Sutanoy Dasgupta
Shape-constrained and unconstrained density estimation using geometric exploration
Dasgupta, Sutanoy; Pati, Debdeep; Jermyn, Ian H.; Srivastava, Anuj
Abstract
The problem of nonparametrically estimating probability density functions (pdfs) from observed data requires posing and solving optimization problems on the space of pdfs. We take a geometric approach and explore this space for optimization using actions of a time-warping group. One action, termed area preserving, is transitive and is applicable to the case of unconstrained density estimation. In this case, we take a two-step approach that involves obtaining any initial estimate of the pdf and then transforming it via this warping action to reach the final estimate by maximizing the log-likelihood function. Another action, termed mode-preserving, is useful in situations where the pdf is constrained in shape, i.e. the number of its modes is known. As earlier, we initialize the estimation with an arbitrary element of the correct shape class, and then search over all time warpings to reach the optimal pdf within that shape class. Optimization over warping functions is performed numerically using the geometry of the group of warping functions. These methods are illustrated using a number of simulated examples.
Citation
Dasgupta, S., Pati, D., Jermyn, I. H., & Srivastava, A. (2018, June). Shape-constrained and unconstrained density estimation using geometric exploration. Presented at IEEE Statistical Signal Processing Workshop (SSP)., Freiburg, Germany
Presentation Conference Type | Conference Paper (published) |
---|---|
Conference Name | IEEE Statistical Signal Processing Workshop (SSP). |
Start Date | Jun 10, 2018 |
End Date | Jun 13, 2018 |
Acceptance Date | Mar 27, 2018 |
Online Publication Date | Aug 30, 2018 |
Publication Date | Aug 30, 2018 |
Deposit Date | Aug 3, 2018 |
Publicly Available Date | Aug 30, 2018 |
Pages | 358-362 |
Series ISSN | 2373-0803 |
Book Title | 2018 IEEE Statistical Signal Processing Workshop (SSP 2018) : 10-13 June 2018, Freiburg im Breisgau, Germany. |
DOI | https://doi.org/10.1109/ssp.2018.8450768 |
Public URL | https://durham-repository.worktribe.com/output/1144912 |
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