Fast multivariate log-concave density estimation
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 maxi...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
30 May 2019
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| In: |
Computational statistics & data analysis
Year: 2019, Volume: 140, Pages: 41-58 |
| DOI: | 10.1016/j.csda.2019.04.005 |
| Online Access: | Verlag, Volltext: https://doi.org/10.1016/j.csda.2019.04.005 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0167947319300891 
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| Author Notes: | Fabian Rathke, Christoph Schnörr |
| Summary: | 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. |
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| Item Description: | Gesehen am 27.08.2019 |
| Physical Description: | Online Resource |
| DOI: | 10.1016/j.csda.2019.04.005 |