Dimension reduction of high-dimension categorical data with two or multiple responses considering interactions between responses

TL;DR

This paper introduces a novel iterative dimension reduction method for high-dimensional categorical data with multiple responses, effectively capturing interactions and outperforming existing techniques in real data applications.

Contribution

The paper develops a new efficient iterative procedure for dimension reduction in multi-response categorical data, with theoretical guarantees and improved empirical performance.

Findings

Method successfully recovers oracle estimators with high probability.

Outperforms existing methods in multiple-response data analysis.

Provides meaningful insights in real datasets.

Abstract

This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of the proposed method under the two- and multiple-response models, demonstrating the uniqueness of the proposed estimator and with the high probability that the proposed method recovers the oracle least squares estimators. For data analysis, we demonstrate that the proposed method is efficient in the multiple-response model and performs better than some existing methods built in the multiple-response models. We apply this modeling and the proposed method to an adult dataset and right heart catheterization dataset and obtain meaningful results.