Related papers: Optimal Experiment Design for Quantum State and Pr…

We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and,…

Physics, chemistry, biology or finance are just some examples out of the many fields where complex Ornstein-Uhlenbeck (OU) processes have various applications in statistical modelling. They play role e.g. in the description of the motion of…

Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoising problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior…

We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an $O ( ( 1 / k ) \log D )$ rate, where $k$ denotes the number of…

Accurate noise estimation is essential for fault-tolerant quantum computing, as decoding performance depends critically on the fidelity of the circuit-level noise parameters. In this work, we introduce a differentiable Maximum Likelihood…

We investigate the optimal convex approximation of the quantum state with respect to a set of available states. By isometric transformation, we have presented the general mathematical model and its solutions together with a triple…

Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of dynamic experiments to generate input-output…

Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…

Quantum state tomography is an indispensable but costly part of many quantum experiments. Typically, it requires measurements to be carried in a number of different settings on a fixed experimental setup. The collected data is often…

In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…

In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to…

Precise estimation of physical parameters underpins both scientific discovery and technological development. A central goal of quantum metrology and sensing is to exploit quantum resources like entanglement to devise optimal strategies for…

In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…

This paper studies the optimal state estimation problem for interconnected systems. Each subsystem can obtain its own measurement in real time, while, the measurements transmitted between the subsystems suffer from random delay. The optimal…

We show how an upper bound for the ability to discriminate any number N of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective…

We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate `null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state.…

We develop a preference elicitation method for a Von Neumann-Morgenstern (VNM)-type decision-maker from pairwise comparison data in the presence of response errors. We apply the maximum likelihood estimation (MLE) method to jointly elicit…

This work considers Maximum Likelihood Estimation (MLE) of a Toeplitz structured covariance matrix. In this regard, an equivalent reformulation of the MLE problem is introduced and two iterative algorithms are proposed for the optimization…

This paper revisits the work of Rauch et al. (1965) and develops a novel method for recursive maximum likelihood particle filtering for general state-space models. The new method is based on statistical analysis of incomplete observations…

We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information…