Weighted SVM (or fuzzy SVM) is the most widely used SVM variant owning its effectiveness to the use of instance weights. Proper selection of the instance weights can lead to increased generalization performance. In this work, we extend the span error bound theory to weighted SVM and we introduce effective hyperparameter selection methods for the weighted SVM algorithm. The significance of the presented work is that enables the application of span bound and span-rule with weighted SVM. The span bound is an upper bound of the leave-one-out error that can be calculated using a single trained SVM model. This is important since leave-one-out error is an almost unbiased estimator of the test error. Similarly, the span-rule gives the actual value of the leave-one-out error. Thus, one can apply span bound and span-rule as computationally lightweight alternatives of leave-one-out procedure for hyperparameter selection. The main theoretical contributions are: (a) we prove the necessary and sufficient condition for the existence of the span of a support vector in weighted SVM; and (b) we prove the extension of span bound and span-rule to weighted SVM. We experimentally evaluate the span bound and the span-rule for hyperparameter selection and we compare them with other methods that are applicable to weighted SVM: the $K$-fold cross-validation and the $ξ-α$ bound. Experiments on 14 benchmark data sets and data sets with importance scores for the training instances show that: (a) the condition for the existence of span in weighted SVM is satisfied almost always; (b) the span-rule is the most effective method for weighted SVM hyperparameter selection; (c) the span-rule is the best predictor of the test error in the mean square error sense; and (d) the span-rule is efficient and, for certain problems, it can be calculated faster than $K$-fold cross-validation.
A Novel Orthogonal Direction Mesh Adaptive Direct Search Approach for SVM Hyperparameter Tuning
École de Technologie Supérieure - Université du Québec（魁北克大学高等技术学院）；University of Santa Catarina（圣卡塔琳娜联邦大学）；Pontifícia Universidade Católica do Paraná（巴拉那天主教大学）
A meta-learning recommender system for hyperparameter tuning: predicting when tuning improves SVM classifiers
Federal Technology University（联邦技术大学）；University of São Paulo（圣保罗大学）；Universidade Estadual Paulista（保利斯塔州立大学）；Eindhoven University of Technology（埃因霍温理工大学）
Alleviating Hyperparameter-Tuning Burden in SVM Classifiers for Pulmonary Nodules Diagnosis with Multi-Task Bayesian Optimization
Yau Mathematical Sciences Center Tsinghua University（姚数学科学中心清华大学）；The First Affiliated Hospital of Guangzhou Medical University（广州医科大学第一附属医院）；China State Key Laboratory of Respiratory Disease（中国呼吸疾病国家重点实验室）；Academy of Mathematics and Systems Science Chinese Academy of Sciences（数学科学学院中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Thoracic Surgery and Oncology The First Affiliated Hospital of Guangzhou Medical University（胸外科与肿瘤科广州医科大学第一附属医院）
A One-Class Support Vector Machine Calibration Method for Time Series Change Point Detection
Department of EECS, University of California, Berkeley（加州大学伯克利分校电子工程与计算机科学系）；California Institute of Technology（加州理工学院）；Institute of Data Science, National University of Singapore（新加坡国立大学数据科学研究所）
Auto-WEKA: Combined Selection and Hyperparameter Optimization of Classification Algorithms
University of British Columbia（不列颠哥伦比亚大学）
存在许多不同的机器学习算法;考虑到每个算法的超参数，总体上存在大量可能的替代方案。我们考虑的问题，同时选择一个学习算法和设置其超参数，超越以前的工作，解决这些问题的孤立。我们表明，这个问题可以通过一个完全自动化的方法来解决，利用贝叶斯优化的最新创新。具体来说，我们考虑了广泛的特征选择技术（结合3搜索和8评估方法）和WEKA中实现的所有分类方法，跨越2集成方法，10元方法，27个基础分类器，和每个分类器的超参数设置。在来自UCI存储库的21个流行数据集、KDD Cup 09、MNIST数据集的变体和CIFAR-10上，我们显示出的分类性能通常比使用标准选择/超参数优化方法要好得多。我们希望我们的方法将帮助非专家用户更有效地识别适合其应用程序的机器学习算法和超参数设置，从而提高性能。
Quantum Kernel Methods: Convergence Theory, Separation Bounds and Applications to Marketing Analytics
Facultat Economia i Empresa, Universitat de Barcelona（巴塞罗那大学经济学院）；Department of Law and Economics, University Mediterranea of Reggio Calabria（雷焦卡拉布里亚地中海大学法律与经济学系）
