Related papers: Statistical Inference in Tensor Completion: Optima…

Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem…

This paper develops a new framework for indirect statistical inference with guaranteed necessity and sufficiency, applicable to continuous random variables. We prove that when comparing exponentially transformed order statistics from an…

Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…

Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…

We consider the Principal Component Analysis problem for large tensors of arbitrary order $k$ under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to…

We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…

We consider the task of estimating a low-rank matrix from non-linear and noisy observations. We prove a strong universality result showing that Bayes-optimal performances are characterized by an equivalent Gaussian model with an effective…

Tensor completion is a core machine learning algorithm used in recommender systems and other domains with missing data. While the matrix case is well-understood, theoretical results for tensor problems are limited, particularly when the…

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Analysis of high-dimensional data, where the number of covariates is larger than the sample size, is a topic of current interest. In such settings, an important goal is to estimate the signal level $\tau^2$ and noise level $\sigma^2$, i.e.,…

Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation…

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…

Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…

One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…

Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…

Complex computer simulations are commonly required for accurate data modelling in many scientific disciplines, making statistical inference challenging due to the intractability of the likelihood evaluation for the observed data.…