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Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and…

Statistics Theory · Mathematics 2015-05-29 Zhiqiang Tan

The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…

Statistics Theory · Mathematics 2026-03-31 Taehyun Kim , Bodhisattva Sen

We consider the fixed-budget best arm identification problem with rewards following normal distributions. In this problem, the forecaster is given $K$ arms (or treatments) and $T$ time steps. The forecaster attempts to find the arm with the…

Machine Learning · Statistics 2024-04-16 Junpei Komiyama

Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…

Methodology · Statistics 2012-07-03 Ryan Martin , Duncan Ermini Leaf , Chuanhai Liu

Most bandit algorithm designs are purely theoretical. Therefore, they have strong regret guarantees, but also are often too conservative in practice. In this work, we pioneer the idea of algorithm design by minimizing the empirical Bayes…

Machine Learning · Computer Science 2020-06-12 Chih-Wei Hsu , Branislav Kveton , Ofer Meshi , Martin Mladenov , Csaba Szepesvari

The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…

Statistics Theory · Mathematics 2016-12-01 Christophe Culan , Claude Adnet

We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by…

Machine Learning · Computer Science 2012-03-19 Mithun Das Gupta , Thomas S. Huang

In this paper, we develop an approach for the exact determination of the minimum sample size for the estimation of a Poisson parameter with prescribed margin of error and confidence level. The exact computation is made possible by reducing…

Statistics Theory · Mathematics 2008-06-19 Xinjia Chen

We consider the nonparametric estimation of the intensity function of a Poisson point process in a circular model from indirect observations $N_1,\ldots,N_n$. These observations emerge from hidden point process realizations with the target…

Statistics Theory · Mathematics 2019-02-19 Martin Kroll

We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…

Methodology · Statistics 2026-01-19 Pierre Alquier , Jean-David Fermanian , Benjamin Poignard

An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This…

Statistics Theory · Mathematics 2012-10-19 Ryan Martin

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…

Machine Learning · Statistics 2012-12-04 Xun Huan , Youssef M. Marzouk

The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…

Statistics Theory · Mathematics 2008-10-30 Patricia Reynaud-Bouret , Vincent Rivoirard

Inference in the presence of outliers is an important field of research as outliers are ubiquitous and may arise across a variety of problems and domains. Bayesian optimization is method that heavily relies on probabilistic inference. This…

Machine Learning · Computer Science 2017-12-14 Ruben Martinez-Cantin , Kevin Tee , Michael McCourt

One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements…

Methodology · Statistics 2017-06-22 Ilja Klebanov , Alexander Sikorski , Christof Schütte , Susanna Röblitz

The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of…

Machine Learning · Computer Science 2019-10-24 Viet Anh Nguyen , Soroosh Shafieezadeh-Abadeh , Man-Chung Yue , Daniel Kuhn , Wolfram Wiesemann

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Machine Learning · Statistics 2020-12-29 Simón Rodríguez Santana , Daniel Hernández-Lobato

We propose an unconstrained stochastic approximation method of finding the optimal measure change (in an a priori parametric family) for Monte Carlo simulations. We consider different parametric families based on the Girsanov theorem and…

Probability · Mathematics 2018-02-20 Vincent Lemaire , Gilles Pagès

The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…

Methodology · Statistics 2022-09-14 Denis Talbot , Miceline Mésidor , Yohann Chiu , Marc Simard , Caroline Sirois

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

Computation · Statistics 2022-08-18 Oskar Gustafsson , Mattias Villani , Pär Stockhammar