arXiv subjects

Halaleh Kamari

Publications and source records attributed to Halaleh Kamari.

3 recordsLinked to original sources

arXiv2021

RKHSMetaMod: An R package to estimate the Hoeffding decomposition of a complex model by solving RKHS ridge group sparse optimization problem

In this paper, we propose an R package, called RKHSMetaMod, that implements a procedure for estimating a meta-model of a complex model. The meta-model approximates the Hoeffding decomposition of the complex model and allows us to perform sensitivity analysis on it. It belongs to a reproducing kernel Hilbert space that is constructed as a direct sum of Hilbert spaces. The estimator of the meta-model is the solution of a penalized empirical least-squares minimization with the sum of the Hilbert norm and the empirical L^2-norm. This procedure, called RKHS ridge group sparse, allows both to select and estimate the terms in the Hoeffding decomposition, and therefore, to select and estimate the Sobol indices that are non-zero. The RKHSMetaMod package provides an interface from R statistical computing environment to the C++ libraries Eigen and GSL. In order to speed up the execution time and optimize the storage memory, except for a function that is written in R, all of the functions of this package are written using the efficient C++ libraries through RcppEigen and RcppGSL packages. These functions are then interfaced in the R environment in order to propose a user-friendly package.

stat.ML↗

arXiv2020

Risk upper bounds for RKHS ridge group sparse estimator in the regression model with non-Gaussian and non-bounded error

We consider the problem of estimating a meta-model of an unknown regression model with non-Gaussian and non-bounded error. The meta-model belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to an additive decomposition including the variables and interactions between them. The estimator of this meta-model is calculated by minimizing an empirical least-squares criterion penalized by the sum of the Hilbert norm and the empirical $L^2$-norm. In this context, the upper bounds of the empirical $L^2$ risk and the $L^2$ risk of the estimator are established.

math.ST↗

arXiv2016

Bayesian estimation of discrete Burr distribution with two parameters

So far, various techniques have been implemented for generating discrete distributions based on continuous distributions. The characteristics and properties of this kind of probability distributions have been studied. Furthermore, the estimation of related parameters have been computed trough classical methods. However, a few studies addressed the parameter estimate issue of these distributions through Bayesian methods. This is essentially because of the complexity of the model whatever the number of parameter is and the fact that in general they contain a large number of parameters to be estimated. This paper deals with computing Bayes estimate of the parameters of discrete Burr distribution with two parameters. Since the resulting posterior distribution of the parameters is not standard, we apply Metropolis-Hastings algorithm to simulate from the posterior density.

stat.CO↗