Related papers: Conformal inference for random objects
Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it…
Constructing valid and informative conformal prediction regions for multi-dimensional outputs remains a fundamental challenge. While conformal prediction provides finite-sample, distribution-free coverage guarantees, its practical…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that…
Conformal prediction is a simple and powerful tool that can quantify uncertainty without any distributional assumptions. Many existing methods only address the average coverage guarantee, which is not ideal compared to the stronger…
Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks. We consider the transductive setting, where decisions are made on a test sample of $m$ new points, giving…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
We develop a unified framework for testing independence and quantifying association between random objects that are located in general metric spaces. Special cases include functional and high-dimensional data as well as networks, covariance…
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
Conformal prediction is a non-parametric technique for constructing prediction intervals or sets from arbitrary predictive models under the assumption that the data is exchangeable. It is popular as it comes with theoretical guarantees on…
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…
Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
Conformal prediction is a distribution-free technique for establishing valid prediction intervals. Although conventionally people conduct conformal prediction in the output space, this is not the only possibility. In this paper, we propose…
This paper introduces a conformal inference method to evaluate uncertainty in classification by generating prediction sets with valid coverage conditional on adaptively chosen features. These features are carefully selected to reflect…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…
Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the…