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DEMANDE: Density Matrix Neural Density Estimation
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DOI：10.1109/ACCESS.2023.3279123.png)
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Abstract
En 中文
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.
Keywords:
Density measurement
Kernel
Computational modeling
Complexity theory
Parametric statistics
Training data
Fourier transforms
Density estimation
kernel methods
neural density estimation
kernel density estimation
density matrices
random Fourier features
adaptive Fourier features
quantum-inspired machine learning