Bandwidth Selection in an EM-Like Algorithm for Nonparametric Multivariate Mixtures

Benaglia, Tatiana; Chauveau, Didier; Hunter, David R.

doi:10.1142/9789814340564_0002

Cited by 18 publications

(24 citation statements)

References 10 publications

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“…This suggests that an iteratively updated bandwidth is possible. Though we do not discuss this issue here, recent work by Benaglia et al (2011) andChauveau et al (2010) does so in detail for related algorithms in a nonregression setting.…”

Section: Discussionmentioning

confidence: 99%

“…The algorithm we introduce here uses the same intuition as those studied by Benaglia et al (2009) and Benaglia et al (2011), though those algorithms were all tailored toward a particular (non-regression) multivariate finite mixture model. Because all of these algorithms bear a strong resemblance to standard EM algorithms for the case of a parametric finite mixture model, we consider them "EM-like" and we retain the so-called "E-step" and "M-step" characteristic of a true EM algorithm.…”

Section: A Semiparametric Em-like Algorithmmentioning

confidence: 99%

“…The usual difficulties are even more pronounced in the case of a finite mixture, since even some standard rules of thumb become impossible to apply in that case. In an article about a similar EM-like algorithm for nonparametric multivariate finite mixtures, Benaglia et al (2011) address this issue and describe an algorithm that recalculates the bandwidth at each iteration of the algorithm. This is particularly helpful once the algorithm has begun to identify the mixture structure, since at that stage the mixture information can be exploited in order to apply standard kernel density estimation techniques.…”

Section: A Semiparametric Em-like Algorithmmentioning

confidence: 99%

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Semiparametric mixtures of regressions

Hunter

Young

2012

Journal of Nonparametric Statistics

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We present an algorithm for estimating parameters in a mixture-of-regressions model in which the errors are assumed to be independent and identically distributed but no other assumption is made. This model is introduced as one of several recent generalizations of the standard fully parametric mixture of linear regressions in the literature. A sufficient condition for the identifiability of the parameters is stated and proved. Several different versions of the algorithm, including one that has a provable ascent property, are introduced. Numerical tests indicate the effectiveness of some of these algorithms.

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Section: Discussionmentioning

confidence: 99%

Section: A Semiparametric Em-like Algorithmmentioning

confidence: 99%

Section: A Semiparametric Em-like Algorithmmentioning

confidence: 99%

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Semiparametric mixtures of regressions

Hunter

Young

2012

Journal of Nonparametric Statistics

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“…Here, this model is referred to as a skewed GMM 17 – 19 . Another model discussed (briefly) does not assume a parametric form for the distribution of flow velocity at all; instead, the distribution is inferred by using kernel estimates 20 – 24 . Such kernel mixture models (KMMs) are flexible in that they accommodate a wide range of distributions (including gaussian).…”

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confidence: 99%

“…[17][18][19] Another model discussed (briefly) does not assume a parametric form for the distribution of flow velocity at all; instead, the distribution is inferred by using kernel estimates. [20][21][22][23][24] Such kernel mixture models (KMMs) are flexible in that they accommodate a wide range of distributions (including gaussian). However, kernel methods involve a smoothing parameter whose value is a priori unknown.…”

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confidence: 99%

Mixture Models for Estimating Maximum Blood Flow Velocity

Marzban

Mourad

2016

J of Ultrasound Medicine

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Nonparametric clustering of RNA‐sequencing data

Lozano,

Atallah,

Levine

2023

Statistical Analysis

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Identification of clusters of co‐expressed genes in transcriptomic data is a difficult task. Most algorithms used for this purpose can be classified into two broad categories: distance‐based or model‐based approaches. Distance‐based approaches typically utilize a distance function between pairs of data objects and group similar objects together into clusters. Model‐based approaches are based on using the mixture‐modeling framework. Compared to distance‐based approaches, model‐based approaches offer better interpretability because each cluster can be explicitly characterized in terms of the proposed model. However, these models present a particular difficulty in identifying a correct multivariate distribution that a mixture can be based upon. In this manuscript, we review some of the approaches used to select a distribution for the needed mixture model first. Then, we propose avoiding this problem altogether by using a nonparametric MSL (maximum smoothed likelihood) algorithm. This algorithm was proposed earlier in statistical literature but has not been, to the best of our knowledge, applied to transcriptomics data. The salient feature of this approach is that it avoids explicit specification of distributions of individual biological samples altogether, thus making the task of a practitioner easier. We performed both a simulation study and an application of the proposed algorithm to two different real datasets. When used on a real dataset, the algorithm produces a large number of biologically meaningful clusters and performs at least as well as several other mixture‐based algorithms commonly used for RNA‐seq data clustering. Our results also show that this algorithm is capable of uncovering clustering solutions that may go unnoticed by several other model‐based clustering algorithms. Our code is publicly available on Github at https://github.com/Matematikoi/non_parametric_clustering

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Bandwidth Selection in an EM-Like Algorithm for Nonparametric Multivariate Mixtures

Cited by 18 publications

References 10 publications

Semiparametric mixtures of regressions

Semiparametric mixtures of regressions

Mixture Models for Estimating Maximum Blood Flow Velocity

Nonparametric clustering of RNA‐sequencing data

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