Article

Robust penalized logistic regression with truncated loss functions.

Department of Health Studies, Chicago, IL 60615, USA.
Canadian Journal of Statistics (Impact Factor: 0.59). 06/2011; 39(2):300-323. DOI: 10.1002/cjs.10105
Source: PubMed

ABSTRACT The penalized logistic regression (PLR) is a powerful statistical tool for classification. It has been commonly used in many practical problems. Despite its success, since the loss function of the PLR is unbounded, resulting classifiers can be sensitive to outliers. To build more robust classifiers, we propose the robust PLR (RPLR) which uses truncated logistic loss functions, and suggest three schemes to estimate conditional class probabilities. Connections of the RPLR with some other existing work on robust logistic regression have been discussed. Our theoretical results indicate that the RPLR is Fisher consistent and more robust to outliers. Moreover, we develop estimated generalized approximate cross validation (EGACV) for the tuning parameter selection. Through numerical examples, we demonstrate that truncating the loss function indeed yields better performance in terms of classification accuracy and class probability estimation.

0 Bookmarks
 · 
158 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Although cancer classification has improved over the past 30 years, there has been no general approach for identifying new cancer classes (class discovery) or for assigning tumors to known classes (class prediction). Here, a generic approach to cancer classification based on gene expression monitoring by DNA microarrays is described and applied to human acute leukemias as a test case. A class discovery procedure automatically discovered the distinction between acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL) without previous knowledge of these classes. An automatically derived class predictor was able to determine the class of new leukemia cases. The results demonstrate the feasibility of cancer classification based solely on gene expression monitoring and suggest a general strategy for discovering and predicting cancer classes for other types of cancer, independent of previous biological knowledge.
    Science 11/1999; 286(5439):531-7. · 31.03 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We have generated a molecular taxonomy of lung carcinoma, the leading cause of cancer death in the United States and worldwide. Using oligonucleotide microarrays, we analyzed mRNA expression levels corresponding to 12,600 transcript sequences in 186 lung tumor samples, including 139 adenocarcinomas resected from the lung. Hierarchical and probabilistic clustering of expression data defined distinct subclasses of lung adenocarcinoma. Among these were tumors with high relative expression of neuroendocrine genes and of type II pneumocyte genes, respectively. Retrospective analysis revealed a less favorable outcome for the adenocarcinomas with neuroendocrine gene expression. The diagnostic potential of expression profiling is emphasized by its ability to discriminate primary lung adenocarcinomas from metastases of extra-pulmonary origin. These results suggest that integration of expression profile data with clinical parameters could aid in diagnosis of lung cancer patients.
    Proceedings of the National Academy of Sciences 12/2001; 98(24):13790-5. · 9.81 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and/or nonconcave. This article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions. These algorithms operate by perturbing the penalty function slightly to render it differentiable, then optimizing this differentiable function using a minorize-maximize (MM) algorithm. MM algorithms are useful extensions of the well-known class of EM algorithms, a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for EM algorithms. In particular, we prove that when our MM algorithms converge, they must converge to a desirable point; we also discuss conditions under which this convergence may be guaranteed. We exploit the Newton-Raphson-like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators. Our method performs well in numerical tests.
    The Annals of Statistics 02/2005; 33(4):1617-1642. · 2.53 Impact Factor

Full-text

Download
0 Downloads
Available from