Related papers: A Linear Programming Approach to Attainable Cramer…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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).…
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…
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…
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…
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…
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…
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…
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…
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…