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Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually…

Information Theory · Computer Science 2016-06-14 Claire Boyer , Jérémie Bigot , Pierre Weiss

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the \textit{sequential predictive conformal inference} (\texttt{SPCI}). We specifically account for the nature that time…

Machine Learning · Statistics 2023-05-31 Chen Xu , Yao Xie

We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…

Disordered Systems and Neural Networks · Physics 2018-08-15 Isaac Pérez Castillo , Fernando L. Metz

Recent developments in statistical regression methodology shift away from pure mean regression towards distributional regression models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire…

Methodology · Statistics 2022-05-24 Manuel Carlan , Thomas Kneib , Nadja Klein

In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the…

Information Theory · Computer Science 2015-06-11 Kezhi Li , Lu Gan , Cong Ling

Science and technology have a growing need for effective mechanisms that ensure reliable, controlled performance from black-box machine learning algorithms. These performance guarantees should ideally hold conditionally on the input-that is…

Machine Learning · Computer Science 2025-03-28 Vincent Blot , Anastasios N Angelopoulos , Michael I Jordan , Nicolas J-B Brunel

Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can…

Statistics Theory · Mathematics 2024-03-15 Ian Waudby-Smith , David Arbour , Ritwik Sinha , Edward H. Kennedy , Aaditya Ramdas

A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…

Computer Vision and Pattern Recognition · Computer Science 2010-10-22 Guoshen Yu , Guillermo Sapiro

Concentration inequalities for the sample mean, like those due to Bernstein, Hoeffding, and Bentkus, are valid for any sample size but overly conservative, yielding confidence intervals that are unnecessarily wide. The central limit theorem…

Probability · Mathematics 2025-12-23 Morgane Austern , Lester Mackey

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

Methodology · Statistics 2025-07-08 Michael Lindon , Dae Woong Ham , Martin Tingley , Iavor Bojinov

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

We consider inference on a scalar regression coefficient under a constraint on the magnitude of the control coefficients. A class of estimators based on a regularized propensity score regression is shown to exactly solve a tradeoff between…

Econometrics · Economics 2023-08-11 Timothy B. Armstrong , Michal Kolesár , Soonwoo Kwon

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

Methodology · Statistics 2021-06-15 Edwin Fong , Chris Holmes

Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…

Statistics Theory · Mathematics 2025-06-17 Felix Gnettner , Claudia Kirch

We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when…

Probability · Mathematics 2017-08-03 Xiequan Fan , Ion Grama , Quansheng Liu

Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by…

Methodology · Statistics 2026-05-11 Stefano Cortinovis , Valentin Kilian , François Caron

Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…

Machine Learning · Statistics 2025-07-21 Zhanli Wu , Fabrizio Leisen , F. Javier Rubio

Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.…

Statistics Theory · Mathematics 2022-04-05 Tudor Manole , Sivaraman Balakrishnan , Larry Wasserman

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…

Machine Learning · Statistics 2026-05-12 Valentin Kilian , Stefano Cortinovis , François Caron

Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…

Statistics Theory · Mathematics 2020-05-11 Jonathan H. Huggins , Daniel M. Roy