Computing of high breakdown regression estimators without sorting on graphics processing units

We present an approach to computing high-breakdown regression estimators in parallel on graphics processing units (GPU).We show that sorting the residuals is not necessary, and it can be substituted by calculating the median. We present and compare various methods to calculate the median and order statistics on GPUs. We introduce an alternative method based on the optimization of a convex function, and showits numerical superiority when calculating the order statistics of very large arrays on GPUs.

Global non-smooth optimization in robust multivariate regression

Robust regression in statistics leads to challenging optimization problems. Here, we study one such problem, in which the objective is non-smooth, non-convex and expensive to calculate. We study the numerical performance of several derivative-free optimization algorithms with the aim of computing robust multivariate estimators. Our experiences demonstrate that the existing algorithms often fail to deliver optimal solutions. We introduce three new methods that use Powell's derivative-free algorithm. The proposed methods are reliable and can be used when processing very large data sets containing outliers.

High breakdown bundle adjustment

Identifying the parameters of a model such that it best fits an observed set of data points is fundamental to the majority of problems in computer vision. This task is particularly demanding when portions of the data has been corrupted by gross outliers, measurements that are not explained by the assumed distributions. In this paper we present a novel method that uses the Least Quantile of Squares (LQS) estimator, a well known but computationally demanding high-breakdown estimator with several appealing theoretical properties. The proposed method is a meta-algorithm, based on the well established principles of proximal splitting, that allows for the use of LQS estimators while still retaining computational efficiency. Implementing the method is straight-forward as the majority of the resulting sub-problems can be solved using existing standard bundle-adjustment packages. Preliminary experiments on synthetic and real image data demonstrate the impressive practical performance of our method as compared to existing robust estimators used in computer vision.

On some Sufficient Conditions for High Breakdown Point of ML Estimators

High breakdown point estimators LME(k) and LT E(k) for location and scale are obtained for symmetrical exponentially decreasing density family.

OWA operators in linear regression and detection of outliers

We consider the use of Ordered Weighted Averaging (OWA) in linear regression. Our goal is to replace the traditional least squares, least absolute deviation, and maximum likelihood criteria with an OWA function of the residuals. We obtain several high breakdown robust regression methods as special cases (least median, least trimmed squares, trimmed likelihood methods). We also present new formulations of regression problem. OWA-based regression is particularly useful in the presence of outliers.

OWA operators in regression problems

We consider an application of fuzzy logic connectives to statistical regression. We replace the standard least squares, least absolute deviation, and maximum likelihood criteria with an ordered weighted averaging (OWA) function of the residuals. Depending on the choice of the weights, we obtain the standard regression problems, high-breakdown robust methods (least median, least trimmed squares, and trimmed likelihood methods), as well as new formulations. We present various approaches to numerical solution of such regression problems. OWA-based regression is particularly useful in the presence of outliers, and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers.

Derivative-free optimization and neural networks for robust regression

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares (LTS) criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks (ANNs) to contaminated data using LTS criterion. We introduce a penalized LTS criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression.

ROBREG: Stata module providing robust regression estimators

robreg provides a number of robust estimators for linear regression models. Among them are the high breakdown-point and high efficiency MM-estimator, the Huber and bisquare M-estimator, and the S-estimator, each supporting classic or robust standard errors. Furthermore, basic versions of the LMS/LQS (least median of squares) and LTS (least trimmed squares) estimators are provided. Note that the moremata package, also available from SSC, is required.

The role of goal importance in predicting university students’ high academic performance

We examined goal importance, focusing on high, but not exclusive priority goals, in the theory of planned behaviour (TPB) to predict students’ academic performance. At the beginning of semester, students in a psychology subject (N = 197) completed TPB and goal importance items for achieving a high grade. Regression analyses revealed partial support for the TPB. Perceived behavioural control, but not attitude or subjective norm, significantly predicted intention, with intention predicting final grade. Goal importance significantly predicted intention, but not final grade, indicating that perceiving a performance goal as highly, but not necessarily exclusively, important impacts on students’ achievement intentions.

Least Median Of Squares Estimation In Power Systems

Static state estimators currently in use in power systems are prone to masking by multiple bad data. This is mainly because the power system regression model contains many leverage points; typically they have a cluster pattern. As reported recently in the statistical literature, only high breakdown point estimators are robust enough to cope with gross errors corrupting such a model. This paper deals with one such estimator, the least median of squares estimator, developed by Rousseeuw in 1984. The robustness of this method is assessed while applying it to power systems. Resampling methods are developed, and simulation results for IEEE test systems discussed. © 1991 IEEE.

Thin nanoporous metal-insulator-metal membranes

Insulating nanoporous materials are promising platforms for soft-ionizing membranes; however, improvement in fabrication processes and the quality and high breakdown resistance of the thin insulator layers are needed for high integration and performance. Here, scalable fabrication of highly porous, thin, silicon dioxide membranes with controlled thickness is demonstrated using plasma-enhanced chemical-vapor-deposition. The fabricated membranes exhibit good insulating properties with a breakdown voltage of 1 × 107 V/cm. Our calculations suggest that the average electric field inside a nanopore of the membranes can be as high as 1 × 106 V/cm; sufficient for ionization of wide range of molecules. These metal–insulator–metal nanoporous arrays are promising for applications such soft ionizing membranes for mass spectroscopy.

A fast 600-V Tandem PiN Schottky (TPS) rectifier with ultra-low on-state voltage

The Tandem PiN Schottky (TPS) rectifier features lowly-doped p-layers in both active and termination regions, and is applied in 600-V rating for the first time. In the active region, the Schottky contact is in series connection with a transparent p-layer, leading to a superior forward performance than the conventional diodes. In addition, due to the benefit of moderate hole injection from the p-layer, the TPS offers a better trade-off between the on-state voltage and the switching speed. The active p-layer also helps to stabilise the Schottky contact, and hence the electrical data distributions are more concentrated. Regarding the floating p-layer in the termination region, its purpose is to reduce the peak electric fields, and the TPS demonstrates a high breakdown voltage with a compact termination width, less than 70% of the state-of-the-art devices on the market. Experimental results have shown that the 600-V TPS rectifier has an ultra-low on-state voltage of 0.98 V at 250 A/cm 2, a fast turn-off time of 75 ns by the standard RG1 test (I F=0.5A, I R=1A, and I RR=0.25A) and a breakdown voltage over 720 V. It is noteworthy that the p-layers in the active and termination regions can be formed at no extra cost for the use of self-alignment process. © 2012 IEEE.