优化AUC的高效分类方法

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"优化AUC的高效分类方法" 在本文中，作者提出了一种高效的方法，用于构建直接优化ROC曲线下的面积（AUC）的分类器。AUC在分类社区中的重要性日益提升，因为它作为比较不同分类器性能的手段。由于大多数分类方法并未直接优化AUC，因此出现了许多直接针对AUC进行优化的分类学习方法。然而，这些方法需要大量计算AUC，导致在大数据集上表现不佳，扩展性较差。为了提高计算AUC的效率，作者基于多项式近似开发了一种方法。通过将这个近似值应用于可扩展的线性分类器的构造，他们使用梯度下降法直接优化AUC。实验结果表明，多项式近似在真实数据集上的准确性和效率都很高。 AUC（Area Under the Receiver Operating Characteristic Curve），即接收者操作特性曲线下的面积，是一种评估二分类模型性能的指标。ROC曲线描绘了真阳性率（True Positive Rate, TPR）与假阳性率（False Positive Rate, FPR）之间的关系，当改变分类阈值时，这两个指标会随之变化。AUC值越大，表示分类器区分正负样本的能力越强，理想情况下AUC为1。传统的分类方法通常关注的是精确率、召回率或F1分数等指标，而AUC作为一个整体性能的度量，不受类别不平衡问题的影响，因此在某些领域，如医学诊断或信用风险评估中，AUC成为了首选的评价标准。为了优化AUC，一些方法如RankSVM和RankBoost已被提出，但这些方法的计算复杂度较高，不适合大规模数据。文章中提出的多项式近似方法旨在解决这一问题，它减少了计算AUC的成本，使得在大样本量下也能有效地训练优化AUC的分类器。实验部分，作者对比了他们的方法与现有技术，展示了其在保持准确性的同时，能显著提高训练速度。这表明，该方法在实际应用中具有很大的潜力，特别是对于那些需要处理大量数据和快速响应的实时分类系统。 "Efficient AUC Optimization for Classification"这篇论文提供了一种新的策略，通过使用多项式近似优化AUC，不仅提升了分类器的性能，还提高了计算效率，这对于大数据环境下的二分类问题具有重要意义。这种方法的出现，可能会对未来的分类算法设计产生积极影响，推动AUC优化技术的发展。

Soft-AUC. For some cla ssiﬁcation algorithms, such as gradient descent, how-

ever, it is problematic that the statistic auc(f, D) is not continuous in f. Further-

more, another dis advantage of the AUC measure is that no weights are assigned

to the diﬀerence in sc ores; auc(f, D) fully takes into account a pair of a higher

scoring positive example with a lower scoring negative example, even if the mar-

gin is small. Both problems: the non-diﬀerentiability and the ins e ns itivity to the

diﬀerence in scores between positive and negative examples , are solved by the

introduction of the following soft-AUC statistic (parameterize d by β):

s auc

(f, D

∪ D

) :=

∈D

sigmoid

(f(t

) − f(t

))

| · |D

where sigmoid

(x) is the function

1+e

−βx

. This function approximates the step

function, but smoothes out the region around 0. For β → ∞, sigmoid

pointwise

converges to the step function. The computational cost of the soft-AUC, however,

is quadratic in the number of tuples. Similar measures have been introduced in

the literature to deal with the non-diﬀerentiability issue. We believe, however,

that soft-AUC has its own merits, and thus propose we it as a measure in its

own right.

Optimizing the AUC Directly. Recently, many new classiﬁcation algo rithms

have been proposed that dire c tly optimize the AUC mea sure [7, 3, 1, 5, 10, 9]. In

these approaches, the AUC has to be computed repeatedly, as the classiﬁer f

is being changed during the training process. Because for large datasets D, the

cost of O(|D|log(|D|)) for every computation o f the AUC-measure can be too

high, it is often measured on only a small sample of the dataset.

In this pap e r, we propose another approach for optimizing the AUC directly.

We propose the use of polynomial approximations of AUC and soft-AUC. These

approximations have the advantage that they are more accurate than sampling,

they ca n be computed in linear time, and it is possible to c ache a c oncise sum-

mary of the dataset that allows, for small changes in the classiﬁcation function,

to compute the AUC without having to re-scan the dataset.

3 Polynomial Approximation of AUC and soft-AUC

The key observation is that the indicator function 1[f(t

) < f(t

)] (resp. sig-

moid) can be approximated by a polynomial. We only give the derivation for the

AUC, because the soft-AUC case is similar.

To approximate the indicator function, we actually approximate the func-

tion H(x) = 1[x > 0], which is the well-known Heaviside step-function. The

required indicator function is then H(f(t

) − f (t

)). In Figure 1, a polynomial

(Chebyshev) approximation of H(x) has been plotted.

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优化AUC的高效分类方法

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