解决分布差异大时密度比估计不稳的问题，提升准确性与鲁棒性。
Dequantified Diffusion-Schr{ö}dinger Bridge for Density Ratio Estimation
- 用去量化扩散桥扩展支持范围，稳定时间得分
- 结合最优传输求解薛定谔桥，提升估计精度
- 适合高维分布或支持域不重叠的场景
密度比估计是处理 f-散度任务的基础，但现有方法在分布显著不同或支持域重叠不足时表现不佳，即存在密度鸿沟和支撑鸿沟问题。此外，以往方法在边界附近产生发散的时间得分，导致不稳定。我们提出 D³RE 框架，实现鲁棒、稳定且高效的密度比估计。设计去量化扩散桥插值器（DDBI），通过扩散桥与高斯去量化扩大支持覆盖并稳定时间得分。在此基础上，提出的去量化薛定谔桥插值器（DSBI）引入最优传输求解薛定谔桥问题，提升准确性和效率。理论上，该方法提供统一逼近与有界时间得分；实验上，在互信息与密度估计任务中优于基线。
原文摘要 · Abstract (English)
Density ratio estimation is fundamental to tasks involving $f$-divergences, yet existing methods often fail under significantly different distributions or inadequately overlapping supports -- the density-chasm and the support-chasm problems. Additionally, prior approaches yield divergent time scores near boundaries, leading to instability. We design $\textbf{D}^3\textbf{RE}$, a unified framework for \textbf{robust}, \textbf{stable} and \textbf{efficient} density ratio estimation. We propose the dequantified diffusion bridge interpolant (DDBI), which expands support coverage and stabilizes time scores via diffusion bridges and Gaussian dequantization. Building on DDBI, the proposed dequantified Schr{ö}dinger bridge interpolant (DSBI) incorporates optimal transport to solve the Schr{ö}dinger bridge problem, enhancing accuracy and efficiency. Our method offers uniform approximation and bounded time scores in theory, and outperforms baselines empirically in mutual information and density estimation tasks.
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