Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches incorporate the low-rank property to the model, and achieve satisfactory performance for certain applications. These approaches all assume that both predictors an...

In this note we introduce a method for robust principal component regression. Robust principal components are computed from the predictor variables, and they are used afterwards for estimating a response variable by performing robust linear multiple regression. The performance of the method is evaluated at a test data set from geochemistry. Then it is used for the prediction of censored values ...

Although the MapReduce framework is now the de facto standard for analyzing massive data sets, many algorithms (in particular, many iterative algorithms popular in machine learning, optimization, and linear algebra) are hard to fit into MapReduce. Consider, e.g., the `p regression problem: given a matrix A ∈ Rm×n and a vector b ∈ R, find a vector x∗ ∈ R that minimizes f(x) = ‖Ax− b‖p. The widel...

In many learning settings, the source data available to train a regression model differs from the target data it encounters when making predictions due to input distribution shift. Appropriately dealing with this situation remains an important challenge. Existing methods attempt to “reweight” the source data samples to better represent the target domain, but this introduces strong inductive bia...

This paper provides a robust statistical approach to nonstationary time series regression and inference. Fully modified extensions of traditional robust statistical procedures are developed that allow for endogeneities in the nonstation-ary regressors and serial dependence in the shocks that drive the regressors and the errors that appear in the equation being estimated. The suggested estima-to...

In regression analysis, the presence of outliers in the data set can strongly distort the classical least squares estimator and lead to unreliable results. To deal with this, several robust-to-outliers methods have been proposed in the statistical literature. In Stata, some of these methods are available through the commands rreg and qreg. Unfortunately, these methods only resist to some specif...

Several applications of continuum regression to non-contaminated data have shown that a significant improvement in predictive power can be obtained compared to the three standard techniques which it encompasses (Ordinary least Squares, Principal Component Regression and Partial Least Squares). For contaminated data continuum regression may yield aberrant estimates due to its non-robustness with...