Related papers: Local solutions of Maximum Likelihood Estimation i…
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…
Quantum error mitigation is an important technique to reduce the impact of noise in quantum computers. With more and more qubits being supported on quantum computers, there are two emerging fundamental challenges. First, the number of shots…
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present…
In standard optical tomographic methods, the off-diagonal elements of a density matrix $\rho$ are measured indirectly. Thus, the reconstruction of $\rho$, even if it is based on linear inversion, typically magnifies small errors in the…
The maximum likelihood strategy to the estimation of group parameters allows to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results…
Given the recent developments in quantum techniques, modeling the physical Hamiltonian of a target quantum many-body system is becoming an increasingly practical and vital research direction. Here, we propose an efficient strategy combining…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
In this paper we present an inexact stepsize selection for the Diluted R\rho R algorithm, used to obtain the maximum likelihood estimate to the density matrix in quantum state tomography. We give a new interpretation for the diluted R\rho R…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
We undertake a detailed study of the performance of maximum likelihood (ML) estimators of the density matrix of finite-dimensional quantum systems, in order to interrogate generic properties of frequentist quantum state estimation. Existing…
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density…
Mixtures of factor analyzers are becoming more and more popular in the area of model based clustering of high-dimensional data. According to the likelihood approach in data modeling, it is well known that the unconstrained log-likelihood…
We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can…
Reconstructing the full quantum state of a many-body system requires the estimation of a number of parameters that grows exponentially with system size. Nevertheless, there are situations in which one is only interested in a subset of these…
We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with $M \geq 3$ components. Our first main result shows that the population likelihood function has bad local maxima even…
Quantum state tomography is a daunting challenge of experimental quantum computing even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the…
The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical…
Motivated by real-world situations found in high energy particle physics, we consider a generalisation of the likelihood-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. By extension, this…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…