Genetic Column Generation for Computing Lower Bounds for Adversarial Classification

• URL: http://arxiv.org/abs/2406.08331v1
• Date: Wed, 12 Jun 2024 15:34:42 GMT
• Title: Genetic Column Generation for Computing Lower Bounds for Adversarial Classification
• Authors: Maximilian Penka,
• Abstract summary: We investigate how ideas from Genetic Column Generation can be used to overcome the curse of dimension in computing the minimal adversarial risk in multi-class classification. In this paper we show that ideas from Genetic Column Generation can be used to overcome the curse of dimension in computing the minimal adversarial risk in multi-class classification.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent theoretical results on adversarial multi-class classification showed a similarity to the multi-marginal formulation of Wasserstein-barycenter in optimal transport. Unfortunately, both problems suffer from the curse of dimension, making it hard to exploit the nice linear program structure of the problems for numerical calculations. We investigate how ideas from Genetic Column Generation for multi-marginal optimal transport can be used to overcome the curse of dimension in computing the minimal adversarial risk in multi-class classification.

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