Pareto-Path Multi-Task Multiple Kernel Learning

A traditional and intuitively appealing Multi-Task Multiple Kernel Learning (MT-MKL) method is to optimize the sum (thus, the average) of objective functions with (partially) shared kernel function, which allows information sharing amongst tasks. We point out that the obtained solution corresponds to a single point on the Pareto Front (PF) of a Multi-Objective Optimization (MOO) problem, which considers the concurrent optimization of all task objectives involved in the Multi-Task Learning (MTL) problem. Motivated by this last observation and arguing that the former approach is heuristic, we propose a novel Support Vector Machine (SVM) MT-MKL framework, that considers an implicitly-defined set of conic combinations of task objectives. We show that solving our framework produces solutions along a path on the aforementioned PF and that it subsumes the optimization of the average of objective functions as a special case. Using algorithms we derived, we demonstrate through a series of experimental results that the framework is capable of achieving better classification performance, when compared to other similar MTL approaches.Comment: Accepted by IEEE Transactions on Neural Networks and Learning System

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field