Convex Loss Functions for Support Vector Machines (SVMs) and Neural Networks

We propose a new convex loss for Support Vector Machines, both for the binary classification and for the regression models. Therefore, we show the mathematical derivation of the dual problems and we experiment with them on several small datasets. The minimal dimension of those datasets is due to the difficult scalability of the SVM method to bigger instances. This preliminary study should prove that using pattern correlations inside the loss function could enhance the generalisation performances. Our method consistently achieved comparable or superior performance, with improvements of up to 2.0% in F1 scores for classification tasks and 1.0% reduction in Mean Squared Error (MSE) for regression tasks across various datasets, compared to standard losses. Coherently, results show that generalisation measures are never worse than the standard losses and several times they are better. In our opinion, it should be considered a careful study of this loss, coupled with shallow and deep neural networks. In fact, we present some novel results obtained with those architectures.

An introductory Generalization of the standard SVMs loss and its applications to Shallow and Deep Neural Networks

We propose a new convex loss for SVMs, both for the binary classification and for the regression models. Therefore, we show the mathematical derivation of the dual problems and we experiment them with several small data-sets. The minimal dimension of those data-sets is due to the difficult scalability of the SVM method to bigger instances. This preliminary study should prove that using pattern correlations inside the loss function could enhance the generalisation performances. Coherently, results show that generalisation measures are never worse than the standard losses and several times they are better. In our opinion, it should be considered a careful study of this loss, coupled with shallow and deep neural networks. In fact, we present some novel results obtained with those architectures.

A Generalized Weighted Loss for SVC and MLP

Usually standard algorithms employ a loss where each error is the mere absolute difference between the true value and the prediction, in case of a regression task. In the present, we introduce several error weighting schemes that are a generalization of the consolidated routine. We study both a binary classification model for Support Vector Classification and a regression net for Multi-layer Perceptron. Results proves that the error is never worse than the standard procedure and several times it is better.

A generalized quadratic loss for SVM and Deep Neural Networks

We consider some supervised binary classification tasks and a regression task, whereas SVM and Deep Learning, at present, exhibit the best generalization performances. We extend the work [3] on a generalized quadratic loss for learning problems that examines pattern correlations in order to concentrate the learning problem into input space regions where patterns are more densely distributed. From a shallow methods point of view (e.g.: SVM), since the following mathematical derivation 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 dual variables until the primal and dual objective functions converge. In addition we propose another algorithm that tries to solve the classification problem directly from the primal problem formulation. We make also use of Multiple Kernel Learning to improve generalization performances. Moreover, we introduce for the first time a custom loss that takes in consideration pattern correlation for a shallow and a Deep Learning task. We propose some pattern selection criteria and the results on 4 UCI data-sets for the SVM method. We also report the results on a larger binary classification data-set based on Twitter, again drawn from UCI, combined with shallow Learning Neural Networks, with and without the generalized quadratic loss. At last, we test our loss with a Deep Neural Network within a larger regression task taken from UCI. We compare the results of our optimizers with the well known solver SVMlight and with Keras Multi-Layers Neural Networks with standard losses and with a parameterized generalized quadratic loss, and we obtain comparable results.