论文标题
基于整数编程的错误校正校正输出代码设计用于鲁棒分类
Integer Programming-based Error-Correcting Output Code Design for Robust Classification
论文作者
论文摘要
错误纠正的输出代码（ECOC）提供了一种将简单二进制分类器组合到多类分类器中的原则方法。在本文中，我们研究了设计最佳ECOC的问题，以使用支持向量机（SVM）和二进制深度学习模型同时实现名义和对抗精度。与以前的文献相反，我们提出了一个整数编程（IP）公式，以设计具有理想的错误校正属性的最小代码簿。我们的工作利用IP求解器的进步来生成具有最佳保证的代码簿。为了实现障碍，我们利用IP公式中设置的约束的基本图理论结构。这使我们能够使用Edge Clique封面大大减少约束集。我们的代码手册相对于标准代码簿（例如，一个VS-ALL，ONE-VS-ONE和致密/稀疏代码）具有很高的名义精度。我们还估计了在白色盒子设置中基于ECOC的分类器的对抗精度。我们的IP生成的代码手册即使没有任何对抗性训练，也可以对对抗性扰动提供非平凡的鲁棒性。
Error-Correcting Output Codes (ECOCs) offer a principled approach for combining simple binary classifiers into multiclass classifiers. In this paper, we investigate the problem of designing optimal ECOCs to achieve both nominal and adversarial accuracy using Support Vector Machines (SVMs) and binary deep learning models. In contrast to previous literature, we present an Integer Programming (IP) formulation to design minimal codebooks with desirable error correcting properties. Our work leverages the advances in IP solvers to generate codebooks with optimality guarantees. To achieve tractability, we exploit the underlying graph-theoretic structure of the constraint set in our IP formulation. This enables us to use edge clique covers to substantially reduce the constraint set. Our codebooks achieve a high nominal accuracy relative to standard codebooks (e.g., one-vs-all, one-vs-one, and dense/sparse codes). We also estimate the adversarial accuracy of our ECOC-based classifiers in a white-box setting. Our IP-generated codebooks provide non-trivial robustness to adversarial perturbations even without any adversarial training.
