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We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…

Reinforcement learning has shown promising results in learning neural network policies for complicated control tasks. However, the lack of formal guarantees about the behavior of such policies remains an impediment to their deployment. We…

Establishing reliable image correspondences is essential for many robotic vision problems. However, existing methods often struggle in challenging scenarios with large viewpoint changes or textureless regions, where incorrect cor-…

We prove a fundamental impossibility theorem: neural networks cannot simultaneously learn well-calibrated confidence estimates with meaningful diversity when trained using binary correct/incorrect supervision. Through rigorous mathematical…

This paper presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence…

We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article…

In a linear regression model of fixed dimension $p \leq n$, we construct confidence regions for the unknown parameter vector based on the Lasso estimator that uniformly and exactly hold the prescribed in finite samples as well as in an…

Providing technologies to communities or domains where training data is scarce or protected e.g., for privacy reasons, is becoming increasingly important. To that end, we generalise methods for unsupervised transfer from multiple input…

The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or…

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…

We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection…

In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable…

We propose a new system identification method, called Sign-Perturbed Sums (SPS), for constructing non-asymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not…

Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…

When a machine learning model is deployed, its predictions can alter its environment, as better informed agents strategize to suit their own interests. With such alterations in mind, existing approaches to uncertainty quantification break.…

A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample…

We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact…

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set,…

Modern biotechnologies often result in high-dimensional data sets with much more variables than observations (n $\ll$ p). These data sets pose new challenges to statistical analysis: Variable selection becomes one of the most important…

Estimation of small failure probabilities is one of the most important and challenging computational problems in reliability engineering. The failure probability is usually given by an integral over a high-dimensional uncertain parameter…