通过模型排序进行模型选择
Model Selection Through Model Sorting
AI总结：
本研究提出基于嵌套模型连续经验超额风险PAC界的NER与S-NER模型选择方法，可高概率选出真实模型阶数与最简约风险模型，在线性回归和UCR数据集分类任务中表现优异。
摘要：
我们提出了一种选择最优数据模型的新方法。基于嵌套模型的独有性质，我们找到了包含风险最小化预测器的最简约模型。我们证明了两个连续嵌套模型的最小经验风险差值（称为连续经验超额风险，SEER）上存在概率近似正确（PAC）界。基于这些界，我们提出了一种名为嵌套经验风险（NER）的模型阶数选择方法。通过排序嵌套经验风险（S-NER）方法对模型进行智能排序，最小风险得以降低。我们构建了一个检验，用于预测扩展模型是否会降低最小风险。以高概率，NER和S-NER分别能选出真实模型阶数和包含风险最小化预测器的最简约模型。我们将S-NER模型选择应用于线性回归，结果表明，无需任何先验信息的S-NER方法，其准确率能够优于借助真实模型阶数先验知识的特征排序算法，如正交匹配追踪（OMP）。此外，在UCR数据集上，NER方法大幅降低了UCR数据集分类的复杂度，而准确率损失可忽略不计。
英文摘要：
We propose a novel approach to select the best model of the data. Based on the exclusive properties of the nested models, we find the most parsimonious model containing the risk minimizer predictor. We prove the existence of probable approximately correct (PAC) bounds on the difference of the minimum empirical risk of two successive nested models, called successive empirical excess risk (SEER). Based on these bounds, we propose a model order selection method called nested empirical risk (NER). By the sorted NER (S-NER) method to sort the models intelligently, the minimum risk decreases. We construct a test that predicts whether expanding the model decreases the minimum risk or not. With a high probability, the NER and S-NER choose the true model order and the most parsimonious model containing the risk minimizer predictor, respectively. We use S-NER model selection in the linear regression and show that, the S-NER method without any prior information can outperform the accuracy of feature sorting algorithms like orthogonal matching pursuit (OMP) that aided with prior knowledge of the true model order. Also, in the UCR data set, the NER method reduces the complexity of the classification of UCR datasets dramatically, with a negligible loss of accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
