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Accurately estimating the properties of quantum systems is a central challenge in quantum computing and quantum information. We propose a method to obtain unbiased estimators of multiple observables with low statistical error by…

Quantum Physics · Physics 2025-07-25 Stefano Mangini , Daniel Cavalcanti

Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network…

Optimization and Control · Mathematics 2012-10-24 Nikolai Krivulin

We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…

Optimization and Control · Mathematics 2020-02-28 Derek Driggs , Jingwei Liang , Carola-Bibiane Schönlieb

In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate---holding in a Gaussian model---for any spectral estimator…

Statistics Theory · Mathematics 2015-06-11 Emmanuel J. Candes , Carlos A. Sing-Long , Joshua D. Trzasko

Hutchinson's estimator is a randomized algorithm that computes an $\epsilon$-approximation to the trace of any positive semidefinite matrix using $\mathcal{O}(1/\epsilon^2)$ matrix-vector products. An improvement of Hutchinson's estimator,…

Numerical Analysis · Mathematics 2024-09-26 Jennifer Zvonek , Andrew Horning , Alex Townsend

We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation with an outer expectation taken with respect to one random…

Numerical Analysis · Mathematics 2023-04-28 Takashi Goda , Wataru Kitade

We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only $O(\log(1/\varepsilon))$ versus…

Statistics Theory · Mathematics 2024-05-28 Ye He , Alireza Mousavi-Hosseini , Krishnakumar Balasubramanian , Murat A. Erdogdu

We develop two novel stochastic variance-reduction methods to approximate solutions of a class of nonmonotone [generalized] equations. Our algorithms leverage a new combination of ideas from the forward-reflected-backward splitting method…

Optimization and Control · Mathematics 2025-05-30 Quoc Tran-Dinh

When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper we derive an estimator that is unbiased when the random-effects…

Econometrics · Economics 2022-06-22 Tom Boot , Gianmaria Niccodemi , Tom Wansbeek

In this note we propose a new variant of the hybrid variance-reduced proximal gradient method in [7] to solve a common stochastic composite nonconvex optimization problem under standard assumptions. We simply replace the independent…

Optimization and Control · Mathematics 2020-08-21 Deyi Liu , Lam M. Nguyen , Quoc Tran-Dinh

Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…

Signal Processing · Electrical Eng. & Systems 2020-07-15 Kamiar Radnosrati , Gustaf Hendeby , Fredrik Gustafsson

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

Machine Learning · Statistics 2017-07-13 Joseph Sakaya , Arto Klami

This paper develops new variance-reduction techniques for the forward-reflected-backward splitting (FRBS) method to solve a class of possibly nonmonotone stochastic composite inclusions. Unlike unbiased estimators such as mini-batching,…

Machine Learning · Computer Science 2026-03-17 Quoc Tran-Dinh , Nghia Nguyen-Trung

We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization…

Machine Learning · Statistics 2020-02-18 Burak Bartan , Mert Pilanci

The problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical Bayes estimators. By taking a different approach, that treats the…

Methodology · Statistics 2017-01-04 Asaf Weinstein , Zhuang Ma , Lawrence D. Brown , Cun-Hui Zhang

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…

Statistics Theory · Mathematics 2018-10-12 Stéphane Guerrier , Mucyo Karemera , Samuel Orso , Maria-Pia Victoria-Feser

We propose the use of U-statistics to reduce variance for gradient estimation in importance-weighted variational inference. The key observation is that, given a base gradient estimator that requires $m > 1$ samples and a total of $n > m$…

Machine Learning · Computer Science 2023-02-28 Javier Burroni , Kenta Takatsu , Justin Domke , Daniel Sheldon

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…

Machine Learning · Statistics 2021-02-26 Kei Ishikawa , Takashi Goda

Gaussian Boson Samplers aim to demonstrate quantum advantage by performing a sampling task believed to be classically hard. The probabilities of individual outcomes in the sampling experiment are determined by the Hafnian of an…

Quantum Physics · Physics 2024-03-07 Alexey Uvarov , Dmitry Vinichenko

We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng,…

Numerical Analysis · Mathematics 2024-12-02 Tyler Chen , Robert Chen , Kevin Li , Skai Nzeuton , Yilu Pan , Yixin Wang