论文标题
关于排名模型混合的可识别性
On the identifiability of mixtures of ranking models
论文作者
论文摘要
排名模型的混合物是排名问题的标准工具。但是，即使是参数可识别性的基本问题也不完全理解：具有两个Bradley-terry-luce（BTL）组件的混合模型的可识别性仍然开放。在这项工作中，我们表明，与两个组件（BTL，具有3号尺寸3或Plackett-luce的板岩的多项式逻辑模型）的流行混合物通常是可识别的，即可以识别基地真实参数，但何时来自Mesual Zero的病理子集。我们提供了一个框架，用于使用代数几何形状验证多项式系统的一般家族的解决方案数量，并将其应用于这些排名模型的这些混合物以建立通用可识别性。该框架可以更广泛地应用于其他学习模型，并可能引起独立的兴趣。
Mixtures of ranking models are standard tools for ranking problems. However, even the fundamental question of parameter identifiability is not fully understood: the identifiability of a mixture model with two Bradley-Terry-Luce (BTL) components has remained open. In this work, we show that popular mixtures of ranking models with two components (BTL, multinomial logistic models with slates of size 3, or Plackett-Luce) are generically identifiable, i.e., the ground-truth parameters can be identified except when they are from a pathological subset of measure zero. We provide a framework for verifying the number of solutions in a general family of polynomial systems using algebraic geometry, and apply it to these mixtures of ranking models to establish generic identifiability. The framework can be applied more broadly to other learning models and may be of independent interest.
