A review of single-source unsupervised domain adaptation <s> Causality <s> Let X denote the feature and Y the target. We consider domain adaptation under three possible scenarios: (1) the marginal PY changes, while the conditional PX/Y stays the same (target shift), (2) the marginal PY is fixed, while the conditional PX/Y changes with certain constraints (conditional shift), and (3) the marginal PY changes, and the conditional PX/Y changes with constraints (generalized target shift). Using background knowledge, causal interpretations allow us to determine the correct situation for a problem at hand. We exploit importance reweighting or sample transformation to find the learning machine that works well on test data, and propose to estimate the weights or transformations by reweighting or transforming training data to reproduce the covariate distribution on the test domain. Thanks to kernel embedding of conditional as well as marginal distributions, the proposed approaches avoid distribution estimation, and are applicable for high-dimensional problems. Numerical evaluations on synthetic and real-world data sets demonstrate the effectiveness of the proposed framework. <s> BIB001 </s> A review of single-source unsupervised domain adaptation <s> Causality <s> This paper is concerned with the problem of domain adaptation with multiple sources from a causal point of view. In particular, we use causal models to represent the relationship between the features X and class label Y, and consider possible situations where different modules of the causal model change with the domain. In each situation, we investigate what knowledge is appropriate to transfer and find the optimal target-domain hypothesis. This gives an intuitive interpretation of the assumptions underlying certain previous methods and motivates new ones. We finally focus on the case where Y is the cause for X with changing PY and PX|Y, that is, PY and PX|Y change independently across domains. Under appropriate assumptions, the availability of multiple source domains allows a natural way to reconstruct the conditional distribution on the target domain; we propose to model PX|Y (the process to generate effect X from cause Y) on the target domain as a linear mixture of those on source domains, and estimate all involved parameters by matching the target-domain feature distribution. Experimental results on both synthetic and real-world data verify our theoretical results. <s> BIB002 </s> A review of single-source unsupervised domain adaptation <s> Causality <s> Domain adaptation arises in supervised learning when the training (source domain) and test (target domain) data have different distributions. Let X and Y denote the features and target, respectively, previous work on domain adaptation mainly considers the covariate shift situation where the distribution of the features P(X) changes across domains while the conditional distribution P(Y∣X) stays the same. To reduce domain discrepancy, recent methods try to find invariant components [Formula: see text] that have similar [Formula: see text] on different domains by explicitly minimizing a distribution discrepancy measure. However, it is not clear if [Formula: see text] in different domains is also similar when P(Y∣X) changes. Furthermore, transferable components do not necessarily have to be invariant. If the change in some components is identifiable, we can make use of such components for prediction in the target domain. In this paper, we focus on the case where P(X∣Y) and P(Y) both change in a causal system in which Y is the cause for X. Under appropriate assumptions, we aim to extract conditional transferable components whose conditional distribution [Formula: see text] is invariant after proper location-scale (LS) transformations, and identify how P(Y) changes between domains simultaneously. We provide theoretical analysis and empirical evaluation on both synthetic and real-world data to show the effectiveness of our method. <s> BIB003
Causality poses an underlying mechanism of why we observe domain shifts BIB001 ,  . Having some knowledge of that underlying mechanism can greatly decrease our uncertainty about assumptions that are made, as demonstrated in BIB003 ,  . For example, knowing that the source domain is produced by a camera with one set of lens settings and the target domain by another, indicates that a subspace mapping approach would be reasonable. Furthermore, knowing that certain confounding variables have been controlled for, i.e. environments in different data-collecting research institutes, is valuable as well BIB002 . It means that the shift is most likely due to other factors influencing the data collection process. Understanding the underlying mechanism that produces differences in domains and leads to new insights is one of the core practical challenges in this.