scholarly journals Wavelet-based robust estimation and variable selection in nonparametric additive models

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Umberto Amato ◽  
Anestis Antoniadis ◽  
Italia De Feis ◽  
Irène Gijbels
Keyword(s):  
Variable Selection ◽  
Robust Estimation ◽  
Convergence Rates ◽  
Additive Model ◽  
Real Data ◽  
Additive Models ◽  
Gradient Algorithm ◽  
Anomalous Data ◽  
Additive Component ◽  
Weak Compatibility

AbstractThis article studies M-type estimators for fitting robust additive models in the presence of anomalous data. The components in the additive model are allowed to have different degrees of smoothness. We introduce a new class of wavelet-based robust M-type estimators for performing simultaneous additive component estimation and variable selection in such inhomogeneous additive models. Each additive component is approximated by a truncated series expansion of wavelet bases, making it feasible to apply the method to nonequispaced data and sample sizes that are not necessarily a power of 2. Sparsity of the additive components together with sparsity of the wavelet coefficients within each component (group), results into a bi-level group variable selection problem. In this framework, we discuss robust estimation and variable selection. A two-stage computational algorithm, consisting of a fast accelerated proximal gradient algorithm of coordinate descend type, and thresholding, is proposed. When using nonconvex redescending loss functions, and appropriate nonconvex penalty functions at the group level, we establish optimal convergence rates of the estimates. We prove variable selection consistency under a weak compatibility condition for sparse additive models. The theoretical results are complemented with some simulations and real data analysis, as well as a comparison to other existing methods.

scholarly journals Automatic Variable Selection for Partially Linear Functional Additive Model and Its Application to the Tecator Data Set

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Yuping Hu ◽  
Sanying Feng ◽  
Liugen Xue
Keyword(s):  
Variable Selection ◽  
Linear Functional ◽  
Additive Model ◽  
Selection Procedure ◽  
Real Data ◽  
Regularity Conditions ◽  
Data Set ◽  
Partially Linear ◽  
Functional Additive ◽  
Selection For

We introduce a new partially linear functional additive model, and we consider the problem of variable selection for this model. Based on the functional principal components method and the centered spline basis function approximation, a new variable selection procedure is proposed by using the smooth-threshold estimating equation (SEE). The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero and simultaneously estimates the nonzero regression coefficients by solving the SEE. The approach avoids the convex optimization problem, and it is flexible and easy to implement. We establish the asymptotic properties of the resulting estimators under some regularity conditions. We apply the proposed procedure to analyze a real data set: the Tecator data set.

scholarly journals Predicting Malaria Transmission Dynamics in Dangassa, Mali: A Novel Approach Using Functional Generalized Additive Models

2020 ◽  
Vol 17 (17) ◽  
pp. 6339
Author(s):  
François Freddy Ateba ◽  
Manuel Febrero-Bande ◽  
Issaka Sagara ◽  
Nafomon Sogoba ◽  
Mahamoudou Touré ◽  
...  
Keyword(s):  
Wind Speed ◽  
Malaria Incidence ◽  
Generalized Additive Models ◽  
Community Health Center ◽  
Additive Model ◽  
Additive Models ◽  
Functional Regression ◽  
Novel Approach ◽  
Malaria Incidence Rate ◽  
Mean Wind Speed

Mali aims to reach the pre-elimination stage of malaria by the next decade. This study used functional regression models to predict the incidence of malaria as a function of past meteorological patterns to better prevent and to act proactively against impending malaria outbreaks. All data were collected over a five-year period (2012–2017) from 1400 persons who sought treatment at Dangassa’s community health center. Rainfall, temperature, humidity, and wind speed variables were collected. Functional Generalized Spectral Additive Model (FGSAM), Functional Generalized Linear Model (FGLM), and Functional Generalized Kernel Additive Model (FGKAM) were used to predict malaria incidence as a function of the pattern of meteorological indicators over a continuum of the 18 weeks preceding the week of interest. Their respective outcomes were compared in terms of predictive abilities. The results showed that (1) the highest malaria incidence rate occurred in the village 10 to 12 weeks after we observed a pattern of air humidity levels >65%, combined with two or more consecutive rain episodes and a mean wind speed <1.8 m/s; (2) among the three models, the FGLM obtained the best results in terms of prediction; and (3) FGSAM was shown to be a good compromise between FGLM and FGKAM in terms of flexibility and simplicity. The models showed that some meteorological conditions may provide a basis for detection of future outbreaks of malaria. The models developed in this paper are useful for implementing preventive strategies using past meteorological and past malaria incidence.

scholarly journals Robust estimation for multivariate wrapped models

METRON ◽  
2021 ◽  
Author(s):  
Giovanni Saraceno ◽  
Claudio Agostinelli ◽  
Luca Greco
Keyword(s):  
Robust Estimation ◽  
Numerical Study ◽  
Real Data ◽  
Likelihood Method ◽  
Weighted Likelihood ◽  
Finite Sample ◽  
Pearson Residuals ◽  
Data Points ◽  
Wrapped Distributions ◽  
Standard Techniques

AbstractA weighted likelihood technique for robust estimation of multivariate Wrapped distributions of data points scattered on a $$p-$$ p - dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise inference for standard techniques such as maximum likelihood method. Therefore, there is the need to handle such model inadequacies in the fitting process by a robust technique and an effective downweighting of observations not following the assumed model. Furthermore, the employ of a robust method could help in situations of hidden and unexpected substructures in the data. Here, it is suggested to build a set of data-dependent weights based on the Pearson residuals and solve the corresponding weighted likelihood estimating equations. In particular, robust estimation is carried out by using a Classification EM algorithm whose M-step is enhanced by the computation of weights based on current parameters’ values. The finite sample behavior of the proposed method has been investigated by a Monte Carlo numerical study and real data examples.

scholarly journals Generalized additive model with embedded variable selection for bankruptcy prediction: Prediction versus interpretation

2019 ◽  
Vol 7 (1) ◽  
pp. 1597956
Author(s):  
Carlos Valencia ◽  
Sergio Cabrales ◽  
Laura Garcia ◽  
Juan Ramirez ◽  
Diego Calderona ◽  
...  
Keyword(s):  
Variable Selection ◽  
Generalized Additive Model ◽  
Additive Model ◽  
Bankruptcy Prediction ◽  
Selection For

ADDITIVE-VETO MODELS FOR CHOICE AND RANKING MULTICRITERIA DECISION PROBLEMS

2013 ◽  
Vol 30 (06) ◽  
pp. 1350026 ◽  
Author(s):  
ADIEL TEIXEIRA DE ALMEIDA
Keyword(s):  
High Performance ◽  
Additive Model ◽  
Additive Models ◽  
Numerical Application ◽  
Multicriteria Decision ◽  
Decision Methods ◽  
Overall Evaluation ◽  
Low Performance ◽  
Ranking Problems ◽  
Multicriteria Decision Problems

Using additive models for aggregation of criteria is an important procedure in many multicriteria decision methods. This compensatory approach, which scores the alternatives straightforwardly, may have significant drawbacks. For instance, the Decision Maker (DM) may prefer not to select alternatives which have a very low performance in whatever criterion. In contrast, such an alternative may have the best overall evaluation, since the additive model may compensate this low performance in one of the criteria as a result of high performance in other criteria. Thus, additive-veto models are proposed with a view to considering the possibility of vetoing alternatives in such situations, particularly for choice and ranking problems. A numerical application illustrates the use of such models, with a detailed discussion related to real practical problems. Moreover, the results obtained from a numerical simulation show that it is not so rare for a veto of the best alternative to occur in the additive model. This is of considerable relevance depending on the DM's preference structure.

scholarly journals p.Arg72Pro polymorphism of P53 and Breast Cancer Risk: A meta-analysis of case-control studies

2020 ◽  
Author(s):  
Brehima Diakite ◽  
Yaya Kassogue ◽  
Guimogo Dolo ◽  
Jun Wang ◽  
Erin Neuschler ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Breast Cancer Risk ◽  
Cancer Risk ◽  
Meta Analysis ◽  
Additive Model ◽  
P53 Gene ◽  
Case Control ◽  
Additive Models ◽  
Case Control Studies ◽  
Genotype Frequencies

Abstract Background :The effect of the p.Arg72Pro variant of the P53 gene on the risk of developmentof breast cancer remains variable in populations. However, the use of strategiessuchas pooling age-matched controls with disease cases may provide a solid meta-analysis. Our goal was to perform a meta-analysis in order to assessthe association of p.Arg72Provariant of P53 gene with breast cancer risk. Methods : Databases such as PubMed, Genetics Medical Literature, Harvard University Library, Web of Science and Genesis Library were used to search articles. Age-matched case-control studies on breast cancer that have evaluated the genotype frequencies of the p.Arg72Pro of P53 gene were selected. The fixed and random effects (Mantel-Haenszel) were calculated using pooled odds ratio of 95% CI to determine the risk of disease. Inconsistency was calculated to determine heterogeneity among the studies. The publication bias was estimated using the funnel plot. Results : Twenty-one publications with cases age-matched controls including7841disease cases and 8876controls were evaluated in this meta-analysis. Overall, our results suggested that p.Arg72ProP53 was associated with a risk for breast cancer for the dominant model (OR= 1.09, 95% CI = 1.02-1.16; P= 0.01) and the additive model (OR= 1.09, 95% CI = 1.01-1.17; P= 0.03), but not in the recessive model (OR = 1.07, 95% CI = 0.97-1.16; P= 0.19). According to the ethnic group, allele Pro has been associated with breast cancer risk in Europeans for the dominant and additive models. Conclusions : This meta-analysis found a significant association between p.Arg72Pro in the P53 gene and the risk of breast cancer. Individuals carrying at least one Pro allele of the P53 gene are more likely to have breast cancer with dominant and additive models than individualsharboringthe Arg allele.

scholarly journals Experimental Design for Optimization of Orthogonal Projection Pursuit Models

2020 ◽  
Vol 34 (06) ◽  
pp. 10235-10242
Author(s):  
Mojmir Mutny ◽  
Johannes Kirschner ◽  
Andreas Krause
Keyword(s):  
Experimental Design ◽  
Orthogonal Projection ◽  
Optimization Problems ◽  
Additive Model ◽  
Projection Pursuit ◽  
Parameter Tuning ◽  
Additive Models ◽  
Function Optimization ◽  
Bayesian Optimization ◽  
Additive Structure

Bayesian optimization and kernelized bandit algorithms are widely used techniques for sequential black box function optimization with applications in parameter tuning, control, robotics among many others. To be effective in high dimensional settings, previous approaches make additional assumptions, for example on low-dimensional subspaces or an additive structure. In this work, we go beyond the additivity assumption and use an orthogonal projection pursuit regression model, which strictly generalizes additive models. We present a two-stage algorithm motivated by experimental design to first decorrelate the additive components. Subsequently, the bandit optimization benefits from the statistically efficient additive model. Our method provably decorrelates the fully additive model and achieves optimal sublinear simple regret in terms of the number of function evaluations. To prove the rotation recovery, we derive novel concentration inequalities for linear regression on subspaces. In addition, we specifically address the issue of acquisition function optimization and present two domain dependent efficient algorithms. We validate the algorithm numerically on synthetic as well as real-world optimization problems.

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