Sutanoy Dasgupta
Modality-Constrained Density Estimation via Deformable Templates
Dasgupta, Sutanoy; Pati, Debdeep; Jermyn, Ian H.; Srivastava, Anuj
Abstract
Estimation of a probability density function (pdf) from its samples, while satisfying certain shape constraints, is an important problem that lacks coverage in the literature. This article introduces a novel geometric, deformable template constrained density estimator (dtcode) for estimating pdfs constrained to have a given number of modes. Our approach explores the space of thus-constrained pdfs using the set of shape-preserving transformations: an arbitrary template from the given shape class is transformed via a shape-preserving transformation to obtain the final optimal estimate. The search for this optimal transformation, under the maximum-likelihood criterion, is performed by mapping transformations to the tangent space of a Hilbert sphere, where they are effectively linearized, and can be expressed using an orthogonal basis. This framework is first applied to (univariate) unconditional densities and then extended to conditional densities. We provide asymptotic convergence rates for dtcode, and an application of the framework to the speed distributions for different traffic flows on Californian highways.
Citation
Dasgupta, S., Pati, D., Jermyn, I. H., & Srivastava, A. (2021). Modality-Constrained Density Estimation via Deformable Templates. Technometrics, 63(4), 536-547. https://doi.org/10.1080/00401706.2020.1867647
Journal Article Type | Article |
---|---|
Acceptance Date | Nov 23, 2020 |
Online Publication Date | Feb 1, 2021 |
Publication Date | 2021 |
Deposit Date | Feb 9, 2021 |
Publicly Available Date | Feb 1, 2022 |
Journal | Technometrics |
Print ISSN | 0040-1706 |
Electronic ISSN | 1537-2723 |
Publisher | American Statistical Association |
Peer Reviewed | Peer Reviewed |
Volume | 63 |
Issue | 4 |
Pages | 536-547 |
DOI | https://doi.org/10.1080/00401706.2020.1867647 |
Public URL | https://durham-repository.worktribe.com/output/1252656 |
Files
Accepted Journal Article
(560 Kb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by-nc/4.0/
Copyright Statement
This is an Accepted Manuscript version of the following article, accepted for publication in Technometrics. Dasgupta, Sutanoy, Pati, Debdeep, Jermyn, Ian H. & Srivastava, Anuj (2021). Modality-Constrained Density Estimation via Deformable Templates. Technometrics 63(4): 536-547. It is deposited under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
You might also like
Numerical Inversion of SRNF Maps for Elastic Shape Analysis of Genus-Zero Surfaces
(2017)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2025
Advanced Search