Exploring Large Feature Spaces with Hierarchical Multiple Kernel Learning

TL;DR

This paper introduces a hierarchical multiple kernel learning framework that efficiently performs kernel selection in large feature spaces using sparsity-inducing norms, improving predictive performance in supervised and unsupervised learning.

Contribution

It proposes a novel polynomial-time method for kernel selection in large decomposable kernel spaces via hierarchical multiple kernel learning.

Findings

Achieves state-of-the-art predictive performance on synthetic and UCI datasets.

Demonstrates efficient exploration of large feature spaces with sparsity-inducing norms.

Provides a polynomial-time algorithm for hierarchical kernel selection.

Abstract

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done through the penalization of predictor functions by Euclidean or Hilbertian norms. In this paper, we explore penalizing by sparsity-inducing norms such as the l1-norm or the block l1-norm. We assume that the kernel decomposes into a large sum of individual basis kernels which can be embedded in a directed acyclic graph; we show that it is then possible to perform kernel selection through a hierarchical multiple kernel learning framework, in polynomial time in the number of selected kernels. This framework is naturally applied to non linear variable selection; our extensive simulations on synthetic datasets and datasets from the UCI repository show that efficiently exploring the large feature space through sparsity-inducing norms leads to state-of-the-art predictive performance.