Related papers: Relaxation of the EM Algorithm via Quantum Anneali…
This paper proposes a quantum-classical algorithm to evaluate and select classical artificial neural networks architectures. The proposed algorithm is based on a probabilistic quantum memory and the possibility to train artificial neural…
With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal…
In this paper, we address the issue of model specification in probabilistic latent variable models (PLVMs) using an infinite-horizon optimal control approach. Traditional PLVMs rely on joint distributions to model complex data, but…
Optimisation plays a central role in a wide range of scientific and industrial applications, and quantum computing has been widely proposed as a means to achieve computational advantages in this domain. To date, research into the design of…
Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization…
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum…
Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…
Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or…
We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. The idea is tested by the two models, the transverse Ising model and the traveling salesman…
In this letter, we employ and design the expectation--conditional maximization either (ECME) algorithm, a generalisation of the EM algorithm, for solving the maximum likelihood direction finding problem of stochastic sources, which may be…
Recent experimental breakthroughs have signalled the imminent arrival of the early fault-tolerant era. However, for a considerable period in the foreseeable future, relying solely on quantum error correction for full error suppression will…
In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other…
The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations…
Although the expectation maximisation (EM) algorithm was introduced in 1970, it remains somewhat inaccessible to machine learning practitioners due to its obscure notation, terse proofs and lack of concrete links to modern machine learning…
Current quantum computers suffer from non-stationary noise channels with high error rates, which undermines their reliability and reproducibility. We propose a Bayesian inference-based adaptive algorithm that can learn and mitigate quantum…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
The EM algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Supplemented EM (SEM; Meng & Rubin,…
Quantum state tomography (QST), the task of estimating an unknown quantum state given measurement outcomes, is essential to building reliable quantum computing devices. Whereas computing the maximum-likelihood (ML) estimate corresponds to…