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arXiv 2502.07151cs.LG
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机器学习中的条件分布量化

Conditional Distribution Quantization in Machine Learning

FOXSTREAM;ESPCI PSL(巴黎高等物理化工学院,PSL大学)

Blaise Delattre, Sylvain Delattre, Alexandre Vérine, Alexandre Allauzen

AI总结:

针对条件期望难以捕捉多模态条件分布复杂性的问题,提出可通过梯度下降学习的n点条件量化方法,适配CLVQ实现Wasserstein距离下的条件分布逼近,经实验验证可用于不确定性量化与多模态生成任务。

摘要:

条件期望$\boldsymbol{\rm E}(Y \mid X)$往往无法捕捉多模态条件分布$\n\mathcal{L}(Y \mid X)$的复杂性。为解决这一问题,我们提出使用n点条件量化——可通过梯度下降学习的X的函数映射——来逼近$\mathcal{L}(Y \mid X)$。该方法适配了Competitive Learning Vector Quantization(CLVQ,竞争学习向量量化),专为条件分布定制。它突破了单值预测的局限,能提供多个更能体现多模态结构的代表点,可在Wasserstein距离下逼近真实条件分布。所得框架具备理论基础,可用于不确定性量化和多模态数据生成任务,例如计算机视觉图像修复中,同一部分观测的输入图像X可能存在多种合理重建结果。我们通过合成数据集与真实数据集上的实验验证了该方法的有效性。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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