2022
DOI: 10.1007/s42484-022-00079-9
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Learning with density matrices and random features

Abstract: A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement, system combination and expectations as linear algebra operations. This paper explores how density matrices can be used as a building block for machine learning models exploiting their ability to straightforwardly combine linear algebra and probability. One of the main resul… Show more

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Cited by 12 publications
(11 citation statements)
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“…We use a deep CNN as a feature extractor. The extracted features are then used as inputs for the QMR method [12]. QMR uses density matrices for regression problems and works as a non-parametric density estimator.…”
Section: Deep Quantum Ordinal Regressormentioning
confidence: 99%
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“…We use a deep CNN as a feature extractor. The extracted features are then used as inputs for the QMR method [12]. QMR uses density matrices for regression problems and works as a non-parametric density estimator.…”
Section: Deep Quantum Ordinal Regressormentioning
confidence: 99%
“…In this paper we present the Deep Quantum Ordinal Regressor (DQOR), a deep probabilistic model that combines a CNN with a differentiable probabilistic regression model, the Quantum Measurement Regression (QMR) [12]. This approach allows us to:…”
Section: Introductionmentioning
confidence: 99%
“…of the KDE estimator for a query point x ∈ R d where we define γ = 1 2σ . Kernel density estimation has multiple applications some examples include: to visualize clusters of crime areas using it as a spatio-temporal modification [18]; to assess injury-related traffic accidents in London, UK [1], to generate the intensity surface in a spatial environment for moving objects couple with time geography [6]; to make a spatial analysis of city noise with information collected from a French mobile application installed on citizens' smartphones using their GPS location data [10]; to generate new samples from a given dataset by dealing with unbalanced datasets [11]; to process the image by subtracting the background in a pixel-based method [13]; to propose an end-to-end pipeline for classification [12]; to propose a classification method using density estimation and random Fourier features [8].…”
Section: Kernel Density Estimationmentioning
confidence: 99%
“…The central idea of the method density matrix kernel density estimation (DMKDE), introduced by [8] and systematically evaluated in [16], is to use density matrices along with random Fourier features to represent arbitrary probability distributions by addressing the important question of how to encode probability density functions in R n into density matrices. The overall process is divided into a training and a testing phases.…”
Section: Quantum Kernel Density Estimation Approximationmentioning
confidence: 99%
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