Out-Of-Domain Unlabeled Data Improves Generalization

Articles in Press

Document Type : Research Article

Authors

1 Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran

2 Department of Computer Engineering, Sharif University of Technology, Tehran, Iran

3 Sharif Center for Information Systems and Data Science, Sharif University of Technology, Tehran, Iran

10.24200/sci.2026.67230.10491

Abstract

We propose a novel framework for incorporating unlabeled data into semi-supervised classification problems, where scenarios involving the minimization of either i) adversarially robust or ii) non-robust loss functions have been considered. Notably, we allow the unlabeled samples to deviate slightly (in total variation sense) from the in-domain distribution. The core idea behind our framework is to combine Distributionally Robust Optimization (DRO) with self-supervised training. As a result, we also leverage efficient polynomial-time algorithms for the training stage. From a theoretical standpoint, we apply our framework on the classification problem of a mixture of two Gaussians in R^d, where in addition to the m independent and labeled samples from the true distribution, a set of n (usually with n≫m) out of domain and unlabeled samples are given as well. Using only the labeled data, it is known that the generalization error can be bounded by (d/m)^1/2. However, using our method on both isotropic and non-isotropic Gaussian mixture models, one can derive a new set of analytically explicit and non-asymptotic bounds which show substantial improvement on the generalization error compared to ERM. Our results underscore two significant insights: 1)out-of-domain samples, even when unlabeled, can be harnessed to narrow the generalization gap, provided that the true data distribution adheres to a form of the cluster assumption, and 2)the semi-supervised learning paradigm can be regarded as a special case of our framework when there are no distributional shifts. We validate our claims through experiments conducted on a variety of synthetic and real-world datasets.

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Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 23 June 2026

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History

  • Receive Date: 26 July 2025
  • Revise Date: 07 January 2026
  • Accept Date: 10 February 2026

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