Pseudo-Labeling for Unsupervised Domain Adaptation with Kernel GLMs

A central problem in unsupervised domain adaptation is determining what to transfer from labeled source domains to an unlabeled target domain. To handle high-dimensional observations (e.g., images), a line of approaches use deep learning to learn latent representations of the observations, which facilitate knowledge transfer in the latent space. However, existing approaches often rely on restrictive assumptions to establish identifiability of the joint distribution in the target domain, such as independent latent variables or invariant label distributions, limiting their real-world applicability. In this work, we propose a general domain adaptation framework that learns compact latent representations to capture distribution shifts relative to the prediction task and address the fundamental question of what representations should be learned and transferred. Notably, we first demonstrate that learning representations based on all the predictive information, i.e., the label's Markov blanket in terms of the learned representations, is often underspecified in general settings. Instead, we show that, interestingly, general domain adaptation can be achieved by partitioning the representations of Markov blanket into those of the label's parents, children, and spouses. Moreover, its identifiability guarantee can be established. Building on these theoretical insights, we develop a practical, nonparametric approach for domain adaptation in a general setting, which can handle different types of distribution shifts.

Source-free universal domain adaptation (SF-UniDA) adapts a pre-trained source model to an unlabeled target domain under both covariate and label shifts, without access to source data. However, existing SF-UniDA methods rely on inefficient techniques such as threshold tuning and clustering. Foundation models (FMs), known for their generalization and zero-shot capabilities, remain underexplored in SF-UniDA. In this paper, we propose a framework that leverages foundation models (LFM) for SF-UniDA. We use a vision-language model (VLM) to compute similarities between target samples and text labels, including those for unknown classes generated by prompting a large language model. The label shift type is determined by analyzing the coefficient of variation of a similarity-based sample-level score. Unknown samples are identified using a binary Gaussian mixture model fitted to another similarity-based metric. Under a consensus strategy, the pseudo-labels generated by the VLM are refined by the target model initialized with the pre-trained source model, integrating knowledge from both the source domain and foundation models. Finally, these refined pseudo-labels are used to train the target model. Extensive experiments across all possible label shifts and multiple benchmarks demonstrate the effectiveness and superiority of our proposed LFM framework. Our code is available at https://github.com/iamjingli/LFM.

This paper investigates convergence properties of regularized Nyström subsampling applied to the unsupervised domain adaptation problem under covariate shift. We focus on the low-smoothness (misspecified) case where the target function lies outside the reproducing kernel Hilbert space. By combining Tikhonov regularization with Nyström projection onto a subsampled subspace, we obtain upper bounds on the excess risk that hold with high probability and are expressed in terms of the source condition, the effective dimension, and the sample sizes. We further extend the analysis to the setting where the Radon-Nikodym derivative between the target and source marginal distributions is unknown and must be approximated, and we identify the minimal additional sample sizes required to maintain the same convergence rate as in the oracle case.