用可学习的量化点捕捉多模态条件分布，提升不确定性建模能力
Conditional Distribution Quantization in Machine Learning
- 提出n点条件量化，通过梯度下降学习输入X对应的多个输出点
- 在Wasserstein距离下逼近真实条件分布，支持多模态生成与不确定性量化
- 适用于图像修复等存在多种合理重建结果的任务
条件期望 𝔼(Y∣X) 常难以刻画多模态条件分布 ℒ(Y∣X) 的复杂结构。为此，我们提出使用n点条件量化——一种可通过梯度下降学习的X到Y的函数映射，以近似 ℒ(Y∣X)。该方法基于竞争性学习向量量化（CLVQ），超越单一值预测，提供多个代表性输出点以更好反映多模态特性，并能在Wasserstein距离下逼近真实条件分布。所提框架理论基础坚实，适用于不确定性量化和多模态数据生成任务。例如，在图像修复中，同一部分缺失的输入图像X可能存在多种合理重建结果。我们在合成数据和真实数据集上验证了该方法的有效性。
原文摘要 · Abstract (English)
Conditional expectation \mathbb{E}(Y \mid X) often fails to capture the complexity of multimodal conditional distributions \mathcal{L}(Y \mid X). To address this, we propose using n-point conditional quantizations--functional mappings of X that are learnable via gradient descent--to approximate \mathcal{L}(Y \mid X). This approach adapts Competitive Learning Vector Quantization (CLVQ), tailored for conditional distributions. It goes beyond single-valued predictions by providing multiple representative points that better reflect multimodal structures. It enables the approximation of the true conditional law in the Wasserstein distance. The resulting framework is theoretically grounded and useful for uncertainty quantification and multimodal data generation tasks. For example, in computer vision inpainting tasks, multiple plausible reconstructions may exist for the same partially observed input image X. We demonstrate the effectiveness of our approach through experiments on synthetic and real-world datasets.
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。