Predicting pairwise interaction affinities with ℓ0-penalized least squares-a nonsmooth bi-objective optimization based approach∗

Abstract

In this paper, we introduce a novel nonsmooth optimization-based method LMBM-Kron & ell;(0) LS for solving large-scale pairwise interaction affinity prediction problems. The aim of LMBM-Kron & ell;0LS is to produce accurate predictions using as sparse a model as possible. We apply the least squares approach with Kronecker product kernels for a loss function and a continuous formulation of & ell;(0) pseudonorm for regularization. Thus, we end up solving a nonsmooth optimization problem. In addition, we apply a specific bi-objective criterion to strike a balance between the prediction accuracy of the learned model and the sparsity of the obtained solution. We compare LMBM-Kron & ell;0LS with some state-of-the-art methods using three benchmark and two simulated data sets under four distinct experimental settings, including zero-shot learning. Moreover, both binary and continuous interaction affinity labels are considered with LMBM-Kron & ell;0LS. The results show that LMBM-Kron & ell;0LS finds sparse solutions without sacrificing too much in the prediction performance.