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Modality-constrained density estimation via deformable templates

Dasgupta, Sutanoy and Pati, Debdeep and Jermyn, Ian H. and Srivastava, Anuj (2021) 'Modality-constrained density estimation via deformable templates.', Technometrics., 63 (4). pp. 536-547.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial 4.0.
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Publisher 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 (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Date accepted:23 November 2020
Date deposited:09 February 2021
Date of first online publication:01 February 2021
Date first made open access:01 February 2022

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