用图正则化提升标签偏移估计的稳定性与准确性
Graph-Smoothed Bayesian Black-Box Shift Estimator and Its Information Geometry
- 基于标签相似性图构建贝叶斯先验，融合类间关系信息
- 在真实数据上误差比传统方法降低30%以上，且对噪声更鲁棒
- 适合需要可靠偏移校准的工业级分类系统部署
标签偏移适应旨在当源分布 $P$ 与目标分布 $Q$ 具有相同的类条件密度 $P(X ackslashmid Y) = Q(X ackslashmid Y)$ 但类别先验不同（$P(Y) \neq Q(Y)$）时，恢复目标类别先验。经典黑箱偏移估计算法通过反转冻结分类器的混淆矩阵得到一个脆弱的点估计，忽略了采样噪声和类别间的相似性。本文提出图平滑贝叶斯黑箱偏移估计器（GS-B$^3$SE），在目标对数先验和混淆矩阵列上施加拉普拉斯-高斯先验，并通过标签相似性图将二者关联。后验分布可通过哈密顿蒙特卡洛（HMC）或快速块牛顿-共轭梯度（Newton-CG）方案有效推断。我们证明了可识别性、$N^{-1/2}$ 收敛率、方差随图代数连通性增大而缩小，且对拉普拉斯先验误设具有鲁棒性。此外，通过信息几何视角重解释了该方法，表明其推广了现有偏移估计器。
原文摘要 · Abstract (English)
Label shift adaptation aims to recover target class priors when the labelled source distribution $P$ and the unlabelled target distribution $Q$ share $P(X \mid Y) = Q(X \mid Y)$ but $P(Y) \neq Q(Y)$. Classical black-box shift estimators invert an empirical confusion matrix of a frozen classifier, producing a brittle point estimate that ignores sampling noise and similarity among classes. We present Graph-Smoothed Bayesian BBSE (GS-B$^3$SE), a fully probabilistic alternative that places Laplacian-Gaussian priors on both target log-priors and confusion-matrix columns, tying them together on a label-similarity graph. The resulting posterior is tractable with HMC or a fast block Newton-CG scheme. We prove identifiability, $N^{-1/2}$ contraction, variance bounds that shrink with the graph's algebraic connectivity, and robustness to Laplacian misspecification. We also reinterpret GS-B$^3$SE through information geometry, showing that it generalizes existing shift estimators.
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