Related papers: On the Information in Extreme Measurements for Par…
The design and analysis of diffusive molecular communication systems generally requires knowledge of the environment's physical and chemical properties. Furthermore, prospective applications might rely on the timely detection of changes in…
Motivated by the poor performance of cross-validation in settings where data are scarce, we propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization.Our approach exploits the optimization problem's…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…
We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is…
One-bit quantization has garnered significant attention in recent years for various signal processing and communication applications. Estimating model parameters from one bit quantized data can be challenging, particularly when the…
Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end,…
The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable…
The tradeoff relation between speed and cost is a central issue in designing fast and efficient information processing devices. We derive an achievable bound on thermodynamic cost for obtaining information through finite-time…
Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
In this paper, we investigate threshold effects associated with swapping of signal and noise subspaces in estimating signal parameters from compressed noisy data. The term threshold effect refers to a sharp departure of mean-squared error…
Measurements on a subset of the boundary are common in electrical impedance tomography, especially any electrode model can be interpreted as a partial boundary problem. The information obtained is different to full-boundary measurements as…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
We formulate the problem of performing optimal data compression under the constraints that compressed data can be used for accurate classification in machine learning. We show that this translates to a problem of minimizing the mutual…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
In a previous paper, we studied a kernel estimate of the upper edge of a two-dimensional bounded set, based upon the extreme values of a Poisson point process. The initial paper "Geffroy J. (1964) Sur un probl\`eme d'estimation…