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We study the well-motivated problem of online distribution shift in which the data arrive in batches and the distribution of each batch can change arbitrarily over time. Since the shifts can be large or small, abrupt or gradual, the length…

Machine Learning · Computer Science 2025-04-11 Dheeraj Baby , Boran Han , Shuai Zhang , Cuixiong Hu , Yuyang Wang , Yu-Xiang Wang

Distribution shift between the training domain and the test domain poses a key challenge for modern machine learning. An extensively studied instance is the \emph{covariate shift}, where the marginal distribution of covariates differs…

Statistics Theory · Mathematics 2025-11-17 Jeonghwan Lee , Cong Ma

Often, constraints arise in deployment settings where even lightweight parameter updates e.g. parameter-efficient fine-tuning could induce model shift or tuning instability. We study test-time adaptation of foundation models for few-shot…

Machine Learning · Statistics 2026-02-04 Tahir Qasim Syed , Behraj Khan

Despite achieving excellent performance on benchmarks, deep neural networks often underperform in real-world deployment due to sensitivity to minor, often imperceptible shifts in input data, known as distributional shifts. These shifts are…

Machine Learning · Computer Science 2025-09-25 Birk Torpmann-Hagen , Pål Halvorsen , Michael A. Riegler , Dag Johansen

We consider a semi-supervised classification problem with non-stationary label-shift in which we observe a labelled data set followed by a sequence of unlabelled covariate vectors in which the marginal probabilities of the class labels may…

Statistics Theory · Mathematics 2024-05-29 Henry W J Reeve

Time-series anomaly detection deals with the problem of detecting anomalous timesteps by learning normality from the sequence of observations. However, the concept of normality evolves over time, leading to a "new normal problem", where the…

Machine Learning · Computer Science 2024-01-23 Dongmin Kim , Sunghyun Park , Jaegul Choo

This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not…

Information Theory · Computer Science 2021-10-05 Haiyun He , Qiaosheng Zhang , Vincent Y. F. Tan

We study confidence intervals based on hard-thresholding, soft-thresholding, and adaptive soft-thresholding in a linear regression model where the number of regressors $k$ may depend on and diverge with sample size $n$. In addition to the…

Statistics Theory · Mathematics 2018-10-08 Ulrike Schneider

We develop methods for forming prediction sets in an online setting where the data generating distribution is allowed to vary over time in an unknown fashion. Our framework builds on ideas from conformal inference to provide a general…

Methodology · Statistics 2021-12-10 Isaac Gibbs , Emmanuel Candès

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…

Computation · Statistics 2020-07-21 Anne van Delft , Michael Eichler

Let $\{(X_i,Y_i)\}_{i\in \{1,..., n\}}$ be an i.i.d. sample from the random design regression model $Y=f(X)+\epsilon$ with $(X,Y)\in [0,1]\times [-M,M]$. In dealing with such a model, adaptation is naturally to be intended in terms of…

Statistics Theory · Mathematics 2008-01-23 Pierpaolo Brutti

Tabular learning transforms raw features into optimized spaces for downstream tasks, but its effectiveness deteriorates under distribution shifts between training and testing data. We formalize this challenge as the Distribution Shift…

Machine Learning · Computer Science 2025-08-28 Wangyang Ying , Nanxu Gong , Dongjie Wang , Xinyuan Wang , Arun Vignesh Malarkkan , Vivek Gupta , Chandan K. Reddy , Yanjie Fu

In this paper, we study the application of Test-Time Training (TTT) as a solution to handling distribution shifts in speech applications. In particular, we introduce distribution-shifts to the test datasets of standard speech-classification…

Sound · Computer Science 2023-10-02 Sri Harsha Dumpala , Chandramouli Sastry , Sageev Oore

This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…

Methodology · Statistics 2026-05-19 Rhea Davis , N. Balakrishna

Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…

Machine Learning · Statistics 2018-02-27 Fredrik D. Johansson , Nathan Kallus , Uri Shalit , David Sontag

This paper studies the prediction of a target $\mathbf{z}$ from a pair of random variables $(\mathbf{x},\mathbf{y})$, where the ground-truth predictor is additive $\mathbb{E}[\mathbf{z} \mid \mathbf{x},\mathbf{y}] = f_\star(\mathbf{x})…

Machine Learning · Computer Science 2023-10-30 Max Simchowitz , Anurag Ajay , Pulkit Agrawal , Akshay Krishnamurthy

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

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

In recent work on time-series prediction, Transformers and even large language models have garnered significant attention due to their strong capabilities in sequence modeling. However, in practical deployments, time-series prediction often…

Machine Learning · Computer Science 2026-02-17 Wenxuan Xie , Fanpu Cao

We develop a timescale synthesis-based probabilistic approach for the modeling of locally stationary signals. Inspired by our previous work, the model involves zero-mean, complex Gaussian wavelet coefficients, whose distribution varies as a…

Statistics Theory · Mathematics 2020-02-10 Adrien Meynard , Bruno Torrésani