让VAE的先验更贴近数据真实分布，提升异常检测能力。
Density-Informed VAE (DiVAE): Reliable Log-Prior Probability via Density Alignment Regularization
- 用数据密度引导先验，使隐变量分布更贴合真实数据结构。
- 在合成数据和MNIST上均提升先验覆盖度与分布对齐效果。
- 计算开销小，适合需可靠不确定性估计的场景。
我们提出密度感知变分自编码器（DiVAE），一种轻量级、数据驱动的正则化方法，通过将变分自编码器的隐空间先验对数概率 $\log p_Z(z)$ 与从数据中估计的对数密度对齐，改进标准VAE仅使用简单先验而忽略数据空间密度结构的问题。DiVAE促使编码器在高密度区域分配更多后验质量，当先验可学习时，也推动其向高密度区域靠拢。该方法通过在ELBO中加入稳健且精度加权的惩罚项实现，计算开销极低。在合成数据集上，DiVAE (i) 提升了隐空间对数密度与真实分布的对齐程度，(ii) 改善了先验覆盖度，(iii) 显著提升分布外样本的不确定性校准性能；在MNIST上，它提升了先验与外部密度估计的一致性，增强模型可解释性，并改善可学习先验下的分布外检测效果。
原文摘要 · Abstract (English)
We introduce Density-Informed VAE (DiVAE), a lightweight, data-driven regularizer that aligns the VAE log-prior probability $\log p_Z(z)$ with a log-density estimated from data. Standard VAEs match latents to a simple prior, overlooking density structure in the data-space. DiVAE encourages the encoder to allocate posterior mass in proportion to data-space density and, when the prior is learnable, nudges the prior toward high-density regions. This is realized by adding a robust, precision-weighted penalty to the ELBO, incurring negligible computational overhead. On synthetic datasets, DiVAE (i) improves distributional alignment of latent log-densities to its ground truth counterpart, (ii) improves prior coverage, and (iii) yields better OOD uncertainty calibration. On MNIST, DiVAE improves alignment of the prior with external estimates of the density, providing better interpretability, and improves OOD detection for learnable priors.
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