mmit

我们展示了 Rigaill 等人的基于边际的区间回归算法的一个关键限制。 (2013) (L1-Linear)：仅限于建模线性模式。为此，我们创建了三个模拟数据集，每个数据集包含 200 个示例和 20 个特征。每个数据集的生成方式使得目标间隔遵循特定模式 f : R → R 根据单个特征，我们称之为信号特征。区间的宽度和 f 的真实值附近的一个小的随机偏移是随机确定的。补充材料中提供了数据生成协议的详细信息。在每个数据集上训练 MMIT（线性铰链损失）和 L1-Linear，使用交叉验证来选择超参数值。结果数据集和每个算法的预测如图 4 所示。正如预期的那样，L1-Linear 无法拟合非线性模式，但实现了对线性模式的近乎完美拟合。相比之下，MMIT 学习真实函数的逐步逼近，这是由于每个叶子预测一个常数值而产生的。注意两种算法模型的波动，这是由于使用了不相关的特征造成的。We demonstrate a key limitation of the margin-based interval regression algorithm proposed by Rigaill et al. (2013) (denoted as L1-Linear): it is restricted to modeling linear patterns. To this end, we created three simulated datasets, each containing 200 instances and 20 features. Each dataset was constructed such that the target intervals follow a specific functional pattern ( f: mathbb{R} ightarrow mathbb{R} ) based on a single feature, which we refer to as the signal feature. The width of the intervals and a small random deviation around the true value of ( f ) were randomly determined. Detailed information on the data generation protocol is provided in the supplementary materials. We trained MMIT (with linear hinge loss) and L1-Linear on each dataset, using cross-validation to select hyperparameter values. The resulting datasets and the predictions of each algorithm are illustrated in Figure 4. As expected, L1-Linear failed to fit non-linear patterns, but achieved near-perfect fitting for linear patterns. In contrast, MMIT learns a stepwise approximation of the true function, which arises from each leaf predicting a constant value. Note the fluctuations in the predictions of both algorithms, which are caused by the inclusion of irrelevant features.

搜集汇总

背景与挑战

背景概述

该数据集为模拟生成，旨在展示基于边际的区间回归算法在建模非线性模式时的局限性。它包含三个数据集，每个有200个示例和20个特征，目标区间基于信号特征遵循特定模式，用于训练和比较MMIT与L1-Linear算法。