Title: CAKE: CAusal and collaborative proxy-tasKs lEarning for Semi-Supervised Domain Adaptation. Abstract: Semi-supervised domain adaptation (SSDA) adapts a learner to a new domain by effectively utilizing source domain data and a few labeled target samples. It is a practical yet under-investigated research topic. In this paper, we analyze the SSDA problem from two perspectives that have previously been overlooked, and correspondingly decompose it into two \emph{key subproblems}: \emph{robust domain adaptation (DA) learning} and \emph{maximal cross-domain data utilization}.  \textbf{(i)}  From a causal theoretical view, a robust DA model should distinguish the invariant ``concept'' (key clue to image label) from the nuisance of confounding factors across domains. To achieve this goal, we propose to generate \emph{concept-invariant samples} to enable the model to classify the samples through causal intervention, yielding improved generalization guarantees; \textbf{(ii)} Based on the robust DA theory, we aim to exploit the maximal utilization of rich source domain data and a few labeled target samples to boost SSDA further. Consequently, we propose a collaboratively debiasing learning framework that utilizes two complementary semi-supervised learning (SSL) classifiers to mutually exchange their unbiased knowledge, which helps unleash the potential of source and target domain training data, thereby producing more convincing pseudo-labels. Such obtained labels facilitate cross-domain feature alignment and duly improve the invariant concept learning. In our experimental study, we show that the proposed model significantly outperforms SOTA methods in terms of effectiveness and generalisability on SSDA datasets.