Neural Conditional Probability for Uncertainty Quantification

2024-07-01

Neural Information Processing Systems

AI Summary

To address the inefficiency of repeatedly retraining models for conditional distribution modeling—required for statistical inference tasks such as conditional confidence intervals, quantiles, means, and covariance estimation—this paper proposes Neural Conditional Probability (NCP). NCP introduces a single-stage, unconditional training paradigm grounded in operator theory, enabling generalization to arbitrary new conditioning values without retraining. It employs deep neural networks to approximate conditional distributions and incorporates a theoretically justified loss function that bridges functional analysis and statistical learning, ensuring both optimization consistency and statistical accuracy. Experiments demonstrate that even with only two hidden layers, NCP matches or surpasses state-of-the-art methods across multiple benchmark tasks, validating the effectiveness of its minimalist architecture and rigorously designed loss.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Learning conditional distributions for statistical inference tasks
• Building conditional confidence regions and extracting key statistics
• Handling complex distributions via neural networks without retraining

Innovation

• Neural Conditional Probability for distribution learning
• Single unconditional training for efficient inference
• Minimalistic architecture with theoretical guarantees