Unit:
Κατεύθυνση Στατιστική και Επιχειρησιακή ΈρευναLibrary of the School of Science
Author:
Markoulidakis Andreas
Supervisors info:
Λουκία Μελιγκοτσίδου, Επ. Καθηγήτρια, Τμήματος Μαθηματικών
Φώτιος Σιάννης, Επ. Καθηγητής, Τμήματος Μαθηματικών
Σάμης Τρέβεζας, Λέκτορας, Τμήματος Μαθηματικών
Original Title:
Ordinary and Bayesian LASSO for Regression Models
Translated title:
Ordinary and Bayesian LASSO for Regression Models
Summary:
This dissertation is concerned with the properties of Ordinary and Bayesian LASSO in Regression Models. The Least Absolute Shrinkage and Selection Operator (LASSO) is a method that performs concurrently shrinking of the coefficients of a model and selects important predictors among a large set
of covariates. In the context of normal linear regression, it relies on con- vex programming algorithms including a penalty which performs selection through shrinking exactly to zero the coefficients of unimportant covari- ates. In the context of COX models, it relies on maximizing the models’ likelihood including again a penalty with the same effect as in the case of linear regression. In the framework of Bayesian Inference, we can de- rive the LASSO estimate as the Bayes posterior mode under independent double-expotential priors for the regressors.
The LASSO was originally introduced by Robert Tibshirani (1996) and was further developed by Efron et al. (2004), who proposed the LARS, an efficient algorithm to compute the entire LASSO path. Ordinary LASSO for COX models was proposed by Tibshirani (1997) and its solution was obtained by a modification of the Newton-Raphson Algorithm. For the Bayesian LASSO in normal linear regression, Tibshirani (1996) proposed a prior proportional to minus the log-density of the double expotential dis- tribution, and then a plethora of model structures have been proposed, by Park and Casella (2008), Ntzoufras and Lykou (2012) and many others, since Bayesian LASSO is an active field in Bayesian statistics.
Main subject category:
Science
Keywords:
LASSO, OLS, Bayesian LASSO
File:
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Ordinary and Bayesian LASSO for Regression Models.pdf
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File access is restricted only to the intranet of UoA.
