充分降维分布回归

中文摘要 AI 辅助

我们提出了充分降维分布回归（SRDR），一种将条件分布估计与非线性充分降维（SDR）相结合的生成式方法。它基于严格适当的评分规则对充分性进行刻画：当且仅当使用降维后的协变量预测响应相对于完整协变量在期望评分上无损失时，降维才是充分的。因此，充分降维变成了一个风险最小化问题。SRDR通过最小化能量分数来联合训练降维映射和生成式预测模型，该分数可以通过采样进行估计，无需密度评估或对抗训练。该框架可扩展到多环境数据和分类问题。我们证明了估计的条件分布在能量距离上收敛到真实分布，这意味着学习到的表示是渐近充分的。在模拟实验以及CT切片定位、超导性和数字分类的应用中，SRDR恢复了低维充分结构，并且在表示质量和预测性能上达到或超过了最先进的非线性SDR方法。

英文摘要

We propose Sufficiently Reduced Distributional Regression (SRDR), a generative method that combines conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). It builds on a characterization of sufficiency through strictly proper scoring rules: a dimension reduction is sufficient if and only if predicting the response from the reduced covariates incurs no loss in expected score relative to the full covariates. Sufficient dimension reduction thus becomes a risk minimization problem. SRDR jointly trains a dimension reduction map and a generative prediction model by minimizing the energy score, which can be estimated by sampling without density evaluation or adversarial training. The framework extends to multi-environment data and to classification. We prove that the estimated conditional distributions converge in energy distance to the true ones, which implies that the learned representation is asymptotically sufficient. In simulations and applications to CT slice localization, superconductivity, and digit classification, SRDR recovers low-dimensional sufficient structure and matches or outperforms state-of-the-art nonlinear SDR methods in representation quality and predictive performance.

发表机构

• Tsinghua University（清华大学）
• University of Washington（华盛顿大学）

机构由 AI 辅助整理，请以论文原文为准。