Related papers: Optimal Confidence Regions for the Multinomial Par…
Quantum State Tomography is the task of inferring the state of a quantum system from measurement data. A reliable tomography scheme should not only report an estimate for that state, but also well-justified error bars. These may be…
We develop large sample theory including nonparametric confidence regions for $r$-dimensional ridges of probability density functions on $\mathbb{R}^d$, where $1\leq r<d$. We view ridges as the intersections of level sets of some special…
We introduce Joint Coverage Regions (JCRs), which unify confidence intervals and prediction regions in frequentist statistics. Specifically, joint coverage regions aim to cover a pair formed by an unknown fixed parameter (such as the mean…
This paper tackles a fundamental inference problem: given $n$ observations from a distribution $P$ over $\mathbb{R}^d$ with unknown mean $\boldsymbol{\mu}$, we must form a confidence set for the index (or indices) corresponding to the…
Within a Bayesian retrospective framework, we present a way of examining the distribution of \cps through a novel set estimator. For a given level, $\alpha$, we aim at smallest sets that cover all \cps with a probability of at least…
We consider the situation when a learner faces a set of unknown discrete distributions $(p_k)_{k\in \mathcal K}$ defined over a common alphabet $\mathcal X$, and can build for each distribution $p_k$ an individual high-probability…
We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. To that end, we develop a locally refitted least squares estimator and obtain component-wise and…
Generalized belief propagation (GBP) has proven to be a promising technique for approximate inference tasks in AI and machine learning. However, the choice of a good set of clusters to be used in GBP has remained more of an art then a…
The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear or quadratic functions) to approximate the true objective…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
Constructing distribution-free confidence intervals for the median, a classic problem in statistics, has seen numerous solutions in the literature. While coverage validity has received ample attention, less has been explored about interval…
Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
Simultaneous confidence bands (SCBs) for percentiles in linear regression are valuable tools with many applications. In this paper, we propose a novel criterion for comparing SCBs for percentiles, termed the Minimum Area Confidence Set…
This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…
Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a \emph{non-conformity score function} that…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…
This paper revisits the classical problem of interval estimation of a binomial proportion under Huber contamination. Our main result derives the rate of optimal interval length when the contamination proportion is unknown under a local…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…
Conformal prediction builds marginally valid prediction intervals that cover the unknown outcome of a randomly drawn test point with a prescribed probability. However, in practice, data-driven methods are often used to identify specific…