Neural Conditional Probability for Uncertainty Quantification

TL;DR

This paper presents Neural Conditional Probability (NCP), a neural operator-based method for efficient and accurate conditional distribution learning, enabling uncertainty quantification and statistical inference with minimal training.

Contribution

NCP introduces a novel operator-theoretic neural approach for learning conditional distributions that allows efficient inference without retraining and provides theoretical guarantees.

Findings

NCP matches or outperforms leading methods in experiments.

A minimalistic neural architecture achieves competitive results.

Theoretical guarantees ensure optimization consistency and statistical accuracy.

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.