DnNP：在 Neural Processes 中显式建模输入噪声的变分去噪方法

实验覆盖合成数据与真实数据：在基于真实空气质量传感器的 PM2.5 空间插值任务上，DnNP 相对标准 NP 将 RMSE 最高降低 30%，NLL 最高降低 73%。理论上，作者证明噪声输入下的 Bayes 最优预测器属于 DnNP 模型类，而使用固定观测方差的 plug-in 模型存在不可消除的 KL 散度差距，DnNP 则可以避开这一差距。

DnNP: Denoising Input Uncertainty in Neural Processes

Neural Processes (NPs) are flexible meta-learning models capable of uncertainty quantification across diverse applications. However, the standard NP framework assumes access to noise-free inputs. This is unrealistic in many practical settings, where sensor noise or measurement errors are unavoidable. This discrepancy between model assumptions and real-world data can significantly degrade prediction quality and uncertainty estimates. We introduce Denoising Neural Processes (DnNPs), a principled extension of the NP framework that explicitly models input uncertainty. We train DnNPs via variational inference. DnNPs jointly learn to denoise corrupted inputs and perform meta-learning, making them robust to noisy training data. We demonstrate DnNPs' effectiveness on both synthetic and real-world datasets, showing consistent improvements in prediction and uncertainty quantification compared to standard NPs. On PM2.5 spatial interpolation from real-world air quality sensors, DnNP reduces RMSE by up to 30% and NLL by up to 73% relative to standard NPs. We also provide theoretical grounding: we show that the Bayes-optimal predictor under noisy inputs belongs to the DnNP model class, and that plug-in models with fixed observation variance incur an irreducible KL divergence gap that DnNP provably avoids.

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信源核验说明：本文原始线索采编自「arXiv cs.LG」（@Fatemeh Tohidian, Chengzhi Shi, Soomi Lee, Matthew Elia, Amy Mueller, Stratis Ioannidis, Jennifer Dy），经 AITOP 多维评分管线结构化提炼。