Related papers: Confidence Sets under Weak Identification: Theory …

We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…

Causal effect estimation from observational data is an important and much studied research topic. The instrumental variable (IV) and local causal discovery (LCD) patterns are canonical examples of settings where a closed-form expression…

We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized…

For linear regression models who are not exactly sparse in the sense that the coefficients of the insignificant variables are not exactly zero, the working models obtained by a variable selection are often biased. Even in sparse cases,…

We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables. Our approach builds on conformal prediction, a powerful framework to…

The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…

Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we…

Low-degree polynomials have emerged as a powerful paradigm for providing evidence of statistical-computational gaps across a variety of high-dimensional statistical models [Wein25]. For detection problems -- where the goal is to test a…

For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…

This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of W and X whose conditional mean given Z and X equals the conditional mean of another variable Y given Z and X. Many…

Parameter estimation, statistical tests and confidence sets are the cornerstones of classical statistics that allow scientists to make inferences about the underlying process that generated the observed data. A key question is whether one…

Global sensitivity analysis is often impracticable for complex and time demanding numerical models, as it requires a large number of runs. The reduced-basis approach provides a way to replace the original model by a much faster to run code.…

Current experimental scientists have been increasingly relying on simulation-based inference (SBI) to invert complex non-linear models with intractable likelihoods. However, posterior approximations obtained with SBI are often…

We study the wild bootstrap inference for instrumental variable regressions in the framework of a small number of large clusters in which the number of clusters is viewed as fixed and the number of observations for each cluster diverges to…

While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…

This paper provides a user's guide to the general theory of approximate randomization tests developed in Canay, Romano, and Shaikh (2017) when specialized to linear regressions with clustered data. An important feature of the methodology is…

Though black-box predictors are state-of-the-art for many complex tasks, they often fail to properly quantify predictive uncertainty and may provide inappropriate predictions for unfamiliar data. Instead, we can learn more reliable models…

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…

We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…