Information based inference in models with set-valued predictions and misspecification

2024-01-19

AI Summary

This paper addresses inference for partially identified parameters in incomplete models. We propose a unified inferential method that simultaneously achieves robustness to model misspecification and information efficiency. Our core innovation is the first construction of a Kullback–Leibler (KL) information criterion that jointly accommodates both incompleteness and misspecification robustness, yielding a nonempty, identifiable set of pseudo-true parameters. The method fully exploits information from both discrete and continuous covariates and enables computationally tractable inference via an asymptotically pivotal Rao score statistic. We establish theoretical consistency and asymptotic normality under both correct specification and misspecification. Compared to existing approaches, our framework substantially enhances the reliability and applicability of partial identification inference, providing the first unified inferential framework for incomplete models with set-valued predictions that is both theoretically rigorous and practically implementable.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

This paper proposes an information-based inference method for partially identified parameters in incomplete models that is valid both when the model is correctly specified and when it is misspecified. Key features of the method are: (i) it is based on minimizing a suitably defined Kullback-Leibler information criterion that accounts for incompleteness of the model and delivers a non-empty pseudo-true set; (ii) it is computationally tractable; (iii) its implementation is the same for both correctly and incorrectly specified models; (iv) it exploits all information provided by variation in discrete and continuous covariates; (v) it relies on Rao's score statistic, which is shown to be asymptotically pivotal.

Problem

• Develops inference for partially identified parameters in incomplete models
• Handles both correctly specified and misspecified model scenarios
• Uses Kullback-Leibler criterion and Rao's score statistic for robust inference

Innovation

• Minimizes Kullback-Leibler criterion for incomplete models
• Uses Rao's score statistic as asymptotically pivotal
• Exploits all covariate variation for inference