Kostic, Vladimir R; Lounici, Karim; Pacreau, Gregoire; Turri, Giacomo; Novelli, Pietro; Pontil, Massimiliano; (2024) Neural Conditional Probability for Uncertainty Quantification. In: Globersons, A and Mackey, L and Belgrave, D and Fan, A and Paquet, U and Tomczak, J and Zhang, C, (eds.) Advances in Neural Information Processing Systems 37 (NeurIPS 2024). (pp. pp. 1-41). NeurIPS: Vancouver, BC, Canada.

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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.

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