Maximum Penalized Likelihood Estimation

Eggermont, P. P. B.; LaRiccia, V. N.

doi:10.1007/978-1-0716-1244-6

Cited by 153 publications

(91 citation statements)

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“…The deconvolution problem was extensively studied both in statistics and in signal processing; see Eggermont and LaRiccia (2001) and references therein. The deconvolution algorithm applied to the count data is summarized in the Appendix.…”

Section: Discussionmentioning

confidence: 99%

“…Unfortunately, direct application of the above-defined algorithm generally shows that fewer and fewer smooth distributions are obtained as the iteration progresses. The standard solution then consists of stating the deconvolution problem as a maximum penalized likelihood estimation problem; see Eggermont and LaRiccia (2001) and references therein. It should be noted that the count data context is far more simple that the general deconvolution problem (also referred to as the contamination problem) since, in this case, the distribution of interest is a discrete distribution defined on a finite support and not a continuous distribution.…”

Section: Deconvolution Algorithmmentioning

confidence: 99%

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Relative Extents of Preformation and Neoformation in Tree Shoots: Analysis by a Deconvolution Method

Guédon¹,

Puntieri²,

Sabatier³

et al. 2006

Annals of Botany

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Section: Discussionmentioning

confidence: 99%

Section: Deconvolution Algorithmmentioning

confidence: 99%

Relative Extents of Preformation and Neoformation in Tree Shoots: Analysis by a Deconvolution Method

Guédon¹,

Puntieri²,

Sabatier³

et al. 2006

Annals of Botany

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“…MPLE approximates u as the maximizer of a log-likelihood term combined with a penalty term, typically enforcing smoothness [3],…”

Section: (A) Maximum Penalized Likelihood Estimationmentioning

confidence: 99%

Non-local crime density estimation incorporating housing information

Woodworth

Mohler

Bertozzi

et al. 2014

Phil. Trans. R. Soc. A.

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Given a discrete sample of event locations, we wish to produce a probability density that models the relative probability of events occurring in a spatial domain. Standard density estimation techniques do not incorporate priors informed by spatial data. Such methods can result in assigning significant positive probability to locations where events cannot realistically occur. In particular, when modelling residential burglaries, standard density estimation can predict residential burglaries occurring where there are no residences. Incorporating the spatial data can inform the valid region for the density. When modelling very few events, additional priors can help to correctly fill in the gaps. Learning and enforcing correlation between spatial data and event data can yield better estimates from fewer events. We propose a non-local version of maximum penalized likelihood estimation based on the H1 Sobolev seminorm regularizer that computes non-local weights from spatial data to obtain more spatially accurate density estimates. We evaluate this method in application to a residential burglary dataset from San Fernando Valley with the non-local weights informed by housing data or a satellite image.

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“…Typical parametric methods [4] [10] [11] of density estimation assume that the data is coming from a known family of distributions, e.g. normal with mean µ and variance σ 2 , and try to estimate the parameters.…”

Section: Introductionmentioning

confidence: 99%

Efficient Density Estimation for High-Dimensional Data

Majdara

Nooshabadi

2022

IEEE Access

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Multivariate density estimation methods, typically work well in low dimensions and their extension to data analytics in high dimensions domain has proven challenging. For density estimation in high-dimensional big data domains, the non-parametric Bayesian sequential partitioning (BSP) algorithm provides an efficient way of partitioning the sample space, based on Bayesian inference. In this paper, we present a detailed analysis of BSP and provide a computationally efficient copula-transformed data structure and algorithm for use in density estimation for data analytics in high dimensions. Using the copula-transformed data structure, we implement the density estimation for marginals in both BSP and kernel density estimation (KDE) methods. The data structures and algorithm are suitably designed for most efficient rendering into parallel processing paradigms of open multi-processing (OPENMP ® ) and message passing interface (MPI).

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Maximum Penalized Likelihood Estimation

Cited by 153 publications

References 0 publications

Relative Extents of Preformation and Neoformation in Tree Shoots: Analysis by a Deconvolution Method

Relative Extents of Preformation and Neoformation in Tree Shoots: Analysis by a Deconvolution Method

Non-local crime density estimation incorporating housing information

Efficient Density Estimation for High-Dimensional Data

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