To the best of our knowledge, this is the first work on broad-match mechanisms for GSP that goes beyond the single-slot case and the full-information setting