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DEMANDE: Density Matrix Neural Density Estimation
Journal article   Open access   Peer reviewed

DEMANDE: Density Matrix Neural Density Estimation

Joseph A. Gallego-Mejia and Fabio A. Gonzalez
IEEE access, v 11, pp 53062-53078
2023
DOI: https://doi.org/10.1109/ACCESS.2023.3279123
url
https://doi.org/10.1109/ACCESS.2023.3279123View
Published, Version of Record (VoR) Open

Abstract

adaptive Fourier features Complexity theory Computational modeling Density estimation density matrices Density measurement Fourier transforms Kernel kernel density estimation kernel methods neural density estimation Parametric statistics quantum-inspired machine learning random Fourier features Training data
Density estimation is a fundamental task in statistics and machine learning that aims to estimate, from a set of samples, the probability density function of the distribution that generated them. There are different methods for addressing this problem but recently deep-neural density estimation methods have emerged as a powerful alternative. This paper presents a novel method for neural density estimation based on density matrices and adaptive Fourier features. Density matrices are commonly used in quantum mechanics to represent the quantum state of a physical system. In this work, they are used to estimate probability densities using an operation called quantum measurement. The proposed method can be trained without optimization using an averaging operation over the samples of the training dataset. It can also be integrated with deep learning architectures and trained using gradient descent. The performance of the proposed method was evaluated on a range of synthetic and real datasets and compared with fast kernel density estimation and state-of-the-art neural density estimation methods. The results demonstrate that the proposed method achieves competitive performance while being faster and more efficient than existing methods.

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2 citations in Web of Science
3 citations in Scopus

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