Research Paper#Machine Learning, Statistical Inference, Embeddings🔬 ResearchAnalyzed: Jan 3, 2026 19:48
Likelihood-Preserving Embeddings for Statistical Inference
Published:Dec 27, 2025 16:21
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
- •Introduces a novel framework for creating likelihood-preserving embeddings.
- •Provides a rigorous theoretical foundation with the Likelihood-Ratio Distortion metric and the Hinge Theorem.
- •Focuses on model-class-specific guarantees for practical applicability.
- •Demonstrates the potential for applications in distributed clinical inference.
Reference
“The Hinge Theorem establishes that controlling the Likelihood-Ratio Distortion metric is necessary and sufficient for preserving inference.”