提出投影寻踪密度比估计新方法，解决高维数据误差问题。
Projection Pursuit Density Ratio Estimation
- 用投影寻踪降低高维数据影响，保持模型灵活性
- 理论证明估计器一致且收敛速度可保证
- 在多种任务中优于现有方法，适合高维场景
密度比估计（DRE）是机器学习中的关键任务，广泛应用于协变量偏移适应、因果推断、独立性检验等多个领域。若参数化方法模型设定错误，可能导致结果偏差；而传统非参数方法在高维数据下会遭遇维度灾难。本文提出一种基于投影寻踪（PP）近似的新型DRE方法，利用投影寻踪缓解高维影响，同时保持模型灵活性以保障估计精度。我们建立了所提估计器的一致性和收敛速率。实验结果表明，该方法在多种应用中均优于现有方法。
原文摘要 · Abstract (English)
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for estimating the density ratio possibly lead to biased results if models are misspecified, while conventional non-parametric methods suffer from the curse of dimensionality when the dimension of data is large. To address these challenges, in this paper, we propose a novel approach for DRE based on the projection pursuit (PP) approximation. The proposed method leverages PP to mitigate the impact of high dimensionality while retaining the model flexibility needed for the accuracy of DRE. We establish the consistency and the convergence rate for the proposed estimator. Experimental results demonstrate that our proposed method outperforms existing alternatives in various applications.
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