Fast multivariate log-concave density estimation

Fabian Rathke and Christoph Schnörr

Computational Statistics & Data Analysis, 2019, vol. 140, issue C, 41-58

Abstract: A novel computational approach to log-concave density estimation is proposed. Previous approaches utilize the piecewise-affine parametrization of the density induced by the given sample set. The number of parameters as well as non-smooth subgradient-based convex optimization for determining the maximum likelihood density estimate cause long runtimes for dimensions d≥2 and large sample sets. The presented approach is based on mildly non-convex smooth approximations of the objective function and sparse, adaptive piecewise-affine density parametrization. Established memory-efficient numerical optimization techniques enable to process larger data sets for dimensions d≥2. While there is no guarantee that the algorithm returns the maximum likelihood estimate for every problem instance, we provide comprehensive numerical evidence that it does yield near-optimal results after significantly shorter runtimes. For example, 10000 samples in R2 are processed in two seconds, rather than in ≈14 hours required by the previous approach to terminate. For higher dimensions, density estimation becomes tractable as well: Processing 10000 samples in R6 requires 35 min. The software is publicly available as CRAN R package fmlogcondens.

Keywords: Log-concavity; Maximum likelihood estimation; Nonparametric density estimation; Adaptive piecewise-affine parametrization (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947319300891
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:140:y:2019:i:c:p:41-58

DOI: 10.1016/j.csda.2019.04.005

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().