Construction of robust regression learning models to fit data with noise is an important and challenging problem of data regression. One of the ways to tackle this problem is the selection of a proper loss function showing insensitivity to noise present in the data. Since Huber function has the property that inputs with large deviations of misfit are penalized linearly and small errors are squared, we present novel robust regularized twin support vector machines for data regression based on Huber and epsilon-insensitive Huber loss functions in this study. The proposed regression models result in solving a pair of strongly convex minimization problems in simple form in primal whose solutions are obtained by functional and Newton-Armijo iterative algorithms. The finite convergence of Newton-Armijo algorithm is proved. Numerical tests are performed on noisy synthetic and benchmark datasets, and their results are compared with few popular regression learning algorithms. The comparative study clearly shows the robustness of the proposed regression methods and further demonstrates their effectiveness and suitability.
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