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Title: Robust mislabel logistic regression without modeling mislabel probabilities Authors:  Hung Hung - National Taiwan University (Taiwan)
Zhi-Yu Jou - National Taiwan University (Taiwan)
Su-Yun Huang - Academia Sinica (Taiwan) [presenting]
Abstract: Logistic regression is among the most widely used statistical methods for linear discriminant analysis. In many applications, we only observe possibly mislabeled responses. Fitting a conventional logistic regression can then lead to biased estimation. One common resolution is to fit a mislabel logistic regression model, which takes into consideration of mislabeled responses. Another common method is to adopt a robust M-estimation by down-weighting suspected instances. We propose a new robust mislabel logistic regression based on gamma-divergence, which is also known as the density power divergence of type zero. The proposal possesses two advantageous features: (1) It does not need to model the mislabel probabilities. (2) The minimum gamma-divergence estimation leads to a weighted estimating equation without the need to include any bias correction term, i.e., it is automatically bias-corrected. These features make the proposed gamma-logistic regression more robust in model fitting and more intuitive for model interpretation through a simple weighting scheme. The method is also easy to implement, and two types of algorithms are included. Simulation studies and real data application will be presented.