Dimensionality reduction using feature extraction and selection approaches is a common stage of many regression and classification tasks. In recent years there have been significant e orts to reduce the dimension of the feature space without lossing information that is relevant for prediction. This objective can be cast into a conditional independence condition between the response or class labels and the transformed features. Building on this, in this work we use measures of statistical dependence to estimate a lower-dimensional linear subspace of the features that retains the su cient information. Unlike likelihood-based and many momentbased methods, the proposed approach is semi-parametric and does not require model assumptions on the data. A regularized version to achieve simultaneous variable selection is presented too. Experiments with simulated data show that the performance of the proposed method compares favorably to well-known linear dimension reduction techniques.Sociedad Argentina de Informática e Investigación Operativa (SADIO)