Proximal Multitask Learning over Networks with Sparsity-inducing Coregularization

In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by non-differentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of $\ell_1$-norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy

High-performance Kernel Machines with Implicit Distributed Optimization and Randomization

In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the underlying statistical dependencies. Kernel methods fit this need well, as they constitute a versatile and principled statistical methodology for solving a wide range of non-parametric modelling problems. However, their high computational costs (in storage and time) pose a significant barrier to their widespread adoption in big data applications. We propose an algorithmic framework and high-performance implementation for massive-scale training of kernel-based statistical models, based on combining two key technical ingredients: (i) distributed general purpose convex optimization, and (ii) the use of randomization to improve the scalability of kernel methods. Our approach is based on a block-splitting variant of the Alternating Directions Method of Multipliers, carefully reconfigured to handle very large random feature matrices, while exploiting hybrid parallelism typically found in modern clusters of multicore machines. Our implementation supports a variety of statistical learning tasks by enabling several loss functions, regularization schemes, kernels, and layers of randomized approximations for both dense and sparse datasets, in a highly extensible framework. We evaluate the ability of our framework to learn models on data from applications, and provide a comparison against existing sequential and parallel libraries.Comment: Work presented at MMDS 2014 (June 2014) and JSM 201