Given a finite i.i.d. dataset of the form (yi, Xi), the Single Index Model (SIM) learning problem is to estimate a regression of the form u o f(xi) where u is some Lipschitz-continuous nondecreasing function and / is a linear function. This paper applies Vapnik's Structural Risk Minimization principle to SIM learning. I show that a risk structure for the space of model functions/gives a risk structure for the space of functions u o f. Second, I provide a practical learning formulation for SIM using a risk structure defined by margin-based capacity control. The new learning formulation is compared with support vector regression.
Thomas Vacek, A practical SIM learning formulation with margin capacity control, Proceedings of 2014 International Joint Conference on Neural Networks (IJCNN), IEEE, June 2014, pp. 4160–4167.