Quantum Adaptive Fourier Features for Neural Density Estimation

Gallego-Mejia, Joseph A.; González, Fabio A.

doi:10.48550/arxiv.2208.00564

Cited by 4 publications

(2 citation statements)

References 16 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

Fast Kernel Density Estimation with Density Matrices and Random Fourier Features

Gallego¹,

Osorio²,

González³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most current big data applications. Several strategies, such as tree-based or hashing-based estimators, have been proposed to improve the efficiency of the kernel density estimation method. The novel density kernel density estimation method (DMKDE) uses density matrices, a quantum mechanical formalism, and random Fourier features, an explicit kernel approximation, to produce density estimates. This method has its roots in the KDE and can be considered as an approximation method, without its memory-based restriction. In this paper, we systematically evaluate the novel DMKDE algorithm and compare it with other state-of-the-art fast procedures for approximating the kernel density estimation method on different synthetic data sets. Our experimental results show that DMKDE is on par with its competitors for computing density estimates and advantages are shown when performed on high-dimensional data. We have made all the code available as an open source software repository.Keywords density matrix • random Fourier features • kernel density estimation • approximations of kernel density estimation • quantum machine learning

show abstract

Section: Quantum Kernel Density Estimation Approximationmentioning

confidence: 99%

Fast Kernel Density Estimation with Density Matrices and Random Fourier Features

Gallego¹,

Osorio²,

González³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The random Fourier feature approximation can be further tuned using gradient descent, in a process called "Adaptive Fourier features". This algorithm was first proposed in [5]. It selects random pairs of data points (x i , x j ) and applies gradient descent to find:…”

Section: Training Strategymentioning

confidence: 99%

LEAN-DMKDE: Quantum Latent Density Estimation for Anomaly Detection

Gallego-Mejia¹,

Bustos-Brinez²,

González³

2022

Preprint

View full text Add to dashboard Cite

This paper presents an anomaly detection model that combines the strong statistical foundation of density-estimation-based anomaly detection methods with the representation-learning ability of deeplearning models. The method combines an autoencoder, for learning a low-dimensional representation of the data, with a density-estimation model based on random Fourier features and density matrices in an end-to-end architecture that can be trained using gradient-based optimization techniques. The method predicts a degree of normality for new samples based on the estimated density. A systematic experimental evaluation was performed on different benchmark datasets. The experimental results show that the method performs on par with or outperforms other state-of-the-art methods. Keywords anomaly detection • density matrix • random Fourier features • kernel density estimation • approximations of kernel density estimation • quantum machine learning • deep learning

show abstract