Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations

Abstract:Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2607.16725 [stat.ML]

(or arXiv:2607.16725v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.16725 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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