  Unsupervised domain adaptation is critical to many real-world applications
where label information is unavailable in the target domain. In general,
without further assumptions, the joint distribution of the features and the
label is not identifiable in the target domain. To address this issue, we rely
on the property of minimal changes of causal mechanisms across domains to
minimize unnecessary influences of distribution shifts. To encode this
property, we first formulate the data-generating process using a latent
variable model with two partitioned latent subspaces: invariant components
whose distributions stay the same across domains and sparse changing components
that vary across domains. We further constrain the domain shift to have a
restrictive influence on the changing components. Under mild conditions, we
show that the latent variables are partially identifiable, from which it
follows that the joint distribution of data and labels in the target domain is
also identifiable. Given the theoretical insights, we propose a practical
domain adaptation framework called iMSDA. Extensive experimental results reveal
that iMSDA outperforms state-of-the-art domain adaptation algorithms on
benchmark datasets, demonstrating the effectiveness of our framework.
