A generalized quadratic loss for SVM and Deep Learning
We consider some supervised binary classification tasks and a regression task, whereas SVM and Deep Learning, at present, exhibitthe best generalization performances. We extend the work [3] on a gen-eralized quadratic loss for learning problems that examines pattern cor-relations in order to concentrate the learning problem into input spaceregions where patterns are more densely distributed. From a shallowmethods point of view (e.g.: SVM), since the following mathematicalderivation of problem (9) in [3] is incorrect, we restart from problem (8)in [3] and we try to solve it with one procedure that iterates over the dualvariables until the primal and dual objective functions converge. In ad-dition we propose another algorithm that tries to solve the classificationproblem directly from the primal problem formulation. We make alsouse of Multiple Kernel Learning to improve generalization performances.Moreover, we introduce for the first time a custom loss that takes in con-sideration pattern correlation for a shallow and a Deep Learning task.We propose some pattern selection criteria and the results on 4 UCIdata-sets for the SVM method. We also report the results on a largerbinary classification data-set based on Twitter, again drawn from UCI,combined with shallow Learning Neural Networks, with and without thegeneralized quadratic loss. At last, we test our loss with a Deep NeuralNetwork within a larger regression task taken from UCI. We comparethe results of our optimizers with the well known solver SVMlightandwith Keras Multi-Layers Neural Networks with standard losses and witha parameterized generalized quadratic loss, and we obtain comparable results.