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Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Numerical Analysis · Mathematics 2026-05-12 Josie König , Elizabeth Qian , Melina A. Freitag

Information from related source studies can often enhance the findings of a target study. However, the distribution shift between target and source studies can severely impact the efficiency of knowledge transfer. In the high-dimensional…

Methodology · Statistics 2025-11-26 Ruiqi Bai , Yijiao Zhang , Hanbo Yang , Zhongyi Zhu

We study linear regression under covariate shift, where the marginal distribution over the input covariates differs in the source and the target domains, while the conditional distribution of the output given the input covariates is similar…

Machine Learning · Computer Science 2022-08-04 Jingfeng Wu , Difan Zou , Vladimir Braverman , Quanquan Gu , Sham M. Kakade

A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. However, such an assumption is often violated in the real world due to non-stationarity of the…

Machine Learning · Computer Science 2021-05-04 Tianyi Zhang , Ikko Yamane , Nan Lu , Masashi Sugiyama

Learning with identical train and test distributions has been extensively investigated both practically and theoretically. Much remains to be understood, however, in statistical learning under distribution shifts. This paper focuses on a…

Machine Learning · Computer Science 2024-11-01 Omar Montasser , Han Shao , Emmanuel Abbe

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

Statistics Theory · Mathematics 2026-05-06 Stephan Clémençon , Anne Sabourin

Deep learning architectures such as convolutional neural networks are the standard in computer vision for image processing tasks. Their accuracy however often comes at the cost of long and computationally expensive training, the need for…

Computer Vision and Pattern Recognition · Computer Science 2022-10-31 Mattia Pugliatti , Francesco Topputo

Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…

Methodology · Statistics 2019-09-27 Lu Li , Kai Tan , Xuerong Meggie Wen , Zhou Yu

Predict a new response from a covariate is a challenging task in regression, which raises new question since the era of high-dimensional data. In this paper, we are interested in the inverse regression method from a theoretical viewpoint.…

Statistics Theory · Mathematics 2018-07-10 Emilie Devijver , Emeline Perthame

The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…

Machine Learning · Statistics 2025-04-03 Shuntuo Xu , Zhou Yu , Jian Huang

Practitioners often face the challenge of deploying prediction models in new environments with shifted distributions of covariates and responses. With observational data, such shifts are often driven by unobserved confounding, and can in…

Machine Learning · Computer Science 2026-04-02 Kulunu Dharmakeerthi , YoonHaeng Hur , Tengyuan Liang

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates $x$) of training and testing samples $\mathrm{p}_\text{tr}(x)$ and $\mathrm{p}_\text{te}(x)$ are different but the label…

Machine Learning · Statistics 2023-06-12 José I. Segovia-Martín , Santiago Mazuelas , Anqi Liu

Distributional shift is one of the major obstacles when transferring machine learning prediction systems from the lab to the real world. To tackle this problem, we assume that variation across training domains is representative of the…

The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community…

Machine Learning · Computer Science 2013-11-27 Yun-Qian Miao , Ahmed K. Farahat , Mohamed S. Kamel

We consider a machine learning setup where one training dataset is used to train multiple models across slightly different data distributions. This occurs when customized models are needed for various deployment environments. To reduce…

Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…

Statistics Theory · Mathematics 2009-04-27 Bing Li , Yuexiao Dong

The main challenge that sets transfer learning apart from traditional supervised learning is the distribution shift, reflected as the shift between the source and target models and that between the marginal covariate distributions. In this…

Machine Learning · Statistics 2024-04-02 Zelin He , Ying Sun , Jingyuan Liu , Runze Li

Reweighting a distribution to minimize a distance to a target distribution is a powerful and flexible strategy for estimating a wide range of causal effects, but can be challenging in practice because optimal weights typically depend on…

Machine Learning · Statistics 2026-02-16 Oscar Clivio , Avi Feller , Chris Holmes

Distribution shifts are problems where the distribution of data changes between training and testing, which can significantly degrade the performance of a model deployed in the real world. Recent studies suggest that one reason for the…

Machine Learning · Computer Science 2023-04-10 Takuro Kutsuna

We evaluate the effectiveness of importance weighting in deep neural networks under label shift and covariate shift. On synthetic 2D data (linearly separable and moon-shaped) using logistic regression and MLPs, we observe that weighting…

Machine Learning · Computer Science 2025-06-18 Thien Nhan Vo