Nonparametric Density Estimation and Bandwidth Selection with B-spline bases: a Novel Galerkin Method

Kirkby, Justin; Rodriguez, Alvaro Leitao; Nguyen, Duy

doi:10.2139/ssrn.3769651

Cited by 1 publication

(3 citation statements)

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“…We implemented P Vs as described in Sections 2 and 3 in Python 3.9.5, leveraging the NumPy [17] and SciPy [18] libraries for computations. We implemented an approximated P BF as described by (6), which was solved with M = 10 using CVXPY [19]. An open-source repository that contains all implementations, including those to generate all the figures in this paper, is available through GitHub 1 .…”

Section: Resultsmentioning

confidence: 99%

“…Practically, pdf estimation remains one of the most common tools in data science [1][2][3], with its basic version (a histogram) being the entry point to any exploratory data analysis. As a result, the field remains active despite its long history [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…1). Recently, Cui et al [5,6] rediscovered the same estimator and studied it in much detail, but did not provide a technique to generate bona fide estimates. In this paper, we present a simple technique based on convex optimization to obtain better estimates that are bona fide pdfs within the same framework.…”

Section: Introductionmentioning

confidence: 99%

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Bona Fide Riesz Projections for Density Estimation

Pol

Unser

2022

ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a projection operator that, in contrast to previous works, guarantees the bona fide properties for the estimate, namely, nonnegativity and total probability mass 1. Our bona fide projection is defined as a convex problem. We propose solution techniques and evaluate them. Results suggest an improved performance, specifically in circumstances prone to rippling effects.

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Section: Resultsmentioning

confidence: 99%