English
Related papers

Related papers: A Linear Programming Approach to Attainable Cramer…

200 papers

Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist…

Quantum Physics · Physics 2024-02-23 Valentin Gebhart , Manuel Gessner , Augusto Smerzi

We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…

Combinatorics · Mathematics 2024-06-25 Aida Abiad , Alexander L. Gavrilyuk , Antonina P. Khramova , Ilia Ponomarenko

The paper derives the theoretical Cramer-Rao lower bound for parameter estimation of a source (of emitting energy, gas, aerosol), monitored by a network of sensors providing binary measurements. The theoretical bound is studied in the…

Applications · Statistics 2014-05-30 Branko Ristic , Ajith Gunatilaka , Ralph Gailis

The linear programming method is applied to the space $\U_n(\C)$ of unitary matrices in order to obtain bounds for codes relative to the diversity sum and the diversity product. Theoretical and numerical results improving previously known…

Information Theory · Computer Science 2008-12-18 Jean Creignou , Hervé Diet

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…

Probability · Mathematics 2015-01-20 Raphael Lachieze-Rey , Ilya Molchanov

Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and…

Probability · Mathematics 2007-05-23 David Gamarnik

In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse…

Statistics Theory · Mathematics 2023-07-19 Mahdi Shaghaghi , Sergiy A. Vorobyov

We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…

Optimization and Control · Mathematics 2019-04-03 Andreas Ernst , Lars Grüne , Janosch Rieger

In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…

Probability · Mathematics 2018-11-22 Xinwei Bai , Jasper Goseling

We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…

Optimization and Control · Mathematics 2024-05-21 Niklas Schmid , Marta Fochesato , Tobias Sutter , John Lygeros

This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…

Quantum Physics · Physics 2020-03-06 Luigi Seveso , Matteo G. A. Paris

We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…

Optimization and Control · Mathematics 2021-06-25 Joshua L. Pulsipher , Victor M. Zavala

Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…

Machine Learning · Statistics 2019-09-26 Shusen Wang

Sampling-based motion planners have proven to be efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that…

Robotics · Computer Science 2014-04-09 Andrew Dobson , George V. Moustakides , Kostas E. Bekris

The constrained Cramer-Rao bound (CCRB) is a lower bound on the mean-squared-error (MSE) of estimators that satisfy some unbiasedness conditions. Although the CCRB unbiasedness conditions are satisfied asymptotically by the constrained…

Information Theory · Computer Science 2019-02-20 Eyal Nitzan , Tirza Routtenberg , Joseph Tabrikian

This paper derives a general expression for the Cram\'er-Rao bound (CRB) of wireless localization algorithms using range measurements subject to bias corruption. Specifically, the a priori knowledge about which range measurements are…

Information Theory · Computer Science 2011-11-10 Tao Wang

A robust model predictive control scheme for a class of constrained norm-bounded uncertain discrete-time linear systems is developed under the hypothesis that only partial state measurements are available for feedback. Off-line calculations…

Systems and Control · Computer Science 2018-07-23 Giuseppe Franzè , Massimiliano Mattei , Luciano Ollio , Valerio Scordamaglia

Small regularizers can preserve linear programming solutions exactly. This paper provides the first average-case analysis of exact regularization: with a standard Gaussian cost vector and fixed constraint set, bounds are established for the…

Optimization and Control · Mathematics 2025-10-16 Michael P. Friedlander , Sharvaj Kubal , Yaniv Plan , Matthew S. Scott

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…

Statistics Theory · Mathematics 2009-09-29 Zvika Ben-Haim , Yonina C. Eldar

We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…

Optimization and Control · Mathematics 2016-03-30 Moritz Schulze Darup