Nonconvex classification method based on risk minimization and its application to credit approvals and medical diagnosis

利用已有的数学优化、金融工程和机器学习的研究成果，从理论上评估了E-ν分类方法的预测性能。支持向量机在实践中取得了相当的成功。然而，到目前为止，还没有令人满意的理论背景。我们提供了这样的背景，并解释了这个非凸优化问题是如何实际求解的。此外，对于金融工程中的投资组合优化问题，我们采用了机器学习中经常使用的“正则项”的概念，成功地提高了投资组合优化模型的预测性能。

Using the existing studies on mathematical optimization, financial engineering and machine learning, I theoretically evaluated the prediction performance of a classification method known as Eν-SVM. The SVM has been quite successful in practice. However, no satisfactory theoretical background existed so far. We provided such background and also explain how this nonconvex optimization problem can actually be solved. Moreover, we adopted the concept of "regularization term" that is often used in machine learning for portfolio optimization problems in financial engineering and succeeded in enhancing the prediction performance of portfolio optimization models.