Likelihood-Preserving Embeddings for Statistical Inference

This paper addresses a critical limitation of modern machine learning embeddings: their incompatibility with classical likelihood-based statistical inference. It proposes a novel framework for creating embeddings that preserve the geometric structure necessary for hypothesis testing, confidence interval construction, and model selection. The introduction of the Likelihood-Ratio Distortion metric and the Hinge Theorem are significant theoretical contributions, providing a rigorous foundation for likelihood-preserving embeddings. The paper's focus on model-class-specific guarantees and the use of neural networks as approximate sufficient statistics highlights a practical approach to achieving these goals. The experimental validation and application to distributed clinical inference demonstrate the potential impact of this research.