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Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…

Statistics Theory · Mathematics 2025-05-01 Simon Viel , Lionel Truquet , Ikko Yamane

High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…

Methodology · Statistics 2022-06-22 Di Wang , Ruey S. Tsay

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle…

Image and Video Processing · Electrical Eng. & Systems 2022-09-05 Tamir Bendory , Ti-Yen Lan , Nicholas F. Marshall , Iris Rukshin , Amit Singer

In this paper we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in $[0,1]^d$ with $d\ge 2$ and $N(0,1)$ noise, the minimax rate for the $\ell_2$ risk is known to be bounded…

Statistics Theory · Mathematics 2020-01-13 Hang Deng , Cun-Hui Zhang

We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…

Machine Learning · Statistics 2016-04-15 Gilles Blanchard , Nicole Mücke

Motivated by the problem of determining the atomic structure of macromolecules using single-particle cryo-electron microscopy (cryo-EM), we study the sample and computational complexities of the sparse multi-reference alignment (MRA) model:…

Information Theory · Computer Science 2021-09-27 Tamir Bendory , Oscar Mickelin , Amit Singer

Estimation of signal-to-noise ratios and residual variances in high-dimensional linear models has various important applications including, e.g. heritability estimation in bioinformatics. One commonly used estimator, usually referred to as…

Statistics Theory · Mathematics 2023-06-09 Xiaohan Hu , Xiaodong Li

Multireference alignment (MRA) refers to the problem of recovering a signal from noisy samples subject to random circular shifts. Expectation--maximization (EM) and variational approaches use statistical modeling to achieve high accuracy at…

Information Theory · Computer Science 2025-10-30 Vahid Shahverdi , Emanuel Ström , Joakim Andén

Multireference alignment (MRA) problem is to estimate an underlying signal from a large number of noisy circularly-shifted observations. The existing methods are always proposed under the hypothesis of a single Gaussian noise. However, the…

Optimization and Control · Mathematics 2021-07-23 Cuicui Zhao , Jun Liu , Xinqi Gong

The use of multichannel data in line spectral estimation (or frequency estimation) is common for improving the estimation accuracy in array processing, structural health monitoring, wireless communications, and more. Recently proposed…

Information Theory · Computer Science 2018-10-15 Zai Yang , Jinhui Tang , Yonina C. Eldar , Lihua Xie

The problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation. We address this problem from a statistical point of view and provide a theoretical…

Statistics Theory · Mathematics 2015-02-03 Olivier Collier , Arnak S. Dalalyan

Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…

Machine Learning · Statistics 2025-04-14 Jihao Long , Xiaojun Peng , Lei Wu

The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the…

Statistics Theory · Mathematics 2013-06-18 Zongming Ma , Yihong Wu

This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…

Information Theory · Computer Science 2021-05-10 Minoh Jeong , Alex Dytso , Martina Cardone

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

Statistics Theory · Mathematics 2018-03-16 William Weimin Yoo , Subhashis Ghosal

We develop a multidimensional version of Gradient-MUSIC for estimating the frequencies of a nonharmonic signal from noisy samples. The guiding principle is that frequency recovery should be based only on the signal subspace determined by…

Optimization and Control · Mathematics 2026-03-31 Albert Fannjiang , Weilin Li

Multireference alignment (MRA) is the problem of estimating a signal from many noisy and cyclically shifted copies of itself. In this paper, we consider an extension called heterogeneous MRA, where $K$ signals must be estimated, and each…

Information Theory · Computer Science 2018-02-02 Nicolas Boumal , Tamir Bendory , Roy R. Lederman , Amit Singer

Motivated by cutting-edge applications like cryo-electron microscopy (cryo-EM), the Multi-Reference Alignment (MRA) model entails the learning of an unknown signal from repeated measurements of its images under the latent action of a group…

Statistics Theory · Mathematics 2022-03-11 Subhro Ghosh , Philippe Rigollet

This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each noisy observation includes a random translation and random…

Signal Processing · Electrical Eng. & Systems 2021-07-06 Matthew Hirn , Anna Little

The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…

Statistics Theory · Mathematics 2021-10-18 Maksym Luz , Mikhail Moklyachuk