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1. Blessings and Curses of Covariate Shifts: Adversarial Learning Dynamics, Directional Convergence, and Equilibria

   Liang, Tengyuan (June 2024, Journal of machine learning research)

   Covariate distribution shifts and adversarial perturbations present robustness challenges to the conventional statistical learning framework: mild shifts in the test covariate distribution can significantly affect the performance of the statistical model learned based on the training distribution. The model performance typically deteriorates when extrapolation happens: namely, covariates shift to a region where the training distribution is scarce, and naturally, the learned model has little information. For robustness and regularization considerations, adversarial perturbation techniques are proposed as a remedy; however, careful study needs to be carried out about what extrapolation region adversarial covariate shift will focus on, given a learned model. This paper precisely characterizes the extrapolation region, examining both regression and classification in an infinite-dimensional setting. We study the implications of adversarial covariate shifts to subsequent learning of the equilibrium—the Bayes optimal model—in a sequential game framework. We exploit the dynamics of the adversarial learning game and reveal the curious effects of the covariate shift to equilibrium learning and experimental design. In particular, we establish two directional convergence results that exhibit distinctive phenomena: (1) a blessing in regression, the adversarial covariate shifts in an exponential rate to an optimal experimental design for rapid subsequent learning; (2) a curse in classification, the adversarial covariate shifts in a subquadratic rate to the hardest experimental design trapping subsequent learning. 

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2. Low-Dimensional Density Ratio Estimation for Covariate Shift Correction

   Petar Stojanov, Mingming Gong (April 2019, Proceedings of Machine Learning Research)

   Covariate shift is a prevalent setting for supervised learning in the wild when the training and test data are drawn from different time periods, different but related domains, or via different sampling strategies. This paper addresses a transfer learning setting, with covariate shift between source and target domains. Most existing methods for correcting covariate shift exploit density ratios of the features to reweight the source-domain data, and when the features are high-dimensional, the estimated density ratios may suffer large estimation variances, leading to poor performance of prediction under covariate shift. In this work, we investigate the dependence of covariate shift correction performance on the dimensionality of the features, and propose a correction method that finds a low-dimensional representation of the features, which takes into account feature relevant to the target Y, and exploits the density ratio of this representation for importance reweighting. We discuss the factors that affect the performance of our method, and demonstrate its capabilities on both pseudo-real data and real-world applications. 

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3. Covariate Shift Detection via Domain Interpolation Sensitivity

   Gokhale, Tejas (July 2022, First Workshop on Interpolation Regularizers and Beyond at NeurIPS 2022)

   Covariate shift is a major roadblock in the reliability of image classifiers in the real world. Work on covariate shift has been focused on training classifiers to adapt or generalize to unseen domains. However, for transparent decision making, it is equally desirable to develop covariate shift detection methods that can indicate whether or not a test image belongs to an unseen domain. In this paper, we introduce a benchmark for covariate shift detection (CSD), that builds upon and complements previous work on domain generalization. We use state-of-the-art OOD detection methods as baselines and find them to be worse than simple confidence-based methods on our CSD benchmark. We propose an interpolation-based technique, Domain Interpolation Sensitivity (DIS), based on the simple hypothesis that interpolation between the test input and randomly sampled inputs from the training domain, offers sufficient information to distinguish between the training domain and unseen domains under covariate shift. DIS surpasses all OOD detection baselines for CSD on multiple domain generalization benchmarks. 

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4. Dangers of Bayesian Model Averaging under Covariate Shift

   Izmailov, Pavel; Nicholson, Patrick; Lotfi, Sanae; Wilson, Andrew G. (January 2021, Advances in neural information processing systems)

   Approximate Bayesian inference for neural networks is considered a robust alternative to standard training, often providing good performance on out-of-distribution data. However, Bayesian neural networks (BNNs) with high-fidelity approximate inference via full-batch Hamiltonian Monte Carlo achieve poor generalization under covariate shift, even underperforming classical estimation. We explain this surprising result, showing how a Bayesian model average can in fact be problematic under covariate shift, particularly in cases where linear dependencies in the input features cause a lack of posterior contraction. We additionally show why the same issue does not affect many approximate inference procedures, or classical maximum a-posteriori (MAP) training. Finally, we propose novel priors that improve the robustness of BNNs to many sources of covariate shift. 

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5. Covariate Balancing Methods for Randomized Controlled Trials Are Not Adversarially Robust

   https://doi.org/10.1109/TNNLS.2023.3266429  

   Babaei, Hossein; Alemohammad, Sina; Baraniuk, Richard G. (April 2023, IEEE Transactions on Neural Networks and Learning Systems)

   The first step toward investigating the effectiveness of a treatment via a randomized trial is to split the population into control and treatment groups then compare the average response of the treatment group receiving the treatment to the control group receiving the placebo. To ensure that the difference between the two groups is caused only by the treatment, it is crucial that the control and the treatment groups have similar statistics. Indeed, the validity and reliability of a trial are determined by the similarity of two groups’ statistics. Covariate balancing methods increase the similarity between the distributions of the two groups’ covariates. However, often in practice, there are not enough samples to accurately estimate the groups’ covariate distributions. In this article, we empirically show that covariate balancing with the standardized means difference (SMD) covariate balancing measure, as well as Pocock and Simon’s sequential treatment assignment method, are susceptible to worst case treatment assignments. Worst case treatment assignments are those admitted by the covariate balance measure, but result in highest possible ATE estimation errors. We developed an adversarial attack to find adversarial treatment assignment for any given trial. Then, we provide an index to measure how close the given trial is to the worst case. To this end, we provide an optimization-based algorithm, namely adversarial treatment assignment in treatment effect trials (ATASTREET), to find the adversarial treatment assignments. 

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