Nonparametric Density Estimation: Toward Computational Tractability

By Alexander G. Gray, Andrew W. Moore. 2003

202 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Evaluation & Benchmarks, Probabilistic & Bayesian Methods, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Evaluation & Benchmarks

In Probabilistic & Bayesian Methods

In Signal Processing

Citations in the corpus

Maximum inner-product search using cone trees (2012, methodology): “The dualtree algorithms have been applied to different tree-based algorithms like nearest-neighbor search [15] and kernel density estimation [16] with theoretical runtime guarantees [31].”
Adaptive density estimation: a curse of support? ✩ (2009, background): “It is worth noting that these kernel methods may have a high computational cost, are often based on asymptotic arguments and do not provide theoretical guarantees from the adaptive minimax point of view.”
Fast High-dimensional Kernel Summations Using the Monte Carlo Multipole Method (2008, methodology): “For example, finite-difference scheme [5, 6] can be used for the CANSUMMARIZEEXACT and SUMMARIZEEXACT functions in any general dimension.”
Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation (2017, methodology): “We use the R package np [23] with kd-trees and Epanechnikov kernels for computational efficiency [19, 25].”
Current Status of Methods for Defining the Applicability Domain of (Quantitative) Structure-Activity Relationships (2005, methodology): “An algorithm for multivariate kernel density estimation has been developed by Gray & Moore (31, 32).”
Multivariate Density Estimation by Bayesian Sequential Partitioning (2013, background): “Additional development in kernel estimates can be found in Gray (2003), Fan and Marron (1994), Wand (1994), and Yang et al. (2003).”
Fast Gaussian process methods for point process intensity estimation (2008, methodology): “Other methods for fast kernel matrix multiplications include Fast Gauss Transforms (FGT) (Raykar et al., 2005) and kd-Trees (Shen et al., 2006; Gray & Moore, 2003 ).”
Linear-time Algorithms for Pairwise Statistical Problems (2009, methodology): “These dual-tree algorithmshave been shown to be significantly more efficient in practice than the corresponding single-tree algorithms for nearest neighbor se a ch and kernel summations [9, 10, 11].”
A Non-parametric Bayesian Network Prior of Human Pose (2013, unknown): “There exist many fast methods for the evaluation of kernel density estimates, but the popular approaches are either not suited for high-dimensional data [7], do not lead to a speed-up for sequential data [26] or are hard to implement due to their complexity [9].”
Nonparametric Conditional Density Estimation in a High-Dimensional Regression Setting (2016, methodology): “Because the cross-validation procedure in Hall, Racine, and Li (2004) is computationally intractable for large sample sizes and high dimensions, we instead use the R package implementation with kd-trees and likelihood-cross-validated bandwidths (Gray and Moore 2003; Holmes, Gray, and Isbell 2012).”
Fast large scale Gaussian process regression using approximate matrix-vector products (2006, methodology): “Fast Matrix-Vector multiplication algorithms: In order to compute the matrix-vector product we experimented with two algorithms–(1) the IFGT 4 [26] and (2) the kd-tree based dual-tree algorithm 5 [4].”