Kernel density estimation via diffusion

By Zdravko I. Botev, Joseph F. Grotowski, Dirk P. Kroese. 2010

1,539 citations recorded by the source corpus.

We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b5b608cff333bce1efcfcd300acb9633804d4278

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In Computational Mechanics

In Computer Vision and Pattern Recognition

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Citations in the corpus

Methods for Summarizing Radiocarbon Datasets (2017, methodology): “Panel (a) shows the comparison of different methods for bandwidth estimation for data sampled from a bimodal normal distribution with centers at ± 10 and standard deviation of 3; blue: Sivermanrule estimate, red: the MatLab KDE module (Botev et al. 2010) and green: the KDE_Plot method described here”
Probit Transformation for Kernel Density Estimation on the Unit Interval (2013, methodology): “For f̂X,diff, the “automatic” bandwidth (see Botev, Grotoswki, and Kroese 2010) was used.”
Revealing the vectors of cellular identity with single-cell genomics (2016, methodology): “To achieve this, DREVI computes a two-dimensional kernel density estimation for f ( X , Y ) via a heat diffusion formulation 183 , derives f ( Y | X ) from it, and visualizes f ( Y | X ) as a heat map.”
Threshold Regression With a Threshold Boundary (2020, methodology): “Pan (2015) adopted a twostep method as in Card, Mas, and Rothstein (2008).”
Kernel Density Estimation on a Linear Network (2017, methodology): “On the real line, Chaudhuri & Marron (2000) drew attention to the relation between kernel density estimation and diffusion, and Botev et al. (2010) exploited this to develop improved density estimators that intrinsically include edge corrections and have faster convergence rates.”
A data-driven statistical framework for post-grasp manipulation (2014, neutral): “al [3].”
A data-driven analysis of energy balance closure across FLUXNET research sites: The role of landscape-scale heterogeneity (2013, methodology): “We used a linear diffusion algorithm following Botev et al. (2010) to choose optimal kernel bandwidths and avoid over- or under-smoothing.”
XSimGCL: Towards Extremely Simple Graph Contrastive Learning for Recommendation (2022, background): “Restrictions apply. density estimation [33] of arctan (feature_y/feature_x) on the unit hypersphere S 1 for a clearer presentation.”
CaImAn an open source tool for scalable calcium imaging data analysis (2019, methodology): “To determine the optimal percentile level an empirical histogram of the trace (or parts of it in case of long traces) is computed using a diffusion kernel density estimator (Botev et al., 2010), and the mode of this density is used to define the baseline and its corresponding percentile level.”
Low-mass dark matter search with CDMSlite (2017, methodology): “The third component was based on a two-dimensional kernel-density estimate [42] of the ∆χ(2)LF”
Bivariate frequency analysis of floods using a diffusion based kernel density estimator (2013, methodology): “…1994], and use of nonconventional kernels such as beta kernels [e.g., Chen, 1999, 2000; Bouezmarni and Scaillet, 2003], gamma kernels [e.g., Bouezmarni and Rombouts, 2009], boundary kernels [e.g., Gasser and M€uller, 1979], and adaptive kernels [e.g., Terrell and Scott, 1992; Botev et al., 2010].”
Parzen Window Density Estimator-Based Probabilistic Power Flow With Correlated Uncertainties (2016, methodology): “A nonparametric based density estimation is presented in [21] where the PDFs of PPF outputs are plotted using linear diffusion method introduced in [22].”
GetDist: a Python package for analysing Monte Carlo samples (2019, positive): “Using a Discrete Cosine Transform (DCT), this can also efficiently handle leading-order boundary effects along parameter axes, so that boundaries are not mistaken for large derivatives [1].”
Are Graph Augmentations Necessary?: Simple Graph Contrastive Learning for Recommendation (2021, methodology): “Then we plot the feature distributions with the nonparametric Gaussian kernel density estimation [3] inR2 (shown in Fig.”