Kernelized Discriminant Analysis for Joint Modeling of Multivariate Categorical Responses
提出一种基于离散核回归的惩罚似然方法，用于联合建模多个分类响应变量与预测变量的关系，在响应变量多、类别多或预测变量多时优于传统方法，并在基因组数据中展示了更好的分类准确性和模型可解释性。
Modeling the joint probability mass of multiple categorical variables as a function of predictors is a fundamental task in categorical data analysis. When the number of response variables, number of categories per response, and/or the number of predictors is large, existing likelihood-based methods cannot be applied or perform poorly. In this article, we propose a novel approach which assumes a variation of the normal linear discriminant analysis model. In order to estimate unknown parameters in way that exploits dependence amongst the response variables, we propose a new penalized likelihood method based on discrete kernel regression. We propose two estimators, each of which can lead to interpretable and parsimonious fitted models. Theoretically, we establish statistical properties of our method and demonstrate a tradeoff between the statistical error and approximation error. Through simulation studies and an application to genomic data, we demonstrate that our method yields better classification accuracy and more interpretable fitted models than existing methods. Software implementing our method, as well as code for reproducing the results in this article, are available for download at https://github.com/yjin07/kernelizedDA.