Neural Conditional Probability for Uncertainty Quantification

• URL: http://arxiv.org/abs/2407.01171v2
• Date: Sat, 31 May 2025 08:54:41 GMT
• Title: Neural Conditional Probability for Uncertainty Quantification
• Authors: Vladimir R. Kostic, Karim Lounici, Gregoire Pacreau, Pietro Novelli, Giacomo Turri, Massimiliano Pontil,
• Abstract summary: We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions.<n>By leveraging the approximation capabilities of neural networks, NCP efficiently handles a wide variety of com- plex probability distributions.<n>In experiments, we show that NCP with a 2-hidden-layer network matches or outperforms leading methods.
• Score: 22.951644463554352
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions with a focus on statistical inference tasks. NCP can be used to build conditional confidence regions and extract key statistics such as conditional quantiles, mean, and covariance. It offers streamlined learning via a single unconditional training phase, allowing efficient inference without the need for retraining even when conditioning changes. By leveraging the approximation capabilities of neural networks, NCP efficiently handles a wide variety of com- plex probability distributions. We provide theoretical guarantees that ensure both optimization consistency and statistical accuracy. In experiments, we show that NCP with a 2-hidden-layer network matches or outperforms leading methods. This demonstrates that a a minimalistic architecture with a theoretically grounded loss can achieve competitive results, even in the face of more complex architectures.

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