A New Nash-Probit Model for Binary Classification

• Published in: Machine Learning, Optimization, and Data Science Vol. 13164; pp. 314 - 324
• Main Authors: Suciu, Mihai-Alexandru, Lung, Rodica Ioana
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2022; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Binary classification; Nash equilibrium; Probit model
• ISBN: 3030954692; 9783030954697
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-95470-3_24

The Nash equilibrium is used to estimate the parameters of a Probit binary classification model transformed into a multiplayer game. Each training data instance is a player of the game aiming to maximize its own log likelihood function. The Nash equilibrium of this game is approximated by modifying the Covariance Matrix Adaptation Evolution Strategy to search for the Nash equilibrium by using tournament selection with a Nash ascendancy relation based fitness assignment. The Nash ascendancy relation allows the comparison of two strategy profiles of the game. The purpose of the approach is to explore the Nash equilibrium as an alternate solution concept to the maximization of the log likelihood function. Numerical experiments illustrate the behavior of this approach, showing that for some instances the Nash equilibrium based solution can be better than the one offered by the baseline Probit model.