Nonparametric Identification of Latent Concepts

2025-09-30

AI Summary

This paper addresses the identifiability of latent concepts in multi-class observational data, where concept types, functional forms, and parametric generative models are unknown. Method: We propose the first nonparametric theoretical framework that requires no prior assumptions on concept structure or data generation. Inspired by human cross-category comparison in cognition, we formalize this mechanism as a theoretical foundation, enabling local identification of concepts and simultaneous recovery of the latent structural relationships between classes and concepts. Contribution/Results: Our framework breaks reliance on global conditional independence assumptions, supporting compositional reasoning and out-of-distribution generalization. Experiments on synthetic and real-world datasets demonstrate that latent concepts are uniquely identifiable under sufficient observational diversity; even under partial observability, identification achieves theoretical optimality. This work establishes the first universal identifiability guarantee for unsupervised concept learning.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Unsupervised & Self-Supervised Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling

Abstract

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

Problem

• Developing theoretical framework for latent concept identifiability
• Ensuring concept recovery without parametric assumptions
• Providing guarantees under diverse observation conditions

Innovation

• Nonparametric concept identification without parametric assumptions
• Using diverse observation classes for latent concept recovery
• Local comparison guarantees for flexible concept extraction