A review of single-source unsupervised domain adaptation <s> FEATURE-BASED APPROACHES <s> In this paper, we introduce a new domain adaptation (DA) algorithm where the source and target domains are represented by subspaces described by eigenvectors. In this context, our method seeks a domain adaptation solution by learning a mapping function which aligns the source subspace with the target one. We show that the solution of the corresponding optimization problem can be obtained in a simple closed form, leading to an extremely fast algorithm. We use a theoretical result to tune the unique hyper parameter corresponding to the size of the subspaces. We run our method on various datasets and show that, despite its intrinsic simplicity, it outperforms state of the art DA methods. <s> BIB001 </s> A review of single-source unsupervised domain adaptation <s> FEATURE-BASED APPROACHES <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> BIB002 </s> A review of single-source unsupervised domain adaptation <s> FEATURE-BASED APPROACHES <s> In pattern recognition and computer vision, one is often faced with scenarios where the training data used to learn a model have different distribution from the data on which the model is applied. Regardless of the cause, any distributional change that occurs after learning a classifier can degrade its performance at test time. Domain adaptation tries to mitigate this degradation. In this article, we provide a survey of domain adaptation methods for visual recognition. We discuss the merits and drawbacks of existing domain adaptation approaches and identify promising avenues for research in this rapidly evolving field. <s> BIB003 </s> A review of single-source unsupervised domain adaptation <s> FEATURE-BASED APPROACHES <s> Domain adaptation is an active, emerging research area that attemptsto address the changes in data distribution across training and testingdatasets. With the availability of a multitude of image acquisition sensors,variations due to illumination, and viewpoint among others, computervision applications present a very natural test bed for evaluatingdomain adaptation methods. In this monograph, we provide a comprehensiveoverview of domain adaptation solutions for visual recognitionproblems. By starting with the problem description and illustrations,we discuss three adaptation scenarios namely, i unsupervised adaptationwhere the "source domain" training data is partially labeledand the "target domain" test data is unlabeled, ii semi-supervisedadaptation where the target domain also has partial labels, and iiimulti-domain heterogeneous adaptation which studies the previous twosettings with the source and/or target having more than one domain,and accounts for cases where the features used to represent the datain each domain are different. For all these topics we discuss existingadaptation techniques in the literature, which are motivated by theprinciples of max-margin discriminative learning, manifold learning,sparse coding, as well as low-rank representations. These techniqueshave shown improved performance on a variety of applications suchas object recognition, face recognition, activity analysis, concept classification,and person detection. We then conclude by analyzing thechallenges posed by the realm of "big visual data", in terms of thegeneralization ability of adaptation algorithms to unconstrained dataacquisition as well as issues related to their computational tractability,and draw parallels with the efforts from vision community on imagetransformation models, and invariant descriptors so as to facilitate improvedunderstanding of vision problems under uncertainty. <s> BIB004 </s> A review of single-source unsupervised domain adaptation <s> FEATURE-BASED APPROACHES <s> Domain transfer learning generalizes a learning model across training data and testing data with different distributions. A general principle to tackle this problem is reducing the distribution difference between training data and testing data such that the generalization error can be bounded. Current methods typically model the sample distributions in input feature space, which depends on nonlinear feature mapping to embody the distribution discrepancy. However, this nonlinear feature space may not be optimal for the kernel-based learning machines. To this end, we propose a transfer kernel learning (TKL) approach to learn a domain-invariant kernel by directly matching source and target distributions in the reproducing kernel Hilbert space (RKHS). Specifically, we design a family of spectral kernels by extrapolating target eigensystem on source samples with Mercer’s theorem. The spectral kernel minimizing the approximation error to the ground truth kernel is selected to construct domain-invariant kernel machines. Comprehensive experimental evidence on a large number of text categorization, image classification, and video event recognition datasets verifies the effectiveness and efficiency of the proposed TKL approach over several state-of-the-art methods. <s> BIB005 </s> A review of single-source unsupervised domain adaptation <s> FEATURE-BASED APPROACHES <s> Recent reports suggest that a generic supervised deep CNN model trained on a large-scale dataset reduces, but does not remove, dataset bias. Fine-tuning deep models in a new domain can require a significant amount of labeled data, which for many applications is simply not available. We propose a new CNN architecture to exploit unlabeled and sparsely labeled target domain data. Our approach simultaneously optimizes for domain invariance to facilitate domain transfer and uses a soft label distribution matching loss to transfer information between tasks. Our proposed adaptation method offers empirical performance which exceeds previously published results on two standard benchmark visual domain adaptation tasks, evaluated across supervised and semi-supervised adaptation settings. <s> BIB006 </s> A review of single-source unsupervised domain adaptation <s> FEATURE-BASED APPROACHES <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> BIB007
In some problem settings, there potentially exists a transformation that maps source data onto target data BIB003 , BIB004 . In the example setting, the average age of patients in Budapest is lower than that of the patients in Long Beach. Age is one of the two features, and constitutes a subspace. One could consider reducing the discrepancy between the hospitals by shifting the age of the Hungarian patients upwards and training a classifier on the shifted data. Figure  4 It has been argued that data transformations are justified by the generalization error bound from Section 2.4, as that would shrink the domain discrepancy term BIB001 , BIB005 , BIB006 ,  . A such, a smaller difference between the empirical error and the true target error would be obtained. However, note that matching the data distributions, p S (t(x)) ≈ p T (t(x)) where t(x) is the transformation function, does not imply that the conditional distributions are matched as well, p S (y | t(x)) ≈ p T (y | t(x)) BIB002 , BIB007 . To achieve such a result, stronger conditions are necessary (c.f. Section 4.2).