Robust continuum regression.

Several applications of continuum regression (CR) 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 (OLS), principal component regression (PCR) and partial least squares (PLS)). For contaminated data continuum regression may yield aberrant estimates due to its non-robustness with respect to outliers. Also for data originating from a distribution which significantly differs from the normal distribution, continuum regression may yield very inefficient estimates. In the current paper, robust continuum regression (RCR) is proposed. To construct the estimator, an algorithm based on projection pursuit (PP) is proposed. The robustness and good efficiency properties of RCR are shown by means of a simulation study. An application to an X-ray fluorescence analysis of hydrometallurgical samples illustrates the method's applicability in practice.Regression; Applications; Data; Ordinary least squares; Least-squares; Squares; Partial least squares; Yield; Outliers; Distribution; Estimator; Projection-pursuit; Robustness; Efficiency; Simulation; Studies;

Robust continuum regression.

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 respect to outliers. Also for data originating from a distribution which significantly differs from the normal distribution, continuum regression may yield very inefficient estimates. In the current paper, robust continuum regression (RCR) is proposed. To construct the estimator, an algorithm based on projection pursuit is proposed. The robustness and good efficiency properties of RCR are shown by means of a simulation study. An application to an X-ray fluorescence analysis of hydrometallurgical samples illustrates the method's applicability in practice.Advantages; Applications; Calibration; Continuum regression (CR); Data; Distribution; Efficiency; Estimator; Least-squares; M-estimators; Methods; Model; Optimal; Ordinary least squares; Outliers; Partial least squares; Precision; Prediction; Projection-pursuit; Regression; Research; Robust continuum regression (RCR); Robust multivariate calibration; Robust regression; Robustness; Simulation; Squares; Studies; Variables; Yield;

Algorithms for Projection - Pursuit robust principal component analysis.

The results of a standard principal component analysis (PCA) can be affected by the presence of outliers. Hence robust alternatives to PCA are needed. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit-based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in the presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real data sets. (c) 2007 Elsevier B.V. All rights reserved.multivariate statistics; optimization; numerical precision; outliers; robustness; scale estimators; estimators; regression;

Distributed Robust Learning

We propose a framework for distributed robust statistical learning on {\em big contaminated data}. The Distributed Robust Learning (DRL) framework can reduce the computational time of traditional robust learning methods by several orders of magnitude. We analyze the robustness property of DRL, showing that DRL not only preserves the robustness of the base robust learning method, but also tolerates contaminations on a constant fraction of results from computing nodes (node failures). More precisely, even in presence of the most adversarial outlier distribution over computing nodes, DRL still achieves a breakdown point of at least $\lambda^*/2$, where $\lambda^*$ is the break down point of corresponding centralized algorithm. This is in stark contrast with naive division-and-averaging implementation, which may reduce the breakdown point by a factor of $k$ when $k$ computing nodes are used. We then specialize the DRL framework for two concrete cases: distributed robust principal component analysis and distributed robust regression. We demonstrate the efficiency and the robustness advantages of DRL through comprehensive simulations and predicting image tags on a large-scale image set.Comment: 18 pages, 2 figure

Integrating joint feature selection into subspace learning: A formulation of 2DPCA for outliers robust feature selection

© 2019 Elsevier Ltd Since the principal component analysis and its variants are sensitive to outliers that affect their performance and applicability in real world, several variants have been proposed to improve the robustness. However, most of the existing methods are still sensitive to outliers and are unable to select useful features. To overcome the issue of sensitivity of PCA against outliers, in this paper, we introduce two-dimensional outliers-robust principal component analysis (ORPCA) by imposing the joint constraints on the objective function. ORPCA relaxes the orthogonal constraints and penalizes the regression coefficient, thus, it selects important features and ignores the same features that exist in other principal components. It is commonly known that square Frobenius norm is sensitive to outliers. To overcome this issue, we have devised an alternative way to derive objective function. Experimental results on four publicly available benchmark datasets show the effectiveness of joint feature selection and provide better performance as compared to state-of-the-art dimensionality-reduction methods

Significance Regression: Robust Regression for Collinear Data

This paper examines robust linear multivariable regression from collinear data. A brief review of M-estimators discusses the strengths of this approach for tolerating outliers and/or perturbations in the error distributions. The review reveals that M-estimation may be unreliable if the data exhibit collinearity. Next, significance regression (SR) is discussed. SR is a successful method for treating collinearity but is not robust. A new significance regression algorithm for the weighted-least-squares error criterion (SR-WLS) is developed. Using the weights computed via M-estimation with the SR-WLS algorithm yields an effective method that robustly mollifies collinearity problems. Numerical examples illustrate the main points