Efficient tensor kernel methods for sparse regression

Recently, classical kernel methods have been extended by the introduction of suitable tensor kernels so to promote sparsity in the solution of the underlying regression problem. Indeed, they solve an lp-norm regularization problem, with p=m/(m-1) and m even integer, which happens to be close to a lasso problem. However, a major drawback of the method is that storing tensors requires a considerable amount of memory, ultimately limiting its applicability. In this work we address this problem by proposing two advances. First, we directly reduce the memory requirement, by introducing a new and more efficient layout for storing the data. Second, we use a Nyström-type subsampling approach, which allows for a training phase with a smaller number of data points, so to reduce the computational cost. Experiments, both on synthetic and real datasets, show the effectiveness of the proposed improvements. Finally, we take care of implementing the code in C++ so to further speed-up the computation.