Related papers: On the Information in Extreme Measurements for Par…

Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to…

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…

This paper applies the recently axiomatized Optimum Information Principle (minimize the Kullback-Leibler information subject to all relevant information) to nonparametric density estimation, which provides a theoretical foundation as well…

Bringing a high-dimensional dataset into science-ready shape is a formidable challenge that often necessitates data compression. Compression has accordingly become a key consideration for contemporary cosmology, affecting public data…

We present a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity. It turns out that this function has a maximum at its fixed point.…

Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…

In this paper we pose the question: After gathering N data points, at what value of the control parameter should the next measurement be done? We propose an on-line algorithm which samples optimally by maximizing the gain in information on…

In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…

Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this…

In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…

We experimentally analyzed the statistical errors in quantum-state estimation and examined whether their lower bound, which is derived from the Cramer-Rao inequality, can be truly attained or not. In the experiments, polarization states of…

In this work we demonstrate the use of neural networks for rapid extraction of signal parameters of discretely sampled signals. In particular, we use dense autoencoder networks to extract the parameters of interest from exponentially…

Several current ultra-wide band applications, such as millimeter wave radar and communication systems, require high sampling rates and therefore expensive and energy-hungry analogto-digital converters (ADCs). In applications where cost and…

When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…

This paper addresses the challenging problem of parameter estimation for multicomponent complex exponential signals, commonly known as sums of cisoids. Traditional approaches that estimate individual component parameters face significant…

Extremes of information combining inequalities play an important role in the analysis of sparse-graph codes under message-passing decoding. We introduce new tools for the derivation of such inequalities, and show by means of a concrete…

This paper studies distance estimation for diffusive molecular communication. The Cramer-Rao lower bound on the variance of the distance estimation error is derived. The lower bound is derived for a physically unbounded environment with…