A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published "Theory of Games and Economic Behavior." In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. <s> BIB001 </s> A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> This letter presents a novel semisupervised method for addressing a domain adaptation problem in the classification of hyperspectral data. To overcome the influence of distribution bias between the source and target domains, we introduce the domain transfer multiple-kernel learning to simultaneously minimize the maximum mean discrepancy criterion and the structural risk functional of support vector machines. Then, the pairwise binary classifiers are merged as the multiclass classifier for solving the classification problem in hyperspectral data. Both bias and nonbias sampling strategies are introduced to evaluate the robustness of the proposed method against the spectral distribution bias. The results obtained from real data sets show that the proposed method can achieve higher classification accuracy even with cross-domain distribution bias and provide robust solutions with different labeled and unlabeled data sizes. <s> BIB002 </s> A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> In many important machine learning applications, the source distribution used to estimate a probabilistic classifier differs from the target distribution on which the classifier will be used to make predictions. Due to its asymptotic properties, sample reweighted empirical loss minimization is a commonly employed technique to deal with this difference. However, given finite amounts of labeled source data, this technique suffers from significant estimation errors in settings with large sample selection bias. We develop a framework for learning a robust bias-aware (RBA) probabilistic classifier that adapts to different sample selection biases using a minimax estimation formulation. Our approach requires only accurate estimates of statistics under the source distribution and is otherwise as robust as possible to unknown properties of the conditional label distribution, except when explicit generalization assumptions are incorporated. We demonstrate the behavior and effectiveness of our approach on binary classification tasks. <s> BIB003 </s> A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> Many learning situations involve learning the conditional distribution p(y|x) when the training instances are drawn from the training distribution ptr(x), even though it will later be used to predict for instances drawn from a different test distribution pte(x). Most current approaches focus on learning how to reweigh the training examples, to make them resemble the test distribution. However, reweighing does not always help, because (we show that) the test error also depends on the correctness of the underlying model class. This paper analyses this situation by viewing the problem of learning under changing distributions as a game between a learner and an adversary. We characterize when such reweighing is needed, and also provide an algorithm, robust covariate shift adjustment (RCSA), that provides relevant weights. Our empirical studies, on UCI datasets and a real-world cancer prognostic prediction dataset, show that our analysis applies, and that our RCSA works effectively. <s> BIB004 </s> A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this work, we describe a minimax framework for statistical learning with ambiguity sets given by balls in Wasserstein space. In particular, we prove a generalization bound that involves the covering number properties of the original ERM problem. As an illustrative example, we provide generalization guarantees for domain adaptation problems where the Wasserstein distance between the source and target domain distributions can be reliably estimated from unlabeled samples. <s> BIB005 </s> A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> Domain-adaptive classifiers learn from a source domain and aim to generalize to a target domain. If the classifier's assumptions on the relationship between domains (e.g. covariate shift) are valid, then it will usually outperform a non-adaptive source classifier. Unfortunately, it can perform substantially worse when its assumptions are invalid. Validating these assumptions requires labeled target samples, which are usually not available. We argue that, in order to make domain-adaptive classifiers more practical, it is necessary to focus on robust methods; robust in the sense that the model still achieves a particular level of performance without making strong assumptions on the relationship between domains. With this objective in mind, we formulate a conservative parameter estimator that only deviates from the source classifier when a lower or equal risk is guaranteed for all possible labellings of the given target samples. We derive the corresponding estimator for a discriminant analysis model, and show that its risk is actually strictly smaller than that of the source classifier. Experiments indicate that our classifier outperforms state-of-the-art classifiers for geographically biased samples. <s> BIB006 </s> A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> Distributionally Robust Supervised Learning (DRSL) is necessary for building reliable machine learning systems. When machine learning is deployed in the real world, its performance can be significantly degraded because test data may follow a different distribution from training data. DRSL with f-divergences explicitly considers the worst-case distribution shift by minimizing the adversarially reweighted training loss. In this paper, we analyze this DRSL, focusing on the classification scenario. Since the DRSL is explicitly formulated for a distribution shift scenario, we naturally expect it to give a robust classifier that can aggressively handle shifted distributions. However, surprisingly, we prove that the DRSL just ends up giving a classifier that exactly fits the given training distribution, which is too pessimistic. This pessimism comes from two sources: the particular losses used in classification and the fact that the variety of distributions to which the DRSL tries to be robust is too wide. Motivated by our analysis, we propose simple DRSL that overcomes this pessimism and empirically demonstrate its effectiveness. <s> BIB007 </s> A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> In this work, we present a method for unsupervised domain adaptation (UDA), where we aim to transfer knowledge from a label-rich domain (i.e., a source domain) to an unlabeled domain (i.e., a target domain). Many adversarial learning methods have been proposed for this task. These methods train domain classifier networks (i.e., a discriminator) to discriminate distinguish the features as either a source or target and train a feature generator network to mimic the discriminator.However, the domain classifier only tries to distinguish the features as a source or target and thus does not consider task-specific decision boundaries between classes. Therefore, a trained generator can generate ambiguous features near class boundaries. ::: To solve the problem, we propose a new approach that attempts to align distributions of source and target by utilizing the task-specific decision boundaries. We propose to utilize task-specific classifiers as discriminators that try to detect target samples that are far from the support of the source. A feature generator learns to generate target features inside the support to fool the classifiers. Since the generator uses feedback from task-specific classifiers, it avoids generating target features near class boundaries. Our method outperforms other methods on several datasets of image classification and semantic segmentation. <s> BIB008 </s> A review of single-source unsupervised domain adaptation <s> Minimax estimators <s> When labeled data is scarce for a specific target task, transfer learning often offers an effective solution by utilizing data from a related source task. However, when transferring knowledge from a less related source, it may inversely hurt the target performance, a phenomenon known as negative transfer. Despite its pervasiveness, negative transfer is usually described in an informal manner, lacking rigorous definition, careful analysis, or systematic treatment. This paper proposes a formal definition of negative transfer and analyzes three important aspects thereof. Stemming from this analysis, a novel technique is proposed to circumvent negative transfer by filtering out unrelated source data. Based on adversarial networks, the technique is highly generic and can be applied to a wide range of transfer learning algorithms. The proposed approach is evaluated on six state-of-the-art deep transfer methods via experiments on four benchmark datasets with varying levels of difficulty. Empirically, the proposed method consistently improves the performance of all baseline methods and largely avoids negative transfer, even when the source data is degenerate. <s> BIB009
One could view domain adaptation as a classification problem where an adversary changes the properties of the test data set from the training set. Adversarial settings are formalized as minimax optimization problems BIB001 , where the classifier minimizes risk, with respect to the classifier's parameters, and an adversary maximizes it, with respect to an uncertain quantity BIB003 ,  , BIB006 . By working under maximal uncertainty, the classifier adapts in a more conservative manner. A straightforward example of such a minimax estimator is the Robust Bias-Aware classifier BIB003 . Its uncertain quantity corresponds to the target domain's posterior distribution. It minimizes risk for one classifier h while the adversary maximizes risk with respect to another classifier g. However, given full freedom, the adversary would always produce the opposite classifier and its optimization procedure would not converge. A constraint is imposed, telling the adversary that it needs to pick posteriors that match the moments of the source distribution's feature statistics. The estimator is now written as BIB003 : where Ξ represents the set of feature statistics that characterize the source domain's distribution and H ∩ Ξ indicates the restriction of the hypothesis class to functions that produce feature statistics equivalent to that of the source domain. This estimator produces a classifier with high-confidence predictions in regions with large probability mass under the source distribution and low-confidence predictions in regions with small source probability mass. Another minimax estimator, called the Target Contrastive Robust risk estimator BIB006 , focuses on the performance gain that can be achieved with respect to the source classifier. By contrasting the empirical target risk of a new classifier with that of the source classifier, one can effectively exclude classifier parameters that are already known to produce worse risks than that of the source classifier. The estimator is formulated as: whereĥ S is the source classifier and q denotes soft target labels. If no parameters can be found that are guaranteed to perform better than that of the source classifier's, then it will not adapt. It thereby explicitly avoids negative transfer  , BIB009 . For discriminant analysis models, it can even be shown that the empirical target risk of the TCR estimate is strictly smaller than that of the source classifier,R T (ĥ T ) < R(ĥ S ), for the given target samples (Theorem 1, [166] ). It is hence a transductive classifier. Its weakness is that it can perform poorly if the source classifier is a bad choice for the target domain to begin with. Figure 5 presents an example of the Target Contrastive Robust risk estimator. By taking into account the uncertainty over the labeling of the target samples, the classifier adapts conservatively (black dashed line). In this case, it is minimizing the empirical risk on the target samples for the worstcase labeling. An alternative quantity with uncertainty is the set of weights from importance-weighting. Small changes in weights could have large effects on the resulting set of classifier parameters and, by extension, generalization performance. One can be less sensitive to poor weights by minimizing risk with respect to worst-case weights BIB004 : where W is restricted to the set of non-negative weights that average to 1 (see Section 3.1). Minimizing the adversarially weighted loss produces more conservative estimates as the domain dissimilarity increases. Worst-case importanceweights have also been studied from a distributionally robust optimization perspective BIB007 . Finally, variations on minimax estimators have been proposed in the context of domain-adversarial networks BIB008 , multiple-kernel support vector machines BIB002 and with using Wasserstein distances BIB005 .