Conditional-Independence-Regularized Distributional Autoencoders for Mixed-Type Data

2026-08-20

AI Summary

本文提出了一种条件独立正则化分布自编码器方法，通过条件分布匹配和结构正则化来学习混合类型数据的低维表示，解决了现有方法在恢复数据完整条件分布上的不足。

Abstract

Mixed-type data containing both numerical and categorical variables arise in many scientific and real-world applications. Existing representation learning and generative modeling approaches typically focus either on reconstruction accuracy or unconditional data generation, but often fail to recover the full conditional distribution of the data while preserving interpretable structural relationships between heterogeneous variable types. In this work, we introduce Conditional-Independence-Regularized Distributional Autoencoders, a framework for learning low-dimensional representations of mixed-type data through conditional distribution matching and structural regularization. Our method combines an energy-score-based objective for numerical variables, a likelihood-based objective for categorical variables, and an auxiliary conditional independence regularization term encouraging the learned representation to capture the dependence between numerical and categorical components. We provide theoretical analysis showing that the optimal representation balances unexplained numerical variability, conditional entropy of categorical variables, and residual conditional dependence. Empirically, the proposed method achieves strong performance on both synthetic and real-world datasets, substantially improving categorical distribution recovery, achieving competitive overall conditional distribution recovery, and preserving mixed-type dependence structure. The code has been made available at GitHub.

Problem

• mixed-type data
• conditional distribution
• heterogeneous variable types

Innovation

• Conditional-Independence-Regularized
• Distributional Autoencoders
• Mixed-Type Data
• Energy-Score-Based Objective
• Likelihood-Based Objective