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Published By Springer-Verlag

1613-9658, 0943-4062

Author(s):  
Liming Wang ◽  
Xingxiang Li ◽  
Xiaoqing Wang ◽  
Peng Lai

Author(s):  
Oskar Allerbo ◽  
Rebecka Jörnsten

AbstractNon-parametric, additive models are able to capture complex data dependencies in a flexible, yet interpretable way. However, choosing the format of the additive components often requires non-trivial data exploration. Here, as an alternative, we propose PrAda-net, a one-hidden-layer neural network, trained with proximal gradient descent and adaptive lasso. PrAda-net automatically adjusts the size and architecture of the neural network to reflect the complexity and structure of the data. The compact network obtained by PrAda-net can be translated to additive model components, making it suitable for non-parametric statistical modelling with automatic model selection. We demonstrate PrAda-net on simulated data, where we compare the test error performance, variable importance and variable subset identification properties of PrAda-net to other lasso-based regularization approaches for neural networks. We also apply PrAda-net to the massive U.K. black smoke data set, to demonstrate how PrAda-net can be used to model complex and heterogeneous data with spatial and temporal components. In contrast to classical, statistical non-parametric approaches, PrAda-net requires no preliminary modeling to select the functional forms of the additive components, yet still results in an interpretable model representation.


Author(s):  
Wagner J. F. Silva ◽  
Renata M. C. R. Souza ◽  
F. J. A. Cysneiros
Keyword(s):  

Author(s):  
Balázs Dobi ◽  
András Zempléni

AbstractControl charts originate from industrial statistics, but are constantly seeing new areas of application, for example in health care (Thor et al. in BMJ Qual Saf 16(5):387–399, 2007. https://doi.org/10.1136/qshc.2006.022194; Suman and Prajapati in Int J Metrol Qual Eng, 2018. https://doi.org/10.1051/ijmqe/2018003). This paper is about the package, an implementation of generalised Markov chain-based control charts with health care applications in mind and with a focus on cost-effectiveness. The methods are based on Zempléni et al. (Appl Stoch Model Bus Ind 20(3):185–200, 2004. https://doi.org/10.1002/asmb.521), Dobi and Zempléni (Qual Reliab Eng Int 35(5):1379–1395, 2019a. https://doi.org/10.1002/qre.2518, Ann Univ Sci Budapestinensis Rolando Eötvös Nomin Sect Comput 49:129–146, 2019b). The implemented ideas in the package were motivated by problems encountered by health care professionals and biostatisticians when assessing the effects and costs of different monitoring schemes and therapeutic regimens. However, the implemented generalisations may be useful in other (e.g., engineering) applications too, as they mainly revolve around the loosening of assumptions seen in traditional control chart theory. The package is able to model processes with random shift sizes (i.e., the degradation of the patient’s health), random repair (i.e., treatment) and random time between samplings (i.e., visits) as well. The article highlights the flexibility of the methods through the modelling of different disease progression and treatment scenarios and also through an application on real-world data of diabetic patients.


Author(s):  
Umberto Amato ◽  
Anestis Antoniadis ◽  
Italia De Feis ◽  
Irène Gijbels

AbstractNonparametric univariate regression via wavelets is usually implemented under the assumptions of dyadic sample size, equally spaced fixed sample points, and i.i.d. normal errors. In this work, we propose, study and compare some wavelet based nonparametric estimation methods designed to recover a one-dimensional regression function for data that not necessary possess the above requirements. These methods use appropriate regularizations by penalizing the decomposition of the unknown regression function on a wavelet basis of functions evaluated on the sampling design. Exploiting the sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, we use some efficient proximal gradient descent algorithms, available in recent literature, for computing the estimates with fast computation times. Our wavelet based procedures, in both the standard and the robust regression case have favorable theoretical properties, thanks in large part to the separability nature of the (non convex) regularization they are based on. We establish asymptotic global optimal rates of convergence under weak conditions. It is known that such rates are, in general, unattainable by smoothing splines or other linear nonparametric smoothers. Lastly, we present several experiments to examine the empirical performance of our procedures and their comparisons with other proposals available in the literature. An interesting regression analysis of some real data applications using these procedures unambiguously demonstrate their effectiveness.


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