Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization

Researchers propose EBiEOT, a novel semi-supervised learning framework that leverages both paired and unpaired data through likelihood maximization and inverse entropic optimal transport. The method demonstrates universal approximation properties and provides an end-to-end algorithm for learning conditional distributions, with potential applications in domain translation and other data-scarce scenarios.

This research addresses a fundamental challenge in machine learning: the scarcity of paired labeled data. Traditional supervised learning requires abundant paired samples (x,y), which are expensive and time-consuming to acquire in many real-world applications like medical imaging, cross-domain translation, and autonomous systems. The proposed EBiEOT framework elegantly bridges this gap by incorporating both limited paired data and abundant unpaired marginal distributions.

The connection to inverse entropic optimal transport is conceptually significant. Optimal transport theory has emerged as a powerful mathematical framework for understanding probability distributions and their relationships, with proven applications in generative modeling and distribution matching. By linking semi-supervised learning to this framework, the authors provide theoretical grounding through universal approximation guarantees—a critical property demonstrating the method can theoretically recover true conditional distributions with arbitrary precision.

For the broader machine learning ecosystem, this work contributes to reducing data annotation bottlenecks that currently constrain AI development in regulated industries. The availability of open-source code enhances reproducibility and adoption potential. The framework's ability to handle mixed data sources simultaneously, rather than through heuristic ensemble methods, represents a methodological advancement that could influence how practitioners approach semi-supervised problems.

The practical implications extend to domains where paired data remains prohibitively expensive. Domain adaptation, medical image synthesis, and cross-lingual translation could benefit from more principled semi-supervised approaches. Future work should evaluate computational efficiency at scale and performance benchmarking against existing semi-supervised baselines on standard datasets.

• →EBiEOT enables seamless integration of paired and unpaired data through likelihood maximization and optimal transport theory
• →Universal approximation property guarantees theoretical convergence to true conditional distributions
• →Framework addresses critical data scarcity challenges in supervised learning across multiple domains
• →Open-source implementation available, promoting reproducibility and practical adoption
• →Research bridges machine learning and optimal transport, establishing new theoretical foundations for semi-supervised learning