标题： 具有未知类条件标签噪声的非紧致特征空间分类 显示英文标题

标题： Classification with unknown class-conditional label noise on non-compact feature spaces

摘要： 我们研究在存在未知类别条件标签噪声的情况下分类问题，其中学习者观察到的标签已被某些未知的类别依赖概率所污染。 为了获得有限样本率，以往针对未知类别条件标签噪声的分类方法要求回归函数在其极大值集上接近其极值。 我们将在这个非紧致度量空间的设置中考虑这个问题，在这种情况下，回归函数不必达到其极值。 在这种设置下，我们确定了最小最大最优学习率（忽略对数因子）。 该速率表现出有趣的阈值行为：当回归函数以足够的速度接近其极值时，最优学习率与无标签噪声情况下的速率处于同一阶。 如果回归函数更缓慢地接近其极值，则分类性能必然下降。 此外，我们提出了一种自适应算法，无需事先了解分布参数或局部密度即可达到这些速率。 这是首次识别出一种在标签噪声设置中可实现有限样本率的情况，但其速率与无标签噪声时的最优速率不同。 显示英文摘要

摘要： We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite sample rates, previous approaches to classification with unknown class-conditional label noise have required that the regression function is close to its extrema on sets of large measure. We shall consider this problem in the setting of non-compact metric spaces, where the regression function need not attain its extrema. In this setting we determine the minimax optimal learning rates (up to logarithmic factors). The rate displays interesting threshold behaviour: When the regression function approaches its extrema at a sufficient rate, the optimal learning rates are of the same order as those obtained in the label-noise free setting. If the regression function approaches its extrema more gradually then classification performance necessarily degrades. In addition, we present an adaptive algorithm which attains these rates without prior knowledge of either the distributional parameters or the local density. This identifies for the first time a scenario in which finite sample rates are achievable in the label noise setting, but they differ from the optimal rates without label noise.