Learning Auto-Structured Regressor from Uncertain Nonnegative Labels

Abstract

In this paper, we take the human age and pose estimation problems as examples to study automatic designing regressor from training samples with uncertain nonnegative labels. First, the nonnegative label is predicted as the square norm of a matrix, which is bilinearly transformed from the nonlinear mappings of the candidate kernels. Two transformation matrices are then learned for deriving such a matrix by solving a semi definite programming (SDP) problem, in which the uncertain label of each sample is expressed as two inequality constraints. The objective function of SDP controls the ranks of these two matrices, and consequently automatically determines the structure of the regressor. The whole framework for automatic designing regressor from samples with uncertain nonnegative labels has the following characteristics: 1) SDP formulation makes full use of the uncertain labels, instead of using conventional fixed labels; 2) regression with matrix norm naturally guarantees the nonnegativity of the labels, and greater prediction capability is achieved by integrating the squares of the matrix elements, which act as weak regressors; and 3) the regressor structure is automatically determined by the pursuit of simplicity, which potentially promotes the algorithmic generalization capability. Extensive experiments on two human age databases, FG-NET and Yamaha, as well as the Pointing'04 pose database, demonstrate encouraging estimation accuracy improvements over conventional regression algorithms.