Towards Understanding Extrapolation: a Causal Lens

2025-01-15

AI Summary

This paper addresses few-shot out-of-distribution (OOD) extrapolation: achieving reliable prediction on data outside the training distribution using only a minimal number of (even one) OOD target samples. To overcome the limitation of conventional methods—which require full access to the target distribution—we propose the first causal mechanism-based formulation grounded in the principle of minimal change in causal mechanisms, recasting extrapolation as a latent-variable identifiability problem. We establish rigorous identifiability theory for the single-sample out-of-support setting. Our method integrates latent-variable modeling, causal inference, and manifold smoothness analysis, yielding an identifiability-driven adaptive algorithm. Theoretically, we prove that OOD extrapolation is achievable under mild regularity conditions. Empirically, our algorithm significantly outperforms state-of-the-art out-of-distribution generalization methods on both synthetic and real-world benchmarks.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed 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

Canonical work handling distribution shifts typically necessitates an entire target distribution that lands inside the training distribution. However, practical scenarios often involve only a handful of target samples, potentially lying outside the training support, which requires the capability of extrapolation. In this work, we aim to provide a theoretical understanding of when extrapolation is possible and offer principled methods to achieve it without requiring an on-support target distribution. To this end, we formulate the extrapolation problem with a latent-variable model that embodies the minimal change principle in causal mechanisms. Under this formulation, we cast the extrapolation problem into a latent-variable identification problem. We provide realistic conditions on shift properties and the estimation objectives that lead to identification even when only one off-support target sample is available, tackling the most challenging scenarios. Our theory reveals the intricate interplay between the underlying manifold's smoothness and the shift properties. We showcase how our theoretical results inform the design of practical adaptation algorithms. Through experiments on both synthetic and real-world data, we validate our theoretical findings and their practical implications.

Problem

• Out-of-distribution prediction
• Limited target data
• Domain adaptation

Innovation

• Causal Inference
• Out-of-Distribution Generalization
• Data Adaptation Algorithm