Fast Kernel Density Estimation with Density Matrices and Random Fourier Features

• URL: http://arxiv.org/abs/2208.01206v1
• Date: Tue, 2 Aug 2022 02:11:10 GMT
• Title: Fast Kernel Density Estimation with Density Matrices and Random Fourier Features
• Authors: Joseph A. Gallego M., Juan F. Osorio, Fabio A. Gonz\'alez
• Abstract summary: kernels density estimation (KDE) is one of the most widely used nonparametric density estimation methods. DMKDE uses density matrices, a quantum mechanical formalism, and random Fourier features, an explicit kernel approximation, to produce density estimates. DMKDE is on par with its competitors for computing density estimates and advantages are shown when performed on high-dimensional data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Density Estimation via Binless Multidimensional Integration [45.21975243399607]
  We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences between neighbouring data points. The method is tested on a variety of complex synthetic high-dimensional datasets, and is benchmarked on realistic datasets from the chemical physics literature.
  arXiv  Detail & Related papers  (2024-07-10T23:45:20Z)
• Variational Weighting for Kernel Density Ratios [11.555375654882525]
  Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. We derive an optimal weight function that reduces bias in standard kernel density estimates for density ratios, leading to improved estimates of prediction posteriors and information-theoretic measures.
  arXiv  Detail & Related papers  (2023-11-06T10:12:19Z)
• AD-DMKDE: Anomaly Detection through Density Matrices and Fourier Features [0.0]
  The method can be seen as an efficient approximation of Kernel Density Estimation (KDE) A systematic comparison of the proposed method with eleven state-of-the-art anomaly detection methods on various data sets is presented.
  arXiv  Detail & Related papers  (2022-10-26T15:43:16Z)
• Learning Transfer Operators by Kernel Density Estimation [0.0]
  We recast the problem within the framework of statistical density estimation. We demonstrate the validity and effectiveness of this approach in estimating the eigenvectors of the Frobenius-Perron operator. We suggest the possibility of incorporating other density estimation methods into this field.
  arXiv  Detail & Related papers  (2022-08-01T14:28:10Z)
• Quantum Adaptive Fourier Features for Neural Density Estimation [0.0]
  This paper presents a method for neural density estimation that can be seen as a type of kernel density estimation. The method is based on density matrices, a formalism used in quantum mechanics, and adaptive Fourier features. The method was evaluated in different synthetic and real datasets, and its performance compared against state-of-the-art neural density estimation methods.
  arXiv  Detail & Related papers  (2022-08-01T01:39:11Z)
• TAKDE: Temporal Adaptive Kernel Density Estimator for Real-Time Dynamic Density Estimation [16.45003200150227]
  We name the temporal adaptive kernel density estimator (TAKDE) TAKDE is theoretically optimal in terms of the worst-case AMISE. We provide numerical experiments using synthetic and real-world datasets, showing that TAKDE outperforms other state-of-the-art dynamic density estimators.
  arXiv  Detail & Related papers  (2022-03-15T23:38:32Z)
• Density Ratio Estimation via Infinitesimal Classification [85.08255198145304]
  We propose DRE-infty, a divide-and-conquer approach to reduce Density ratio estimation (DRE) to a series of easier subproblems. Inspired by Monte Carlo methods, we smoothly interpolate between the two distributions via an infinite continuum of intermediate bridge distributions. We show that our approach performs well on downstream tasks such as mutual information estimation and energy-based modeling on complex, high-dimensional datasets.
  arXiv  Detail & Related papers  (2021-11-22T06:26:29Z)
• Density-Based Clustering with Kernel Diffusion [59.4179549482505]
  A naive density corresponding to the indicator function of a unit $d$-dimensional Euclidean ball is commonly used in density-based clustering algorithms. We propose a new kernel diffusion density function, which is adaptive to data of varying local distributional characteristics and smoothness.
  arXiv  Detail & Related papers  (2021-10-11T09:00:33Z)
• Meta-Learning for Relative Density-Ratio Estimation [59.75321498170363]
  Existing methods for (relative) density-ratio estimation (DRE) require many instances from both densities. We propose a meta-learning method for relative DRE, which estimates the relative density-ratio from a few instances by using knowledge in related datasets. We empirically demonstrate the effectiveness of the proposed method by using three problems: relative DRE, dataset comparison, and outlier detection.
  arXiv  Detail & Related papers  (2021-07-02T02:13:45Z)
• A Note on Optimizing Distributions using Kernel Mean Embeddings [94.96262888797257]
  Kernel mean embeddings represent probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. We show that when the kernel is characteristic, distributions with a kernel sum-of-squares density are dense. We provide algorithms to optimize such distributions in the finite-sample setting.
  arXiv  Detail & Related papers  (2021-06-18T08:33:45Z)
• Nonparametric Density Estimation from Markov Chains [68.8204255655161]
  We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estor. Our estimator presents several benefits with respect to the usual ones and can be used straightforwardly as a foundation in all density-based algorithms.
  arXiv  Detail & Related papers  (2020-09-08T18:33:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.