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This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…

Statistics Theory · Mathematics 2022-12-08 Samuel Bronstein , Stefan Engblom , Robin Marin

Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…

Machine Learning · Statistics 2020-07-07 Hossein Taheri , Ramtin Pedarsani , Christos Thrampoulidis

Variational inference is a powerful tool for approximate inference. However, it mainly focuses on the evidence lower bound as variational objective and the development of other measures for variational inference is a promising area of…

Machine Learning · Computer Science 2016-12-06 Michael Figurnov , Kirill Struminsky , Dmitry Vetrov

Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…

Statistics Theory · Mathematics 2026-03-17 Yanjun Han , Abhishek Shetty , Jacob Shkrob

Manski's celebrated maximum score estimator for the discrete choice model, which is an optimal linear discriminator, has been the focus of much investigation in both the econometrics and statistics literatures, but its behavior under…

Statistics Theory · Mathematics 2020-08-11 Debarghya Mukherjee , Moulinath Banerjee , Ya'acov Ritov

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…

Machine Learning · Statistics 2016-01-27 Akshay Krishnamurthy

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

We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…

Quantum Physics · Physics 2025-04-02 Giacomo Mauro D'Ariano , Massimiliano Federico Sacchi , Jonas Kahn

As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality,…

Applications · Statistics 2009-03-09 Vincent Y. F. Tan , Vivek K. Goyal

We study online classification of features into labels with general hypothesis classes. In our setting, true labels are determined by some function within the hypothesis class but are corrupted by unknown stochastic noise, and the features…

Machine Learning · Computer Science 2024-09-27 Changlong Wu , Ananth Grama , Wojciech Szpankowski

Recent research shows the susceptibility of machine learning models to adversarial attacks, wherein minor but maliciously chosen perturbations of the input can significantly degrade model performance. In this paper, we theoretically analyse…

Statistics Theory · Mathematics 2025-05-14 Jingfu Peng , Yuhong Yang

It is well known that Empirical Risk Minimization (ERM) may attain minimax suboptimal rates in terms of the mean squared error (Birg\'e and Massart, 1993). In this paper, we prove that, under relatively mild assumptions, the suboptimality…

Statistics Theory · Mathematics 2025-11-04 Gil Kur , Eli Putterman , Alexander Rakhlin

We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…

Quantum Physics · Physics 2012-09-26 Ulrike Herzog

This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common…

Machine Learning · Statistics 2017-03-20 Andrea Locatelli , Alexandra Carpentier , Samory Kpotufe

We study the learnability of linear separators in $\Re^d$ in the presence of bounded (a.k.a Massart) noise. This is a realistic generalization of the random classification noise model, where the adversary can flip each example $x$ with…

Machine Learning · Computer Science 2015-03-13 Pranjal Awasthi , Maria-Florina Balcan , Nika Haghtalab , Ruth Urner

This paper addresses the detection of a stochastic process in noise from irregular samples. We consider two hypotheses. The \emph{noise only} hypothesis amounts to model the observations as a sample of a i.i.d. Gaussian random variables…

Information Theory · Computer Science 2009-09-25 Walid Hachem , Eric Moulines , Francois Roueff

Empirical risk minimization (ERM) is the workhorse of machine learning, whether for classification and regression or for off-policy policy learning, but its model-agnostic guarantees can fail when we use adaptively collected data, such as…

Machine Learning · Statistics 2021-06-04 Aurélien Bibaut , Antoine Chambaz , Maria Dimakopoulou , Nathan Kallus , Mark van der Laan

An unknown $m$ by $n$ matrix $X_0$ is to be estimated from noisy measurements $Y=X_0+Z$, where the noise matrix $Z$ has i.i.d. Gaussian entries. A popular matrix denoising scheme solves the nuclear norm penalization problem $\operatorname…

Statistics Theory · Mathematics 2014-11-05 David Donoho , Matan Gavish

Training neural network models with discrete (categorical or structured) latent variables can be computationally challenging, due to the need for marginalization over large or combinatorial sets. To circumvent this issue, one typically…

Machine Learning · Computer Science 2020-12-29 Gonçalo M. Correia , Vlad Niculae , Wilker Aziz , André F. T. Martins

We consider inference for M-estimators after model selection using a sparsity-inducing penalty. While existing methods for this task require bespoke inference procedures, we propose a simpler approach, which relies on two insights: (i)…

Methodology · Statistics 2026-01-21 Ronan Perry , Snigdha Panigrahi , Daniela Witten