This research proposes EBiEOT, a new learning paradigm that utilizes inverse entropic optimal transport (OT) and data likelihood maximization to effectively learn conditional distributions in semi-supervised settings, leveraging both paired and unpaired data.
Learning conditional distributions $\pi^*(x|y)$ is crucial in machine learning, often requiring paired data, which is frequently unavailable. This paper addresses the challenge of semi-supervised learning by introducing EBiEOT, a novel method that seamlessly integrates paired and unpaired data using data likelihood maximization techniques. The approach connects these concepts with inverse entropic optimal transport (OT), enabling the establishment of an end-to-end learning algorithm for conditional distributions. The work demonstrates that EBiEOT can effectively learn these distributions simultaneously and derives a universal approximation property, ensuring that the method can theoretically recover true conditional distributions with arbitrarily small error. Empirical tests confirm the method's effectiveness, providing a strong framework for handling data scarcity.