File:MULTIVARIATE PROBABILITY DENSITY ESTIMATION USING PIECEWISE AFFINE FUNCTIONS (IA multivariateprob1094562732).pdf
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[edit]MULTIVARIATE PROBABILITY DENSITY ESTIMATION USING PIECEWISE AFFINE FUNCTIONS
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| Author |
Samudio, Gabriel M. |
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| Title |
MULTIVARIATE PROBABILITY DENSITY ESTIMATION USING PIECEWISE AFFINE FUNCTIONS |
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| Publisher |
Monterey, CA; Naval Postgraduate School |
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| Description |
Continuous multivariate data is ubiquitous in U.S. Military Operations Research. Since continuous distributions are fully characterized by their probability density functions, we concentrate on estimating such functions. Current estimation methods perform well for low dimensions; however, they can be too restrictive to capture the actual data characteristics, and can become intractable beyond three dimensions. This work develops a new estimation technique that seeks to increase flexibility and mitigate the curse of dimensionality. We achieve both by modeling the actual density using piecewise affine functions; however, we impose a nonconvex maximum likelihood optimization problem. The problem includes nine parameters, which can each affect the resulting estimate likelihood value and computation time. We conduct case studies on estimating the density for data up to five dimensions on sample sizes as low as 100 points. The results indicate progress in moderating the nonconvexity challenge to optimize the likelihood, and demonstrate potential advantages over currently used methods. Subjects: maximum likelihood; piecewise affine functions; smooth maximum likelihood problem; relative log likelihood |
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| Language | English | |
| Publication date | June 2019 | |
| Current location |
IA Collections: navalpostgraduateschoollibrary; fedlink |
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| Accession number |
multivariateprob1094562732 |
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| Source | ||
| Permission (Reusing this file) |
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States. | |
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| This file has been identified as being free of known restrictions under copyright law, including all related and neighboring rights. | ||
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| current | 03:42, 23 July 2020 |  | 1,275 × 1,650, 68 pages (2.48 MB) | Fæ (talk | contribs) | FEDLINK - United States Federal Collection multivariateprob1094562732 (User talk:Fæ/IA books#Fork8) (batch 1993-2020 #22496) |
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