Related papers: Uniform sample generation in semialgebraic sets
Rejection sampling is a common tool for low dimensional problems ($d \leq 2$), often touted as an "easy" way to obtain valid samples from a distribution $f(\cdot)$ of interest. In practice it is non-trivial to apply, often requiring…
We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
Quantifying uncertainty in automatically generated text is important for letting humans check potential hallucinations and making systems more reliable. Conformal prediction is an attractive framework to provide predictions imbued with…
We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…
In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
In this paper, we present a study of a kernel-based consensual aggregation on randomly projected high-dimensional features of predictions for regression. The aggregation scheme is composed of two steps: the high-dimensional features of…
In this paper, we study three asymptotic regimes that can be applied to ranking and selection (R&S) problems with general sample distributions. These asymptotic regimes are constructed by sending particular problem parameters (probability…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…
Estimating the mode of a unimodal distribution is a classical problem in statistics. Although there are several approaches for point-estimation of mode in the literature, very little has been explored about the interval-estimation of mode.…
We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary…
This article presents a novel, general, and effective simulation-inspired approach, called {\it repro samples method}, to conduct statistical inference. The approach studies the performance of artificial samples, referred to as {\it repro…
We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
In this work we consider the problem of fitting Random Utility Models (RUMs) to user choices. Given the winner distributions of the subsets of size $k$ of a universe, we obtain a polynomial-time algorithm that finds the RUM that best…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
We study the problem of approximating an unknown function $f:\mathbb{R}\to\mathbb{R}$ by a degree-$d$ polynomial using as few function evaluations as possible, where error is measured with respect to a probability distribution $\mu$.…