Learning data discretization via convex optimization

• Published in: Machine learning Vol. 107; no. 2; pp. 333 - 355
• Main Authors: Franc, Vojtech, Fikar, Ondrej, Bartos, Karel, Sofka, Michal
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2018; Springer Nature B.V
• Subjects: Accuracy; Artificial Intelligence; Classification; Computational geometry; Computer Science; Continuity (mathematics); Control; Convex analysis; Convexity; Discretization; Functions (mathematics); Machine learning; Mathematical models; Mechatronics; Natural Language Processing (NLP); Optimization; Robotics; Simulation and Modeling; Histograms; Piecewise linear embedding; Convex optimization; Piecewise constant embedding; Parameter discretization; Classification
• ISSN: 0885-6125; 1573-0565
• DOI: 10.1007/s10994-017-5654-4

Discretization of continuous input functions into piecewise constant or piecewise linear approximations is needed in many mathematical modeling problems. It has been shown that choosing the length of the piecewise segments adaptively based on data samples leads to improved accuracy of the subsequent processing such as classification. Traditional approaches are often tied to a particular classification model which results in local greedy optimization of a criterion function. This paper proposes a technique for learning the discretization parameters along with the parameters of a decision function in a convex optimization of the true objective. The general formulation is applicable to a wide range of learning problems. Empirical evaluation demonstrates that the proposed convex algorithms yield models with fewer number of parameters with comparable or better accuracy than the existing methods.