Convex Learning of Multiple Tasks and their Structure

Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context a fundamental question is how to incorporate the tasks structure in the learning problem.We tackle this question by studying a general computational framework that allows to encode a-priori knowledge of the tasks structure in the form of a convex penalty; in this setting a variety of previously proposed methods can be recovered as special cases, including linear and non-linear approaches. Within this framework, we show that tasks and their structure can be efficiently learned considering a convex optimization problem that can be approached by means of block coordinate methods such as alternating minimization and for which we prove convergence to the global minimum.Comment: 26 pages, 1 figure, 2 table

Interference alignment for one-hop and two-hops MIMO systems with uncoordinated interference

Providing higher data rate is a momentous goal for wireless communications systems, while interference is an important obstacle to reach this purpose. To cope with this problem, interference alignment (IA) has been proposed. In this paper, we propose two rank minimization methods to enhance the performance of IA in the presence of uncoordinated interference, i.e., interference that cannot be properly aligned with the rest of the network and thus is a crucial issue. In this scenario, perfect and imperfect channel state information (CSI) cases are considered. Our proposed approaches employ the l2 and the Schatten-p norms to approximate the rank function, due to its non-convexity. Also, we propose a new convex relaxation to expand the feasible set of our optimization problem, providing lower rank solutions compared to other IA methods from the literature. In addition, we propose a modified weighted-sum method to deal with interference in the relay-aided MIMO interference channel, which employs a set of weighting parameters in order to find more solutions