Neural Conditional Probability for Uncertainty Quantification
Vladimir R Kostic, gregoire pacreau, Giacomo Turri, Pietro Novelli, Karim Lounici, Massimiliano Pontil
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 complex 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.
BibTeX
@inproceedings{
kostic2024neural,
title={Neural Conditional Probability for Uncertainty Quantification},
author={Vladimir R Kostic and gregoire pacreau and Giacomo Turri and Pietro Novelli and Karim Lounici and Massimiliano Pontil},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=zXfhHJnMB2}
}