Algoritmos online baseados em vetores suporte para regressão clássica e ortogonal

Abstract

In this work, we introduce a new formulation for orthogonal regression. The problem is defined as minimization of the empirical risk with respect to a tube loss function de veloped for orthogonal regression, named ρ-insensitive. The method is constructed via an stochastic gradient descent approach. The algorithm can be used in primal or in dual variables. The latter formulation allows the introduction of kernels and soft margins. To the best of our knowledge, this is the first method that allows the introduction of kernels via the so-called “kernel-trick” for orthogonal regression. Also, we present an algorithm to solve the classical regression problem using the ε-insensitive loss function. A conver gence proof that guarantees a finite number of updates is presented for this algorithm. In addition, an incremental strategy algorithm is introduced, which can be used to find sparse solutions and also an approximation to the “minimal tube” containing the data. Numerical experiments are shown and the results compared with other methods.