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The group lasso for logistic regression

Lukas Meier, Sara Van De Geer, Peter Bühlmann
2008 Journal of The Royal Statistical Society Series B-statistical Methodology  
The group lasso estimator for logistic regression is shown to be statistically consistent even if the number of predictors is much larger than sample size but with sparse true underlying structure.  ...  We extend the group lasso to logistic regression models and present an efficient algorithm, that is especially suitable for high dimensional problems, which can also be applied to generalized linear models  ...  Acknowledgements We thank two referees and Sylvain Sardy for constructive comments.  ... 
doi:10.1111/j.1467-9868.2007.00627.x fatcat:lhau2op7tzce7lbw4zxjrpmcjm

Comparison between Common Statistical Modeling Techniques Used in Research, Including: Discriminant Analysis vs Logistic Regression, Ridge Regression vs LASSO, and Decision Tree vs Random Forest

Azad Abdulhafedh
2022 OALib  
This paper compares common statistical approaches, including regression vs classification, discriminant analysis vs logistic regression, ridge regression vs LASSO, and decision tree vs random forest.  ...  Ridge Regression vs LASSO Ridge regression and lasso are both regularization (shrinkage) methods. LASSO regression stands for "Least Absolute Shrinkage and Selection Operator".  ...  Lasso is another extension built on regularized linear regression, but with a small twist.  ... 
doi:10.4236/oalib.1108414 fatcat:6hqkvmped5f5pmoogu4umv47vm

Adaptive group-regularized logistic elastic net regression [article]

Magnus M. Münch, Carel F.W. Peeters, Aad W. van der Vaart, Mark A. van de Wiel
2018 arXiv   pre-print
As a solution to this problem, we propose a group-regularized (logistic) elastic net regression method, where each penalty parameter corresponds to a group of features based on the external information  ...  The method, termed gren, makes use of the Bayesian formulation of logistic elastic net regression to estimate both the model and penalty parameters in an approximate empirical-variational Bayes framework  ...  Note that if m i = 1 for i = 1, . . . , n, the model reduces to a binary logistic regression model.  ... 
arXiv:1805.00389v1 fatcat:b2pimzhq4bbjhaxdhlm5gnq6z4

A More Accurate Estimation of Semiparametric Logistic Regression

Xia Zheng, Yaohua Rong, Ling Liu, Weihu Cheng
2021 Mathematics  
Specifically, in this paper, based on the regularization method and an innovative class of garrotized kernel functions, we propose a novel penalized kernel machine method for a semiparametric logistic  ...  Thus, our task is to construct a method which can guarantee the estimation accuracy by removing redundant variables.  ...  In addition, for comparison, we also apply the LSKM method based on Gaussian kernel and the LASSO method for logistic regression to this adjusted breast cancer data.  ... 
doi:10.3390/math9192376 fatcat:r3vvs6ridvghtpfipfyh57bz3u

Sparse Logistic Regression with Lp Penalty for Biomarker Identification

Zhenqiu Liu, Feng Jiang, Guoliang Tian, Suna Wang, Fumiaki Sato, Stephen J. Meltzer, Ming Tan
2007 Statistical Applications in Genetics and Molecular Biology  
In this paper, we propose a novel method for sparse logistic regression with non-convex regularization Lp (p <1).  ...  Biomarkers identified with our methods are compared with that in the literature. Our computational results show that Lp Logistic regression (p <1) outperforms the L1 logistic regression and SCAD SVM.  ...  Theoretically, when sample size n m, logistic regression with L p (p < 1) gives asymptotically unbiased estimates of the nonzero parameters while shrinking the estimates of zero (or small) parameters to  ... 
doi:10.2202/1544-6115.1248 pmid:17402921 fatcat:sbdavwwabravxjdmndfn643jr4

Regularized (bridge) logistic regression for variable selection based on ROC criterion

Hong-Bin Fang, Zhenqiu Liu, Ming T. Tan, Guo-Liang Tian
2009 Statistics and its Interface  
Despite advances in the last several decades in developing such regularized regression models, issues regarding the choice of penalty parameter and the computational methods for models fitting with parameter  ...  It is well known that the bridge regression (with tuning parameter less or equal to 1) gives asymptotically unbiased estimates of the nonzero regression parameters while shrinking smaller regression parameters  ...  The authors thank the editor and the referees for their constructive comments. Received 11 December 2008  ... 
doi:10.4310/sii.2009.v2.n4.a10 fatcat:igtprm53zff3lm6ewk46hb3yfi

Geographically weighted elastic net logistic regression

Alexis Comber, Paul Harris
2018 Journal of Geographical Systems  
The approach is compared with other logistic regressions.  ...  Model comparisons show that standard geographically weighted logistic regression over-estimated relationship non-stationarity because it fails to adequately deal with collinearity and model selection.  ...  the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10109-018-0280-7 fatcat:kh3ubdipvzasdj3r3oxferpltm

Distributed Parallel Sparse Multinomial Logistic Regression

Dajiang Lei, Meng Du, Hao Chen, Zhixing Li, Yu Wu
2019 IEEE Access  
INDEX TERMS Alternating Direction Method of Multipliers, big data, distributed parallel, sparse multinomial logistic regression. 55496 2169-3536  ...  We have reinvestigated the classification accuracy and running efficiency of the algorithm for solving SMLR problems using the Alternating Direction Method of Multipliers (ADMM), which is called fast SMLR  ...  Since solving directly with the original logistic regression is prone to overfitting, the more common practice is to introduce regularization term [1] .  ... 
doi:10.1109/access.2019.2913280 fatcat:eeaxgs37rzafrax2fk3w5tlbmq

Robust Variable and Interaction Selection for Logistic Regression and Multiple Index Models [article]

Yang Li, Jun S. Liu
2017 arXiv   pre-print
We propose Stepwise cOnditional likelihood variable selection for Discriminant Analysis (SODA) to detect both main and quadratic interaction effects in logistic regression and quadratic discriminant analysis  ...  Compared with existing variable selection methods based on the Sliced Inverse Regression (SIR) (Li 1991), SODA requires neither the linearity nor the constant variance condition and is much more robust  ...  However, a direct application of Lasso on logistic regression with all second-order terms is prohibitive for moderately large p (e.g., p ≥ 1000).  ... 
arXiv:1611.08649v2 fatcat:onohvoa5zjgv5e2ls6h5cydblq

High Dimensional Logistic Regression Model using Adjusted Elastic Net Penalty

Zakariya Y Algamal, Muhammad Hisyam Lee
2015 Pakistan Journal of Statistics and Operation Research  
with other existing penalized methods.  ...  Reduction of the high dimensional binary classification data using penalized logistic regression is one of the challenges when the explanatory variables are correlated.  ...  We end this paper with a conclusion in section 7. Penalized Logistic Regression Model Logistic regression is a statistical method to model a binary classification problem.  ... 
doi:10.18187/pjsor.v11i4.990 fatcat:gsz7tcprybgefm34kfebidbqhm

ADMM-SOFTMAX : An ADMM Approach for Multinomial Logistic Regression [article]

Samy Wu Fung, Sanna Tyrväinen, Lars Ruthotto, Eldad Haber
2019 arXiv   pre-print
We present ADMM-Softmax, an alternating direction method of multipliers (ADMM) for solving multinomial logistic regression (MLR) problems.  ...  Our method is geared toward supervised classification tasks with many examples and features. It decouples the nonlinear optimization problem in MLR into three steps that can be solved efficiently.  ...  We also thank the Isaac Newton Institute (INI) for Mathematical Sciences for the support and hospitality during the programme on Generative Models, Parameter  ... 
arXiv:1901.09450v2 fatcat:lj2stje43fgwjipfhueerbdxhi

Network-regularized Sparse Logistic Regression Models for Clinical Risk Prediction and Biomarker Discovery [article]

Wenwen Min, Juan Liu, Shihua Zhang
2016 arXiv   pre-print
Here, we first introduce a general regularized Logistic Regression (LR) framework with regularized term λw_1 + ηw^TMw, which can reduce to different penalties, including Lasso, elastic net, and network-regularized  ...  And we develop two efficient algorithms to solve it. Finally, we test our methods and compare them with the related ones using simulated and real data to show their efficiency.  ...  Logistic regression (LR) is one of such a classical method and has been widely used for classification [13] .  ... 
arXiv:1609.06480v1 fatcat:ugc5gv47lncxrgnbpwarxnllli

The Generalized LASSO

V. Roth
2004 IEEE Transactions on Neural Networks  
For regression functionals which can be modeled as iteratively reweighted least-squares (IRLS) problems, we present a highly efficient algorithm with guaranteed global convergence.  ...  This defies a unique framework for sparse regression models in the very rich class of IRLS models, including various types of robust regression models and logistic regression.  ...  This leads us to the LASSO method which optimizes a -constrained regression functional.  ... 
doi:10.1109/tnn.2003.809398 pmid:15387244 fatcat:65x4jj3hkfaohc5x3gxibz3dxu

The Impact of Regularization on High-dimensional Logistic Regression [article]

Fariborz Salehi, Ehsan Abbasi, Babak Hassibi
2019 arXiv   pre-print
Logistic regression is commonly used for modeling dichotomous outcomes.  ...  Our results generalize those of Sur and Candes and we provide a detailed study for the cases of ℓ_2^2-RLR and sparse (ℓ_1-regularized) logistic regression.  ...  Summary of contributions In this paper, we study regularized logistic regression (RLR) for parameter estimation in high-dimensional logistic models.  ... 
arXiv:1906.03761v4 fatcat:darxyqznd5fung73zqdvmh63am

Estimation of Distribution Algorithms as Logistic Regression Regularizers of Microarray Classifiers

C. Bielza, V. Robles, P. Larranaga
2009 Methods of Information in Medicine  
Methods: Those difficulties are tackled by introducing a new way of regularizing the logistic regression.  ...  Obtaining the regularized estimates of the logistic classifier amounts to maximizing the likelihood function via our EDA, without having to be penalized.  ...  Acknowledgments The authors are grateful to the referees for their constructive comments.  ... 
doi:10.3414/me9223 pmid:19387512 fatcat:jo7nlzwd5bhv7bebx4h7chmrei
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