In this paper, we deal with the ridge-type estimator for fuzzy nonlinear regression models using fuzzy numbers and Gaussian basis functions. Shrinkage regularization methods are used in linear and nonlinear regression models to yield consistent estimators. Here, we propose a weighted ridge penalty on a fuzzy nonlinear regression model, then select the number of basis functions and smoothing par...

We consider the problem of model selection and estimation in sparse high dimensional linear regression models with strongly correlated variables. First, we study the theoretical properties of the dual Lasso solution, and we show that joint consideration of the Lasso primal and its dual solutions are useful for selecting correlated active variables. Second, we argue that correlation among active...

In recent years, there has been a considerable amount of research on the use of regularization methods for inference and prediction in quantitative genetics. Such research mostly focuses on selection of markers and shrinkage of their effects. In this review paper, the use of ridge regression for prediction in quantitative genetics using single-nucleotide polymorphism data is discussed. In parti...

Augmentation of deficient and atrophic alveolar ridges is an important aspect of dental implant therapy with the goal of providing a functional restoration in harmony with adjacent natural dentition. Bone splitting technique is considered a distinguished augmentation method for treatment of deficient alveolar ridges. According to this procedure, the compromised alveolar ridge is opened from the...

Description This function is used to classify microarray data. Since the underlying model fit is based on penalized discriminant methods, there is no need for a pre-filtering step to reduce the number of genes. Usage pdmClass(formula , method = c("pls", "pcr", "ridge"), keep.fitted = Arguments formula A symbolic description of the model to be fit. Details given below. method One of "pls", "pcr"...

We propose a fast algorithm for ridge regression when the number of features is much larger than the number of observations (p n). The standard way to solve ridge regression in this setting works in the dual space and gives a running time of O(np). Our algorithm Subsampled Randomized Hadamard TransformDual Ridge Regression (SRHT-DRR) runs in time O(np log(n)) and works by preconditioning the de...

Adaptive ridge is a special form of ridge regression, balancing the quadratic penalization on each parameter of the model. This paper shows the equivalence between adaptive ridge and lasso (least absolute shrinkage and selection operator). This equivalence states that both procedures produce the same estimate. Least absolute shrinkage can thus be viewed as a particular quadratic penalization. F...