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Recent works have investigated the sample complexity necessary for fair machine learning. The most advanced of such sample complexity bounds are developed by analyzing multicalibration uniform convergence for a given predictor class. We…

Machine Learning · Computer Science 2022-02-10 Harrison Rosenberg , Robi Bhattacharjee , Kassem Fawaz , Somesh Jha

We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…

Quantum Physics · Physics 2010-01-28 Garry Goldstein , Mikhail D. Lukin , Paola Cappellaro

In some estimation problems, not all the parameters can be identified, which results in singularity of the Fisher Information Matrix (FIM). The Cram\'er-Rao Bound (CRB), which is the inverse of the FIM, is then not defined. To regularize…

Information Theory · Computer Science 2018-07-24 Elisabeth de Carvalho , Dirk Slock

We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…

Machine Learning · Statistics 2025-05-15 Monica Welfert , Nathan Stromberg , Mario Diaz , Lalitha Sankar

Pseudo-measurements are the dominant source of uncertainty in distribution system state estimation (DSSE), yet their distributional assumptions are treated as fixed inputs by existing uncertainty quantification methods. This paper…

Systems and Control · Electrical Eng. & Systems 2026-05-14 Betül Mamudi , Jochen Stiasny , Jochen Cremer

Probabilistic regression models trained with maximum likelihood estimation (MLE), can sometimes overestimate variance to an unacceptable degree. This is mostly problematic in the multivariate domain. While univariate models often optimize…

Artificial Intelligence · Computer Science 2024-09-24 Daan Roordink , Sibylle Hess

A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…

Statistics Theory · Mathematics 2023-03-02 Shuo Tang , Gerald LaMountain , Tales Imbiriba , Pau Closas

In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…

Information Theory · Computer Science 2019-07-24 Lucien Bacharach , Carsten Fritsche , Umut Orguner , Eric Chaumette

The quantum Cram\'er-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a…

Quantum Physics · Physics 2021-09-15 Aaron Z. Goldberg , Luis L. Sánchez-Soto , Hugo Ferretti

This paper presents a Cramer-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of a tensor from noisy observations, (i.e., the tensor plus a…

Other Statistics · Statistics 2014-02-10 Petr Tichavsky , Anh Huy Phan , Zbynek Koldovsky

The Gauss Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via…

Machine Learning · Computer Science 2023-11-30 Tzvi Diskin , Yonina C. Eldar , Ami Wiesel

Mobile communication networks were designed to mainly support ubiquitous wireless communications, yet they are also expected to achieve radio sensing capabilities in the near future. However, most prior studies on radio sensing usually rely…

Information Theory · Computer Science 2023-03-13 Huizhi Wang , Zhiqiang Xiao , Yong Zeng

In modern radar systems, precise target localization using azimuth and velocity estimation is paramount. Traditional unbiased estimation methods have utilized gradient descent algorithms to reach the theoretical limits of the Cramer Rao…

Signal Processing · Electrical Eng. & Systems 2024-04-24 Shyam Venkatasubramanian , Sandeep Gogineni , Bosung Kang , Muralidhar Rangaswamy

In statistical classification and machine learning, classification error is an important performance measure, which is minimized by the Bayes decision rule. In practice, the unknown true distribution is usually replaced with a model…

Machine Learning · Computer Science 2025-01-28 Zijian Yang , Vahe Eminyan , Ralf Schlüter , Hermann Ney

In the framework of matrix valued observables with low rank means, Stein's unbiased risk estimate (SURE) can be useful for risk estimation and for tuning the amount of shrinkage towards low rank matrices. This was demonstrated by Cand\`es…

Statistics Theory · Mathematics 2017-09-01 Niels Richard Hansen

In this paper we explore the maximum precision attainable in the location of a point source imaged by a pixel array detector in the presence of a background, as a function of the detector properties. For this we use a well-known result from…

Instrumentation and Methods for Astrophysics · Physics 2015-06-15 Rene Mendez , Jorge Silva , Rodrigo Lobos

In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…

Machine Learning · Computer Science 2018-03-02 Alan Mackey , Xiyang Luo , Elad Eban

We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the…

Statistics Theory · Mathematics 2015-06-29 Yen-Huan Li , Ya-Ping Hsieh , Nissim Zerbib , Volkan Cevher

Class-conditional noise commonly exists in machine learning tasks, where the class label is corrupted with a probability depending on its ground-truth. Many research efforts have been made to improve the model robustness against the…

Machine Learning · Computer Science 2021-05-18 Ming-Kun Xie , Sheng-Jun Huang

Constrained Markov Decision Processes are a class of stochastic decision problems in which the decision maker must select a policy that satisfies auxiliary cost constraints. This paper extends upper confidence reinforcement learning for…

Machine Learning · Computer Science 2020-01-28 Liyuan Zheng , Lillian J. Ratliff