论文标题
标签排名的多类分类方法
A Multiclass Classification Approach to Label Ranking
论文作者
论文摘要
在多类分类中，目标是学习如何预测一个随机标签$ y $，以$ \ mathcal {y} = \ {1，\; \ ldots，\;基于观察R.V. $ x $，以$ \ mathbb {r}^q $为$ q \ geq 1 $说，通过分类规则$ g：\ mathbb {r}^q \ to \ mathcal {y} $，具有最低误差$ $ \ mathbb {p} p} \ y \ y \ y \ n neq g（n neq g（neq g（n neq））但是，在各种情况下，针对目标的任务可能更加雄心勃勃，包括对所有可能的标签值$ y $排序，可以通过减少后验概率$η_y（x）= \ mathbb {p} y = y = y = y = y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \} $来分配给$ x $。本文致力于分析此统计学习问题，多类分类和后验概率估计（回归）之间的一半，并在此处称为标签排名。我们强调了这样一个事实，即可以将其视为排名中值回归（RMR）的特定变体，其中而不是观察到分配给输入矢量$ x $的随机置换$σ$，并从Bradley-terry-terry-terry-terry-terry-luce-luce-luce-luce-luce-luce-plackett模型中绘制为有条件的偏好vectoral $（x），x（x），\; \ ldots;训练标签排名规则是顶部排名的标签$ y $，即$σ^{ - 1}（1）$。受RMR的最新结果的启发，我们证明，在适当的噪声条件下，单分类产率的单一单位（OVO）方法作为副产品，是具有压倒性概率的标签的最佳排名。除了理论保证之外，实验结果支持了本文促进的标签排名方法的相关性。
In multiclass classification, the goal is to learn how to predict a random label $Y$, valued in $\mathcal{Y}=\{1,\; \ldots,\; K \}$ with $K\geq 3$, based upon observing a r.v. $X$, taking its values in $\mathbb{R}^q$ with $q\geq 1$ say, by means of a classification rule $g:\mathbb{R}^q\to \mathcal{Y}$ with minimum probability of error $\mathbb{P}\{Y\neq g(X) \}$. However, in a wide variety of situations, the task targeted may be more ambitious, consisting in sorting all the possible label values $y$ that may be assigned to $X$ by decreasing order of the posterior probability $η_y(X)=\mathbb{P}\{Y=y \mid X \}$. This article is devoted to the analysis of this statistical learning problem, halfway between multiclass classification and posterior probability estimation (regression) and referred to as label ranking here. We highlight the fact that it can be viewed as a specific variant of ranking median regression (RMR), where, rather than observing a random permutation $Σ$ assigned to the input vector $X$ and drawn from a Bradley-Terry-Luce-Plackett model with conditional preference vector $(η_1(X),\; \ldots,\; η_K(X))$, the sole information available for training a label ranking rule is the label $Y$ ranked on top, namely $Σ^{-1}(1)$. Inspired by recent results in RMR, we prove that under appropriate noise conditions, the One-Versus-One (OVO) approach to multiclassification yields, as a by-product, an optimal ranking of the labels with overwhelming probability. Beyond theoretical guarantees, the relevance of the approach to label ranking promoted in this article is supported by experimental results.
