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Title: Sufficient reductions in regression with mixed predictors Authors:  Efstathia Bura - Vienna University of Technology (Austria) [presenting]
Liliana Forzani - Universidad Nacional del Litoral (Argentina)
Rodrigo Garcia Arancibia - Universidad Nacional del Litoral (Argentina)
Pamela Llop - Facultad de Ingenieria Quimica, UNL-CONICET (Argentina)
Diego Tomassi - Universidad Nacional del Litoral (Argentina)
Abstract: Most data sets comprise measurements of continuous and categorical variables. Modelling high-dimensional mixed predictors has received limited attention in regression and classification Statistics literature. We study the general regression problem of inferring a variable of interest based on high dimensional mixed continuous and binary predictors. The aim is to find a lower dimensional function of the mixed predictor vector that contains all the modeling information in the mixed predictors for the response, which can be either continuous or categorical. The approach we propose identifies sufficient reductions by reversing the regression and modeling the mixed predictors conditional on the response. We derive the maximum likelihood estimator of the sufficient reductions, asymptotic tests for dimension, and a regularized estimator, which simultaneously achieves variable (feature) selection and dimension reduction (feature extraction). We study the performance of the proposed method and compare it with other approaches through simulations and real data examples.