classification in machine learning

Sparse Multiple Kernel Learning: Alternating Best Response and Semidefinite Relaxations

  • Dimitris Bertsimas
  • Caio de Próspero Iglesias
  • Nicholas A. G. Johnson
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , , , ,

    We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing \(\ell_1\)‐regularized approaches that approximate a sparsifying penalty, we formulate the problem by imposing an explicit cardinality constraint on the kernel weights and add an \(\ell_2\) penalty for robustness. … Read more

    Pareto-optimal trees and Pareto forest: a bi-objective optimization model for binary classification

  • Marianna De Santis
  • Daniele Patria
  • Justo Puerto
    • Categories Data Science Applications, Multi-Criteria Optimization, Optimization in Data Science Tags , ,

    As inherently transparent models, classification trees play a central role in interpretable machine learning by providing easily traceable decision paths that allow users to understand how input features contribute to specific predictions. In this work, we introduce a new class of interpretable binary classification models, named Pareto-optimal trees, which aim at combining the complementary strengths … Read more

    A classification method based on a cloud of spheres

  • Tiago Dias
  • Paula Alexandra Amaral
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Quadratic Programming Tags , , ,

    In this article we propose a binary classification model to distinguish a specific class that corresponds to a characteristic that we intend to identify (fraud, spam, disease). The classification model is based on a cloud of spheres that circumscribes the points of the class to be identified. It is intended to build a model based … Read more

    Sparse Approximations with Interior Point Methods

  • Valentina De Simone
  • Daniela di Serafino
  • Jacek Gondzio
  • Spyridon Pougkakiotis
  • Marco Viola
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , , , ,

    Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience … Read more