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Logistic regression is one of the most popular statistical techniques for solving (binary) classification problems in various applications (e.g. credit scoring, cancer detection, ad click predictions and churn classification). Typically, the maximum likelihood estimator is used, which is very sensitive to outlying observations. In this paper, we propose a robust and sparse logistic regression estimator where robustness is achieved by means of the γ -divergence. An elastic net penalty ensures sparsity in the regression coefficients such that the model is more stable and interpretable. We show that the influence function is bounded and demonstrate its robustness properties in simulations. The good performance of the proposed estimator is also illustrated in an empirical application that deals with classifying the type of fuel used by cars. [ABSTRACT FROM AUTHOR]

Instance-dependent cost-sensitive (IDCS) learning methods have proven useful for binary classification tasks where individual instances are associated with variable misclassification costs. However, we demonstrate in this paper by means of a series of experiments that IDCS methods are sensitive to noise and outliers in relation to instance-dependent misclassification costs and their performance strongly depends on the cost distribution of the data sample. Therefore, we propose a generic three-step framework to make IDCS methods more robust: (i) detect outliers automatically, (ii) correct outlying cost information in a data-driven way, and (iii) construct an IDCS learning method using the adjusted cost information. We apply this framework to cslogit, a logistic regression-based IDCS method, to obtain its robust version, which we name r-cslogit. The robustness of this approach is introduced in steps (i) and (ii), where we make use of robust estimators to detect and impute outlying costs of individual instances. The newly proposed r-cslogit method is tested on synthetic and semi-synthetic data and proven to be superior in terms of savings compared to its non-robust counterpart for variable levels of noise and outliers. All our code is made available online at https://github.com/SimonDeVos/Robust-IDCS. [ABSTRACT FROM AUTHOR]

Two new methods for sparse dimension reduction are introduced, based on martingale difference divergence and ball covariance, respectively. These methods can be utilized straightforwardly as sufficient dimension reduction (SDR) techniques to estimate a sufficient dimension reduced subspace, which contains all information sufficient to explain a dependent variable. Moreover, owing to their sparsity, they intrinsically perform sufficient variable selection (SVS) and present two attractive new approaches to variable selection in a context of nonlinear dependencies that require few model assumptions. The two new methods are compared to a similar existing approach for SDR and SVS based on distance covariance, as well as to classical and robust sparse partial least squares. A simulation study shows that each of the new estimators can achieve correct variable selection in highly nonlinear contexts, yet are sensitive to outliers and computationally intensive. The study sheds light on the subtle differences between the methods. Two examples illustrate how they can be applied in practice, with a slight preference for the option based on martingale difference divergence in a bioinformatics example. [ABSTRACT FROM AUTHOR]

Kernel principal component analysis (KPCA) extends linear PCA from a real vector space to any high dimensional kernel feature space. The sensitivity of linear PCA to outliers is well-known and various robust alternatives have been proposed in the literature. For KPCA such robust versions received considerably less attention. In this article we present kernel versions of three robust PCA algorithms: spherical PCA, projection pursuit and ROBPCA. These robust KPCA algorithms are analyzed in a classification context applying discriminant analysis on the KPCA scores. The performances of the different robust KPCA algorithms are studied in a simulation study comparing misclassification percentages, both on clean and contaminated data. An outlier map is constructed to visualize outliers in such classification problems. A real life example from protein classification illustrates the usefulness of robust KPCA and its corresponding outlier map. [ABSTRACT FROM AUTHOR]