<p>The area under the receiver operating characteristic curve (AUC) finds applications in imbalance data classifying and many advanced surrogate losses are developed to solve it. In contrast, this paper considers the AUC aiming at directly solving the original AUC model by virtue of the step function (dubbed as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3013_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$l_{0/1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mrow> <mn>0</mn> <mo stretchy="false">/</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>-AUC). To this end, we first explore the optimality theory of the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3013_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$l_{0/1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mrow> <mn>0</mn> <mo stretchy="false">/</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>-AUC, e.g., the existence of the optimal solutions, P-stationary points and the relationship between them, and make a deep analysis to the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3013_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$l_{0/1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mrow> <mn>0</mn> <mo stretchy="false">/</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>-AUC to derive a working set. Then a light Newton-like method is designed to solve the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3013_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$l_{0/1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mrow> <mn>0</mn> <mo stretchy="false">/</mo> <mn>1</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>-AUC loss. Experiments on a heap of datasets show the superiority of the proposed method compared with the existing methods.</p>

Step Function based Light Newton-Like Method for AUC

期刊论文
发表日期：

2025年8月5日

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Hui Zhang,
Zijian Yu,
Naihua Xiu,
Yiju Wang

摘要

The area under the receiver operating characteristic curve (AUC) finds applications in imbalance data classifying and many advanced surrogate losses are developed to solve it. In contrast, this paper considers the AUC aiming at directly solving the original AUC model by virtue of the step function (dubbed as $l_{0/1}$ $l_{0 / 1}$ -AUC). To this end, we first explore the optimality theory of the $l_{0/1}$ $l_{0 / 1}$ -AUC, e.g., the existence of the optimal solutions, P-stationary points and the relationship between them, and make a deep analysis to the $l_{0/1}$ $l_{0 / 1}$ -AUC to derive a working set. Then a light Newton-like method is designed to solve the $l_{0/1}$ $l_{0 / 1}$ -AUC loss. Experiments on a heap of datasets show the superiority of the proposed method compared with the existing methods.