用配对的变分自编码器实现条件生成与最优传输映射。
Paired Wasserstein Autoencoders for Conditional Sampling
- 设计双自编码器结构，共享潜在空间实现最优传输耦合。
- 在成本一致约束下，可从耦合分布中进行条件采样。
- 适用于需要精准数据映射与条件生成的任务场景。
生成式自编码器通过联合优化的编码器-解码器对学习数据分布的紧凑潜在表示。其中，沃瑟斯坦自编码器（WAE）最小化一个松弛的最优传输（OT）目标，通过代价最小化的联合分布（OT耦合）来衡量分布间的相似性。除了分布匹配，神经最优传输方法还旨在通过OT耦合学习两个数据分布之间的映射。基于WAE损失的构造，我们推导出一种新损失函数，可通过两个具有共享潜在空间的配对WAE实现从OT型耦合中的采样。所得到的全参数化联合分布能够：(i) 通过确定性编码器学习两个数据分布间代价最优的传输映射；在成本一致性约束下，进一步实现(ii) 通过随机解码器从OT型耦合中进行条件采样。作为概念验证，我们使用具有已知且可可视化的边缘分布和条件分布的合成数据进行实验。
原文摘要 · Abstract (English)
Generative autoencoders learn compact latent representations of data distributions through jointly optimized encoder--decoder pairs. In particular, Wasserstein autoencoders (WAEs) minimize a relaxed optimal transport (OT) objective, where similarity between distributions is measured through a cost-minimizing joint distribution (OT coupling). Beyond distribution matching, neural OT methods aim to learn mappings between two data distributions induced by an OT coupling. Building on the formulation of the WAE loss, we derive a novel loss that enables sampling from OT-type couplings via two paired WAEs with shared latent space. The resulting fully parametrized joint distribution yields (i) learned cost-optimal transport maps between the two data distributions via deterministic encoders. Under cost-consistency constraints, it further enables (ii) conditional sampling from an OT-type coupling through stochastic decoders. As a proof of concept, we use synthetic data with known and visualizable marginal and conditional distributions.
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