scholarly journals Incorporating Clustering Techniques into GAMLSS

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 916-930
Author(s):  
Thiago G. Ramires ◽  
Luiz R. Nakamura ◽  
Ana J. Righetto ◽  
Andréa C. Konrath ◽  
Carlos A. B. Pereira
Keyword(s):  
Mixture Models ◽  
Latent Variable ◽  
Generalized Additive Models ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Additive Models ◽  
Clustering Methods ◽  
Response Variable ◽  
Explanatory Variables ◽  
Variable Cluster

A method for statistical analysis of multimodal and/or highly distorted data is presented. The new methodology combines different clustering methods with the GAMLSS (generalized additive models for location, scale, and shape) framework, and is therefore called c-GAMLSS, for “clustering GAMLSS. ” In this new extended structure, a latent variable (cluster) is created to explain the response-variable (target). Any and all parameters of the distribution for the response variable can also be modeled by functions of the new covariate added to other available resources (features). The method of selecting resources to be used is carried out in stages, a step-based method. A simulation study considering multiple scenarios is presented to compare the c-GAMLSS method with existing Gaussian mixture models. We show by means of four different data applications that in cases where other authentic explanatory variables are or are not available, the c-GAMLSS structure outperforms mixture models, some recently developed complex distributions, cluster-weighted models, and a mixture-of-experts model. Even though we use simple distributions in our examples, other more sophisticated distributions can be used to explain the response variable.

The Relationship between Mobility and COVID-19 in Germany: Modeling Case Occurrence using Apple's Mobility Trends Data

2021 ◽  
Author(s):  
Mark David Walker ◽  
Mihály Sulyok
Keyword(s):  
Generalized Additive Models ◽  
Information Criterion ◽  
Additive Models ◽  
Online Data ◽  
German Government ◽  
Explanatory Variables ◽  
Mobility Data ◽  
Community Mobility ◽  
The Relationship ◽  
Potential Use

Abstract Background Restrictions on social interaction and movement were implemented by the German government in March 2020 to reduce the transmission of coronavirus disease 2019 (COVID-19). Apple's “Mobility Trends” (AMT) data details levels of community mobility; it is a novel resource of potential use to epidemiologists. Objective The aim of the study is to use AMT data to examine the relationship between mobility and COVID-19 case occurrence for Germany. Is a change in mobility apparent following COVID-19 and the implementation of social restrictions? Is there a relationship between mobility and COVID-19 occurrence in Germany? Methods AMT data illustrates mobility levels throughout the epidemic, allowing the relationship between mobility and disease to be examined. Generalized additive models (GAMs) were established for Germany, with mobility categories, and date, as explanatory variables, and case numbers as response. Results Clear reductions in mobility occurred following the implementation of movement restrictions. There was a negative correlation between mobility and confirmed case numbers. GAM using all three categories of mobility data accounted for case occurrence as well and was favorable (AIC or Akaike Information Criterion: 2504) to models using categories separately (AIC with “driving,” 2511. “transit,” 2513. “walking,” 2508). Conclusion These results suggest an association between mobility and case occurrence. Further examination of the relationship between movement restrictions and COVID-19 transmission may be pertinent. The study shows how new sources of online data can be used to investigate problems in epidemiology.

A robust non-rigid point set registration method based on inhomogeneous Gaussian mixture models

2017 ◽  
Vol 34 (10) ◽  
pp. 1399-1414 ◽  
Author(s):  
Wanxia Deng ◽  
Huanxin Zou ◽  
Fang Guo ◽  
Lin Lei ◽  
Shilin Zhou ◽  
...  
Keyword(s):  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Registration Method ◽  
Point Set Registration ◽  
Point Set

scholarly journals Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part I: Theory and Scheme

2013 ◽  
Vol 141 (6) ◽  
pp. 1737-1760 ◽  
Author(s):  
Thomas Sondergaard ◽  
Pierre F. J. Lermusiaux
Keyword(s):  
Data Assimilation ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Expectation Maximization Algorithm ◽  
Planck Equation ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Field Equations ◽  
Dynamical Equations ◽  
Prior Probabilities

Abstract This work introduces and derives an efficient, data-driven assimilation scheme, focused on a time-dependent stochastic subspace that respects nonlinear dynamics and captures non-Gaussian statistics as it occurs. The motivation is to obtain a filter that is applicable to realistic geophysical applications, but that also rigorously utilizes the governing dynamical equations with information theory and learning theory for efficient Bayesian data assimilation. Building on the foundations of classical filters, the underlying theory and algorithmic implementation of the new filter are developed and derived. The stochastic Dynamically Orthogonal (DO) field equations and their adaptive stochastic subspace are employed to predict prior probabilities for the full dynamical state, effectively approximating the Fokker–Planck equation. At assimilation times, the DO realizations are fit to semiparametric Gaussian Mixture Models (GMMs) using the Expectation-Maximization algorithm and the Bayesian Information Criterion. Bayes’s law is then efficiently carried out analytically within the evolving stochastic subspace. The resulting GMM-DO filter is illustrated in a very simple example. Variations of the GMM-DO filter are also provided along with comparisons with related schemes.

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