论文标题
分类响应的小组稀疏logit模型的后收缩
Posterior contraction in group sparse logit models for categorical responses
论文作者
论文摘要
本文研究了具有较稀疏结构的先验的多类logit模型中的后验收率。我们将一类logit模型类别考虑，其中包括众所周知的多项式logit模型作为一种特殊情况。当预测变量自然聚集并且对于多项式logit模型中的变量选择特别有用时，组稀疏性很有用。我们为群体parse logit模型的后部收缩率提供了一个统一的平台，其中包括个人稀疏下的二进制逻辑回归。在这项研究中，没有直接施加大小限制。除了在组稀疏下建立多类logit模型的有史以来的第一个收缩特性外，这项工作还完善了有关贝叶斯二进制逻辑回归理论的最新发现。
This paper studies posterior contraction rates in multi-category logit models with priors incorporating group sparse structures. We consider a general class of logit models that includes the well-known multinomial logit models as a special case. Group sparsity is useful when predictor variables are naturally clustered and particularly useful for variable selection in the multinomial logit models. We provide a unified platform for posterior contraction rates of group-sparse logit models that include binary logistic regression under individual sparsity. No size restriction is directly imposed on the true signal in this study. In addition to establishing the first-ever contraction properties for multi-category logit models under group sparsity, this work also refines recent findings on the Bayesian theory of binary logistic regression.
