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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

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…

Statistics Theory · Mathematics 2026-04-14 Stefano Rizzelli , Judith Rousseau , Sonia Petrone

Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…

Machine Learning · Computer Science 2024-12-11 Koby Bibas

We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…

Statistics Theory · Mathematics 2019-05-24 Ujan Gangopadhyay , Gourab Mukherjee

Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…

Statistics Theory · Mathematics 2009-09-29 Mihaela Aslan

In this paper, the bit error performance of a family of likelihood ascent search (LAS) multiuser detectors is analyzed. An upper bound on the BER of any LAS detector is obtained by bounding the fixed point region with the worst initial…

Information Theory · Computer Science 2016-11-15 Yi Sun

The Reward-Biased Maximum Likelihood Estimate (RBMLE) for adaptive control of Markov chains was proposed to overcome the central obstacle of what is variously called the fundamental "closed-identifiability problem" of adaptive control, the…

Machine Learning · Computer Science 2021-05-18 Akshay Mete , Rahul Singh , Xi Liu , P. R. Kumar

Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…

Information Theory · Computer Science 2012-11-13 T. Tony Cai , Yihong Wu

We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…

Information Theory · Computer Science 2015-12-31 Yanjun Han , Jiantao Jiao , Tsachy Weissman

In parametric Bayesian learning, a prior is assumed on the parameter $W$ which determines the distribution of samples. In this setting, Minimum Excess Risk (MER) is defined as the difference between the minimum expected loss achievable when…

Machine Learning · Computer Science 2021-07-20 Hassan Hafez-Kolahi , Behrad Moniri , Shohreh Kasaei , Mahdieh Soleymani Baghshah

Maximum likelihood (ML) detection is an optimal signal detection scheme, which is often difficult to implement due to its high computational complexity, especially in a multiple-input multiple-output (MIMO) scenario. In a system with $N_t$…

Information Theory · Computer Science 2022-08-16 Sharan Mourya , Amit Kumar Dutta

The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…

Information Theory · Computer Science 2019-04-24 Nir Weinberger , Yuval Kochman

We study the uniform convergence rate of the nonparametric maximum likelihood estimator (MLE) for the sub-distribution functions in the current status data with competing risks model. It is known that the MLE have $L^2$-norm convergence…

Statistics Theory · Mathematics 2019-09-16 Sergey V. Malov

We provide a decision theoretic analysis of bandit experiments under local asymptotics. Working within the framework of diffusion processes, we define suitable notions of asymptotic Bayes and minimax risk for these experiments. For normally…

Econometrics · Economics 2025-05-06 Karun Adusumilli

The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a long established result. Explicit bounds for the distributional distance between the distribution of the MLE and the normal distribution have recently been obtained for…

Statistics Theory · Mathematics 2016-09-20 Andreas Anastasiou

The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of…

Machine Learning · Statistics 2019-03-04 Hiva Ghanbari , Minhan Li , Katya Scheinberg

Minimum Bayes Risk (MBR) decoding optimizes output selection by maximizing the expected utility value of an underlying human distribution. While prior work has shown the effectiveness of MBR decoding through empirical evaluation, few…

Computation and Language · Computer Science 2025-06-23 Yuki Ichihara , Yuu Jinnai , Kaito Ariu , Tetsuro Morimura , Eiji Uchibe

This paper presents a general stochastic model developed for a class of cooperative wireless relay networks, in which imperfect knowledge of the channel state information at the destination node is assumed. The framework incorporates…

Applications · Statistics 2015-05-19 Gareth W. Peters , Ido Nevat , Scott A. Sisson , Yanan Fan , Jinhong Yuan

We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…

Statistics Theory · Mathematics 2026-03-06 Ben Adcock , Gregor Maier , Rahul Parhi

We study the multi-task linear regression problem in the presence of contaminated tasks. We address the setting where the unknown parameters of a majority of tasks are close in the $\ell_2$-norm, while a fraction of tasks are arbitrary…

Machine Learning · Statistics 2026-05-19 Seok-Jin Kim