Unsupervised Domain Adaptation aims to learn a model on a source domain with labeled data in order to perform well on unlabeled data of a target domain. Current approaches focus on learning . It relies on the assumption that such representations are well-suited for learning the supervised task in the target domain. We rather believe that a better and minimal assumption for performing Domain Adaptation is the hypothesis. Such approach consists in learning a representation of the data such that the label distribution conditioned on this representation is domain invariant. From the Hidden Covariate Shift assumption, we derive an optimization procedure which learns to match an estimated joint distribution on the target domain and a re-weighted joint distribution on the source domain. The re-weighting is done in the representation space and is learned during the optimization procedure. We show on synthetic data and real world data that our approach deals with both and . We report state-of-the-art performances on Amazon Reviews dataset blitzer2007biographies demonstrating the viability of this approach.
@cite_37: 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 τ (X) that have similar P(τ (X)) on different domains by explicitly minimizing a distribution discrepancy measure. However, it is not clear if P(Y|τ (X)) 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 P(τ (X)|Y) 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.
@cite_15: Top-performing deep architectures are trained on massive amounts of labeled data. In the absence of labeled data for a certain task, domain adaptation often provides an attractive option given that labeled data of similar nature but from a different domain (e.g. synthetic images) are available. Here, we propose a new approach to domain adaptation in deep architectures that can be trained on large amount of labeled data from the source domain and large amount of unlabeled data from the target domain (no labeled target-domain data is necessary). As the training progresses, the approach promotes the emergence of "deep" features that are (i) discriminative for the main learning task on the source domain and (ii) invariant with respect to the shift between the domains. We show that this adaptation behaviour can be achieved in almost any feed-forward model by augmenting it with few standard layers and a simple new gradient reversal layer. The resulting augmented architecture can be trained using standard backpropagation. Overall, the approach can be implemented with little effort using any of the deep-learning packages. The method performs very well in a series of image classification experiments, achieving adaptation effect in the presence of big domain shifts and outperforming previous state-of-the-art on Office datasets.
@cite_8: 
@cite_32: Unsupervised Domain Adaptation (UDA) aims to transfer domain knowledge from existing well-defined tasks to new ones where labels are unavailable. In the real-world applications, as the domain (task) discrepancies are usually uncontrollable, it is significantly motivated to match the feature distributions even if the domain discrepancies are disparate. Additionally, as no label is available in the target domain, how to successfully adapt the classifier from the source to the target domain still remains an open question. In this paper, we propose the Re-weighted Adversarial Adaptation Network (RAAN) to reduce the feature distribution divergence and adapt the classifier when domain discrepancies are disparate. Specifically, to alleviate the need of common supports in matching the feature distribution, we choose to minimize optimal transport (OT) based Earth-Mover (EM) distance and reformulate it to a minimax objective function. Utilizing this, RAAN can be trained in an end-to-end and adversarial manner. To further adapt the classifier, we propose to match the label distribution and embed it into the adversarial training. Finally, after extensive evaluation of our method using UDA datasets of varying difficulty, RAAN achieved the state-of-the-art results and outperformed other methods by a large margin when the domain shifts are disparate.
@cite_3: 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.
@cite_24: 
@cite_19: We propose two statistical tests to determine if two samples are from different distributions. Our test statistic is in both cases the distance between the means of the two samples mapped into a reproducing kernel Hilbert space (RKHS). The first test is based on a large deviation bound for the test statistic, while the second is based on the asymptotic distribution of this statistic. The test statistic can be computed in O(m2) time. We apply our approach to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where our test performs strongly. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.
@cite_5: In domain adaptation, maximum mean discrepancy (MMD) has been widely adopted as a discrepancy metric between the distributions of source and target domains. However, existing MMD-based domain adaptation methods generally ignore the changes of class prior distributions, i.e., class weight bias across domains. This remains an open problem but ubiquitous for domain adaptation, which can be caused by changes in sample selection criteria and application scenarios. We show that MMD cannot account for class weight bias and results in degraded domain adaptation performance. To address this issue, a weighted MMD model is proposed in this paper. Specifically, we introduce class-specific auxiliary weights into the original MMD for exploiting the class prior probability on source and target domains, whose challenge lies in the fact that the class label in target domain is unavailable. To account for it, our proposed weighted MMD model is defined by introducing an auxiliary weight for each class in the source domain, and a classification EM algorithm is suggested by alternating between assigning the pseudo-labels, estimating auxiliary weights and updating model parameters. Extensive experiments demonstrate the superiority of our weighted MMD over conventional MMD for domain adaptation.
@cite_31: Unsupervised domain adaptation tries to adapt a classifier trained on a labeled source domain to a related but unlabeled target domain. Methods based on adversarial learning try to learn a representation that is at the same time discriminative for the labels yet incapable of discriminating the domains. We propose a very simple and efficient method based on this approach which only aligns predicted class probabilities across domains. Experiments show that this strikingly simple adversarial domain adaptation method is robust to overfitting and achieves state-of-the-art results on datasets for image classification.
Addressing is known as a difficult problem. @cite_31 and @cite_5 has shown it is possible to adapt respectively the adversarial framework of @cite_15 and MMD based methods @cite_19 for learning invariant representation by re-weighting at each training step the domain discrepancy measure with an estimated class distribution in the target domain. In the context of Optimal Transport based discrepancy measure @cite_24 @cite_8 , @cite_32 suggests to learn adversarially the class ratio incorporating it into the supremum over the dual critic function of the Wasserstein measure. (where @math may change while keeping @math constant) is also a current assumption for extending invariant representation methods in challenging context of distributional shift. They traditionally use a local-scale transformation for learning such @math @cite_3 . @cite_37 suggests a component-wise version of local-scale transformations for avoiding noisy features which can not be well matched. Those methods are naturally extended in their original work to the context of both target shift and conditional shift using class ratio estimation.