让VAE能处理数据相关性，提升降维与分类效果
Integrating Random Effects in Variational Autoencoders for Dimensionality Reduction of Correlated Data
- 将潜在变量拆分为独立的固定部分和相关的随机部分
- 在真实与模拟数据上均显著降低重建误差和负对数似然
- 适合有空间、时间或聚类相关性的表格与图像数据
变分自编码器（VAE）广泛用于大规模表格和图像数据的降维，但通常假设数据观测相互独立。实际上，数据常存在相关性，如空间、时间或聚类结构。受线性混合模型（LMM）启发，本文提出LMMVAE：将经典VAE的潜在变量分解为固定部分（独立）和随机部分（同类簇间相关，如邻近位置或连续测量）。相应地修改了VAE架构与损失函数。LMMVAE在多种应用场景和相关性场景下的真实与模拟数据上，显著改善了未见数据的平方重建误差和负对数似然。同时，在下游任务（如监督分类）中，基于学习表征的表现也有所提升。
原文摘要 · Abstract (English)
Variational Autoencoders (VAE) are widely used for dimensionality reduction of large-scale tabular and image datasets, under the assumption of independence between data observations. In practice, however, datasets are often correlated, with typical sources of correlation including spatial, temporal and clustering structures. Inspired by the literature on linear mixed models (LMM), we propose LMMVAE -- a novel model which separates the classic VAE latent model into fixed and random parts. While the fixed part assumes the latent variables are independent as usual, the random part consists of latent variables which are correlated between similar clusters in the data such as nearby locations or successive measurements. The classic VAE architecture and loss are modified accordingly. LMMVAE is shown to improve squared reconstruction error and negative likelihood loss significantly on unseen data, with simulated as well as real datasets from various applications and correlation scenarios. It also shows improvement in the performance of downstream tasks such as supervised classification on the learned representations.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。