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We introduce $\textit{Backward Conformal Prediction}$, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and…

Machine Learning · Statistics 2026-02-13 Etienne Gauthier , Francis Bach , Michael I. Jordan

We introduce estimation and test procedures through divergence minimiza- tion for models satisfying linear constraints with unknown parameter. These procedures extend the empirical likelihood (EL) method and share common features with…

Statistics Theory · Mathematics 2016-11-25 Michel Broniatowski , Amor Keziou

Nonparametric two-sample tests such as the Maximum Mean Discrepancy (MMD) are often used to detect differences between two distributions in machine learning applications. However, the majority of existing literature assumes that error-free…

Machine Learning · Statistics 2023-08-08 Ron Nafshi , Maggie Makar

Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…

Methodology · Statistics 2024-04-16 Robin Dunn , Aditya Gangrade , Larry Wasserman , Aaditya Ramdas

We study a basic problem of approximating the size of an unknown set $S$ in a known universe $U$. We consider two versions of the problem. In both versions the algorithm can specify subsets $T\subseteq U$. In the first version, which we…

Data Structures and Algorithms · Computer Science 2014-04-23 Dana Ron , Gilad Tsur

Conformal Prediction methods have finite-sample distribution-free marginal coverage guarantees. However, they generally do not offer conditional coverage guarantees, which can be important for high-stakes decisions. In this paper, we…

Machine Learning · Statistics 2024-09-27 Ruijiang Gao , Mingzhang Yin , James McInerney , Nathan Kallus

Recent advances in diffusion models attempt to handle conditional generative tasks by utilizing a differentiable loss function for guidance without the need for additional training. While these methods achieved certain success, they often…

Machine Learning · Computer Science 2024-07-08 Lingxiao Yang , Shutong Ding , Yifan Cai , Jingyi Yu , Jingya Wang , Ye Shi

We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…

Statistics Theory · Mathematics 2009-08-26 Hannes Leeb

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

Statistics Theory · Mathematics 2023-01-03 Lang Liu , Zaid Harchaoui

When evaluating the performance of a model for individualised risk prediction, the sample size needs to be large enough to precisely estimate the performance measures of interest. Current sample size guidance is based on precisely…

We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…

Optimization and Control · Mathematics 2020-07-09 Henry Lam , Fengpei Li

We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…

Computational Complexity · Computer Science 2016-08-16 Vitaly Feldman , Elena Grigorescu , Lev Reyzin , Santosh Vempala , Ying Xiao

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…

Information Theory · Computer Science 2010-01-26 Galen Reeves , Michael Gastpar

In this work we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, we consider mechanisms which perform a sequence of pairwise comparisons…

Computer Science and Game Theory · Computer Science 2021-07-07 Ioannis Anagnostides , Dimitris Fotakis , Panagiotis Patsilinakos

The probabilities of causation are commonly used to solve decision-making problems. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of…

Artificial Intelligence · Computer Science 2022-10-12 Ang Li , Ruirui Mao , Judea Pearl

We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(\cdot \mid S)$ for an unknown truncation set $S$ that may hide up to an…

Machine Learning · Statistics 2026-05-05 Yuhao Wang , Roberto Imbuzeiro Oliveira , Themis Gouleakis

Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…

Optimization and Control · Mathematics 2018-05-22 Mark Cannon

We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…

Statistics Theory · Mathematics 2026-03-10 Raunak Shevade , Monika Bhattacharjee

We consider the problem of estimating a $d$-dimensional $s$-sparse discrete distribution from its samples observed under a $b$-bit communication constraint. The best-known previous result on $\ell_2$ estimation error for this problem is…

Machine Learning · Statistics 2021-06-17 Wei-Ning Chen , Peter Kairouz , Ayfer Özgür

Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even…

Machine Learning · Computer Science 2026-02-02 Md Musfiqur Rahman , Ziwei Jiang , Hilaf Hasson , Murat Kocaoglu
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