发表机构
School of Mathematics & Statistics（数学与统计学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高维缺失数据补全问题，基于流形假设与混合变分自编码器，采用SIR采样结合潜空间扩散模型实现符合底层几何结构的缺失值补全，性能优异且可量化不确定性、支持动态补全。
AI 中文摘要
流形假设认为高维数据集中分布在一个低维嵌入流形附近。混合变分自编码器（VAE）的最新进展为可靠提取这类底层结构提供了强大工具。得到的几何结构自然引入变量间的局部与全局关联，进而为缺失数据补全提供系统化途径。本文提出一种基于模型的补全方法，可通过采样重要性重采样（SIR）流程从条件分布 \( p(\bm{x}_{\mathrm{mis}} \mid \bm{x}_{\mathrm{obs}}) \) 中采样，还可在潜空间中联合扩散模型做进一步增强。该方法在补全缺失数据时兼顾底层几何特性，与现有最优方法相比取得了有竞争力的性能，可量化补全结果的不确定性，且因基于模型无需重跑全流程即可实现动态补全。
英文摘要
The manifold hypothesis posits that high-dimensional data are concentrated near a low-dimensional embedded manifold. Recent advances in mixture variational autoencoders (VAEs) provide a powerful tool for extracting such underlying structure in a faithful manner. The resulting geometric structure naturally introduces local and global relationships among variables, thereby providing a systematic way of imputing missing data. We propose a model-based imputation method that enables sampling from \( p(\bm{x}_{\mathrm{mis}} \mid \bm{x}_{\mathrm{obs}}) \) via a sampling-importance-resampling (SIR) procedure, which can be further augmented with a joint diffusion model in the latent space. Our method imputes missing data while respecting the underlying geometry, achieves competitive performance compared to state-of-the-art procedures, quantifies uncertainty in the imputations, and is model-based, thereby enabling on-the-fly imputation without rerunning the entire procedure.
Commentsupdate the author list and some minor text polish
