On Causality in Domain Adaptation and Semi-Supervised Learning: an Information-Theoretic Analysis for Parametric Models

• URL: http://arxiv.org/abs/2205.04641v2
• Date: Mon, 16 Sep 2024 13:48:17 GMT
• Title: On Causality in Domain Adaptation and Semi-Supervised Learning: an Information-Theoretic Analysis for Parametric Models
• Authors: Xuetong Wu, Mingming Gong, Jonathan H. Manton, Uwe Aickelin, Jingge Zhu,
• Abstract summary: We study the learning performance of prediction in the target domain from an information-theoretic perspective. We show that in causal learning, the excess risk depends on the size of the source sample at a rate of $O(frac1m)$ only if the labelling distribution between the source and target domains remains unchanged. In anti-causal learning, we show that the unlabelled data dominate the performance at a rate of typically $O(frac1n)$.
• Score: 40.97750409326622
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent advancements in unsupervised domain adaptation (UDA) and semi-supervised learning (SSL), particularly incorporating causality, have led to significant methodological improvements in these learning problems. However, a formal theory that explains the role of causality in the generalization performance of UDA/SSL is still lacking. In this paper, we consider the UDA/SSL scenarios where we access $m$ labelled source data and $n$ unlabelled target data as training instances under different causal settings with a parametric probabilistic model. We study the learning performance (e.g., excess risk) of prediction in the target domain from an information-theoretic perspective. Specifically, we distinguish two scenarios: the learning problem is called causal learning if the feature is the cause and the label is the effect, and is called anti-causal learning otherwise. We show that in causal learning, the excess risk depends on the size of the source sample at a rate of $O(\frac{1}{m})$ only if the labelling distribution between the source and target domains remains unchanged. In anti-causal learning, we show that the unlabelled data dominate the performance at a rate of typically $O(\frac{1}{n})$. These results bring out the relationship between the data sample size and the hardness of the learning problem with different causal mechanisms.

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