B1259
Title: Metric learning via cross-validation
Authors: Linlin Dai - Southwestern University of Finance and Economics (China) [presenting]
Abstract: A cross-validation metric learning approach is presented for learning a distance metric for dimension reduction in the multiple-index model. The leave-one-out cross-validation-type loss function is minimized, where a metric-based kernel-smoothing function approximates the unknown link function. It is deemed to be the first application for the reduction of the dimensionality for multiple-index models in a framework of metric learning. The resulting metric contains crucial information on the central mean sub-space and the optimal kernel-smoothing bandwidth. Under weak assumptions on the design of predictors, asymptotic theories are established for the consistency and convergence rate of estimated directions as well as the optimal rate of bandwidth. Furthermore, a novel estimation procedure is developed for determining the structural dimension of the central mean subspace. It is relatively easy to implement numerically by employing fast gradient-based algorithms. Various empirical studies illustrate its advantages over other existing methods.
