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In this paper, we study the low-rank matrix completion problem, a class of machine learning problems, that aims at the prediction of missing entries in a partially observed matrix. Such problems appear in several challenging applications…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
The purpose of this research is to develop an MCMC algorithm for estimating the Q-matrix. Based on the DINA model, the algorithm starts with estimating correlated attributes. Using a saturated model and a binary decimal conversion, the…
Parameter inference for stochastic differential equation mixed effects models (SDEMEMs) is a challenging problem. Analytical solutions for these models are rarely available, which means that the likelihood is also intractable. In this case,…
Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such…
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
The implementation and practicality of quantum algorithms highly hinge on the quality of operations within a quantum processor. Therefore, including realistic error models in quantum computing simulation platforms is crucial for testing…
The discrete nature of transmitted symbols poses challenges for achieving optimal detection in multiple-input multiple-output (MIMO) systems associated with a large number of antennas. Recently, the combination of two powerful machine…
We study quantum anomaly detection with density estimation and multivariate Gaussian distribution. Both algorithms are constructed using the standard gate-based model of quantum computing. Compared with the corresponding classical…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
In the following article we develop a particle filter for approximating Feynman-Kac models with indicator potentials. Examples of such models include approximate Bayesian computation (ABC) posteriors associated with hidden Markov models…
In this paper we describe in detail and generalize a method for quantum process tomography that was presented in [A. Bendersky, F. Pastawski, J. P. Paz, Physical Review Letters 100, 190403 (2008)]. The method enables the efficient…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Quantum Error Mitigation (QEM) enables the extraction of high-quality results from the presently-available noisy quantum computers. In this approach, the effect of the noise on observables of interest can be mitigated using multiple…
We present a universal technique for quantum state estimation based on the maximum-likelihood method. This approach provides a positive definite estimate for the density matrix from a sequence of measurements performed on identically…
In the framework of noisy quantum homodyne tomography with efficiency parameter $0 < \eta \leq 1$, we propose two estimators of a quantum state whose density matrix elements $\rho_{m,n}$ decrease like $e^{-B(m+n)^{r/ 2}}$, for fixed known…