arXiv subjects

Adel Bedoui

Publications and source records attributed to Adel Bedoui.

3 recordsLinked to original sources

arXiv2022

Bayesian Elastic Net based on Empirical Likelihood

We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution, performs well when the variables are highly correlated, and enables more straightforward inference by providing posterior distributions of the regression coefficients. The Hamiltonian Monte Carlo method implemented in Bayesian empirical likelihood overcomes the challenges that the posterior distribution lacks a closed analytic form and its domain is nonconvex. We develop the leapfrog parameter tuning algorithm for Bayesian empirical likelihood. We also show that the posterior distributions of the regression coefficients are asymptotically normal. Simulation studies and real data analysis demonstrate the advantages of the proposed method in prediction accuracy.

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arXiv2021

Applying k-nearest neighbors to time series forecasting : two new approaches

K-nearest neighbors algorithm is one of the prominent techniques used in classification and regression. Despite its simplicity, the k-nearest neighbors has been successfully applied in time series forecasting. However, the selection of the number of neighbors and feature selection is a daunting task. In this paper, we introduce two methodologies to forecasting time series that we refer to as Classical Parameters Tuning in Weighted Nearest Neighbors and Fast Parameters Tuning in Weighted Nearest Neighbors. The first approach uses classical parameters tuning that compares the most recent subsequence with every possible subsequence from the past of the same length. The second approach reduces the neighbors' search set, which leads to significantly reduced grid size and hence a lower computational time. To tune the models' parameters, both methods implement an approach inspired by cross-validation for weighted nearest neighbors. We evaluate the forecasting performance and accuracy of our models. Then, we compare them to some classical approaches, especially, Seasonal Autoregressive Integrated Moving Average, Holt-Winters and Exponential Smoothing State Space Model. Real data examples on retail and food services sales in the USA and milk production in the UK are analyzed to demonstrate the application and the efficiency of the proposed approaches.

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arXiv2020

Comparison of Bayesian Nonparametric Density Estimation Methods

In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based solely on a parametric family of probability distributions. Thus, the fitted models are more robust to model misspecification. Also, with the Bayesian approach, we have the entire posterior distribution of our parameter of interest; it can be summarized through credible intervals, mean, median, standard deviation, quantiles, etc. The Lindsey, penalized Gaussian mixtures, and Dirichlet process mixture methods are reviewed. The estimations are performed via Markov chain Monte Carlo (MCMC) methods. The penalized Gaussian mixtures method is implemented via Hamiltonian Monte Carlo (HMC). We show that under certain regularity conditions, and as n increases, the posterior distribution of the weights converges to a Normal distribution. Simulation results and data analysis are reported.

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