Robust Regression Method Research Articles

Preferential reducts and constructs in robust multiple criteria ranking and sorting

We revisit the multiple criteria ranking and sorting methods based on ordinal regression, which accept preference information in the form of, respectively, pairwise comparisons or assignment examples for some reference alternatives. Robust ordinal regression methods consider the whole set of value functions reproducing these holistic statements provided at the input. Its impact on the recommendation is expressed in terms of the necessary and possible preference relations or assignments. We propose methods for generating explanations of this impact, showing pieces of preference information provided by the decision maker (DM), which led to the observed outcomes. In particular, the minimal set of preference information pieces, called preferential reduct, is identified to justify some result observable for the whole set of compatible value functions (e.g., the truth of the necessary relation for some pair of alternatives). Further, the maximal set of preference information pieces, called preferential construct, is discovered to reveal the conditions under which some result non-observable for the whole set of compatible value functions (e.g., the falsity of the possible relation for some pair of alternatives) is possible. Knowing such explanations, the DM can better understand the impact of each piece of preference information on the result and, in consequence, get conviction about the obtained recommendation.

The impact of new goods and service products on firm growth: evidence from Austrian-linked firm-level data

Using a matched innovation survey and structural business statistics, we investigate the impact of the introduction of new service products and other types of technological innovations on firm growth measured as subsequent two-year employment growth. Results, based on median and robust regression methods for manufacturing firms, show that, on average, both the introduction of new goods and process innovations have a significant and positive impact on subsequent firm growth. In contrast, the introduction of new services does not, on average, have a significant impact on firm growth for both manufacturing and service firms. However, quantile regressions show that the introduction of new service products has a significant and positive impact on firm growth for high-growth service firms. Finally, in manufacturing, the introduction of product innovations has a positive impact on firm growth at both the lower and higher ends of distribution (i.e. for both high-growth and shrinking firms).

Parameter C Optimizing for Robust ε-Support Vector Regression

In case of experimental data contaminated with errors and noise, the robust ε-support vector regression has good forecast accuracy and high generalization ability. However, it depends on the selection of system parameter. Firstly, this paper introduces the robust ε-support vector regression method. Secondly, as the experiments prove, the new method achieves high forecast accuracy by virtue of the optimal penalty parameter C. Finally, the optimal method of parameter C is presented in the last section.

Robust Transition Estimation for Community Evolution and Evolutionary Outlier Detection

PDF HTML阅读 XML下载 导出引用 引用提醒 社群演化的稳健迁移估计及演化离群点检测 DOI: 10.3724/SP.J.1001.2013.04477 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金(61375069,61105069);中国博士后科学基金(2011M500846);江苏省科技支撑计划(BE2012181);江苏省教育厅自然科学基金(11KJB520001);江苏高校优势学科建设工程资助项目;计算机软件新技术国家重点实验室自主课题(ZZKT2013B11) Robust Transition Estimation for Community Evolution and Evolutionary Outlier Detection Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:时序数据集中的社群演化模式是网络行为动力学研究与应用的重要领域.基于社群演化的离群点检测不仅能够发现新颖的异常行为模式,同时也有利于更准确地理解社群的演化趋势.运用成员关于社群隶属关系的变化,提出了社群演化迁移矩阵的概念,研究并揭示了迁移矩阵的若干性质及其与社群结构演化之间的关系.在采用稳健回归M-估计方法进一步优化迁移矩阵降低异常点干扰的同时,对社群演化离群点加以刻画和定义.鉴于复杂网络包含大量随机游走的边缘个体,所定义的离群点综合考虑其在社群中角色的变化和相对于社群总体迁移模式的差异.基于上述思想提出的演化离群点检测算法能够适应各类社群演化趋势,更有效地聚焦和发现大规模社会网络中重要成员的异常演化行为.实验结果表明,所提出的方法能够从大规模社会网络演化序列中发现重要的离群演化模式,并在现实中找到合理的解释. Abstract:Community evolutionary pattern analysis in temporal datasets is a key issue in social network dynamics research and applications. Identifying outlying objects against main community evolution trends is not only meaningful by itself for the purpose of finding novel evolution behaviors, but also helpful for better understanding the mainstream of community evolution. Upon giving the belonging matrix of community members, this study defines a type of transition matrix to characterize the pattern of the evolutionary dynamic between two consecutive belonging snapshots. A set of properties about the transition matrix is discussed, which reveals its close relation to the gradual community structural change in quantity. The transition matrix is further optimized using M-estimator Robust Regression methods by minimizing the disturbance incurred by the outliers, and the abnormality of the outlier objects can then be computed at the same time. Considering that large proportion of trivial but nomadic objects may exist in large datasets like those of complex social networks, focus is placed only on the community evolutionary outliers that show remarkable difference from the main bodies of their communities and sharp change of their membership role within the communities. A definition on such type of local and global outliers is given, and an algorithm on detection such kind of outliers is proposed in this paper. Experimental results on both synthetic and real datasets show that the proposed approach is highly effective in discovering interesting evolutionary community outliers. 参考文献 相似文献 引证文献

A predictive DEA model for outlier detection

Outlier detection is one of the key issues in any data-driven analytics. In this paper, we propose Bi-super DEA, a super DEA-based method that constructs both efficient and inefficient frontiers for outlier detection. In evaluating its predictive performance, we develop a novel predictive DEA procedure, PDEA, which extends the conventional DEA approaches that have been primarily used for in-sample efficiency estimation, to predict outputs for the out-of-sample. This enables us to compare the predictive performance of our approach against several popular outlier detection methods including the parametric robust regression in statistics and non-parametric k-means in data mining. We conduct comprehensive simulation experiments to examine the relative performance of these outlier detection methods under the influence of five factors: sample size, linearity of production function, normality of noise distribution, homogeneity of data, and levels of random noise contaminating the data generating process (DGP). We find that, somewhat surprisingly, Bi-super CCR consistently outperforms Bi-super BCC in detecting outliers. Under the linearity, normality and homogeneity conditions, the parametric robust regression method works best. However, when the DGP violates these conditions, Bi-super DEA emerges as the better choice due to its distribution-free property. Our results shed light on the conditions that each method excels or fails and provide users with practical guidelines on how to choose appropriate methods to detect outliers.

Grey relational effort analysis technique using robust regression methods for individual projects

Efficient development of software requires accurate estimates. It is unlikely to expect very accurate estimates of software development effort because of the inherent uncertainty in software development projects and the complex and dynamic interaction of factors that impact software development. In this study, two analogy methods based on integration of Grey Relational Effort Analysis Technique using Robust Regression Methods with and without feature subset selection have been proposed. In the previous, Grey Relational based effort estimation studies, GRA is used to assess similarity between projects with m features and effort is estimated from k most similar projects. In the proposed methodologies, the effort of the reference project is estimated by applying regression techniques to k most similar projects obtained using GRA as the similarity metric. Empirical results obtained are statistically significant, indicating that the methodology has great potential and can be used as a candidate approach for software effort estimation.

A New Robust Method for Nonlinear Regression.

When outliers are present, the least squares method of nonlinear regression performs poorly. The main purpose of this paper is to provide a robust alternative technique to the Ordinary Least Squares nonlinear regression method. This new robust nonlinear regression method can provide accurate parameter estimates when outliers and/or influential observations are present. Real and simulated data for drug concentration and tumor size-metastasis are used to assess the performance of this new estimator. Monte Carlo simulations are performed to evaluate the robustness of our new method in comparison with the Ordinary Least Squares method. In simulated data with outliers, this new estimator of regression parameters seems to outperform the Ordinary Least Squares with respect to bias, mean squared errors, and mean estimated parameters. Two algorithms have been proposed. Additionally and for the sake of computational ease and illustration, a Mathematica program has been provided in the Appendix. The accuracy of our robust technique is superior to that of the Ordinary Least Squares. The robustness and simplicity of computations make this new technique more appropriate and useful tool for the analysis of nonlinear regressions.

Nonlinear Model of Image Noise: An Application on Computed Tomography including Beam Hardening and Image Processing Algorithms

This paper proposes a more inclusive statistical model for predicting image noise in Computed Tomography (CT), associated with scanning factors, considering the effect of beam hardening and image processing filters. It is based on power functions where the levels of the parameters will determine the rate of noise variation with respect to a given scanning factor. It includes the influence of tube potential, tube current, slice thickness, Field of View (FOV), reconstruction methods and post-processing filters. To validate the model, tomographic measurements were made by using a PMMA phantom that simulates paediatric head and adult abdomen, a PET bottle was used to simulate the head of the new-born. The influence of ROI (Region Of Interest) size over nonlinear model parameters was analysed, and high variations of powers of attenuation and FOV were found depending on ROI size. A nonlinear robust regression method was used. The validation was performed graphically by weighted residual analysis. A nonlinear noise model was obtained with an adjusted coefficient of determination for ROI sizes between 10% and 70% of the phantom diameter or FOV. The model confirms the significance of the tube current, slice thickness and beam hardening effect on image. The process of estimation of the parameters of the model by Nonlinear Robust Regression turned out to be optimal.

On the implementation of LIR: the case of simple linear regression with interval data

This paper considers the problem of simple linear regression with interval-censored data. That is, $$n$$ n pairs of intervals are observed instead of the $$n$$ n pairs of precise values for the two variables (dependent and independent). Each of these intervals is closed but possibly unbounded, and contains the corresponding (unobserved) value of the dependent or independent variable. The goal of the regression is to describe the relationship between (the precise values of) these two variables by means of a linear function. Likelihood-based Imprecise Regression (LIR) is a recently introduced, very general approach to regression for imprecisely observed quantities. The result of a LIR analysis is in general set-valued: it consists of all regression functions that cannot be excluded on the basis of likelihood inference. These regression functions are said to be undominated. Since the interval data can be unbounded, a robust regression method is necessary. Hence, we consider the robust LIR method based on the minimization of the residuals' quantiles. For this method, we prove that the set of all the intercept-slope pairs corresponding to the undominated regression functions is the union of finitely many polygons. We give an exact algorithm for determining this set (i.e., for determining the set-valued result of the robust LIR analysis), and show that it has worst-case time complexity $$O(n^{3}\log n)$$ O ( n 3 log n ) . We have implemented this exact algorithm as part of the R package linLIR.

Regression with outlier shrinkage

We propose a robust regression method called regression with outlier shrinkage (ROS) for the traditional n>p cases. It improves over the other robust regression methods such as least trimmed squares (LTS) in the sense that it can achieve maximum breakdown value and full asymptotic efficiency simultaneously. Moreover, its computational complexity is no more than that of LTS. We also propose a sparse estimator, called sparse regression with outlier shrinkage (SROS), for robust variable selection and estimation. It is proven that SROS can not only give consistent selection but also estimate the nonzero coefficients with full asymptotic efficiency under the normal model. In addition, we introduce a concept of nearly regression equivariant estimator for understanding the breakdown properties of sparse estimators, and prove that SROS achieves the maximum breakdown value of nearly regression equivariant estimators. Numerical examples are presented to illustrate our methods.

The sensitivity of winter tourism to exchange rate changes: Evidence for the Swiss Alps

This paper investigates the impact of the appreciation of the Swiss franc on international tourism in Swiss Alpine resorts, city and lake destinations using annual data for winter seasons 2007/2008 to 2010/2011. Using median regression models, we find that the nominal and real appreciation of the Swiss franc has a large and significantly negative impact on international tourism demand in Alpine destinations during winter months. The elasticities of the relative price (to those of competing countries) range between −3.0 for foreign hotel nights and −2.1 for foreign hotel arrivals. In contrast, the real exchange rate effect is much lower in absolute terms for city and lake destinations. The results are not sensitive with respect to different measures of international tourism demand (arrivals, hotel nights and the length of stay). Income elasticities are also significant and large with values of two and higher. In general, these findings are robust to alternative estimation methods (i.e., median regression, robust regression method and ordinary least squares in first differences).

Estimating performance aspects of Greek equity funds with a liquidity-augmented factor model

The present study, employing a survivorship-bias free dataset, assesses the performance of Greek domestic equity funds during the period June 2001–December 2009 controlling for the thin trading risk that is inherent in the Greek stock market. Augmenting Carhart's multi-benchmark model (1997) with a stock-level liquidity factor, we document the absence of skills among domestic equity fund managers. However, at a fund level, we detect the evidence of a statistically and economically significant outperformance. Additionally, we examine the relationship between fund performance and a series of cost and operational attributes employing a robust quantile regression method. Cross-sectional results demonstrate a significant inverse relationship between fund performance and expenses. Moreover, our findings show that the larger the fund, the lower the performance.

Reducing Poisson noise and baseline drift in x-ray spectral images with bootstrap Poisson regression and robust nonparametric regression

X-ray spectral imaging provides quantitative imaging of trace elements in a biological sample with high sensitivity. We propose a novel algorithm to promote the signal-to-noise ratio (SNR) of x-ray spectral images that have low photon counts. Firstly, we estimate the image data area that belongs to the homogeneous parts through confidence interval testing. Then, we apply the Poisson regression through its maximum likelihood estimation on this area to estimate the true photon counts from the Poisson noise corrupted data. Unlike other denoising methods based on regression analysis, we use the bootstrap resampling method to ensure the accuracy of regression estimation. Finally, we use a robust local nonparametric regression method to estimate the baseline and subsequently subtract it from the x-ray spectral data to further improve the SNR of the data. Experiments on several real samples show that the proposed method performs better than some state-of-the-art approaches to ensure accuracy and precision for quantitative analysis of the different trace elements in a standard reference biological sample.

From toe to head: Use of robust regression methods in stature estimation based on foot remains

Stature estimation is a standard procedure in the fields of forensic and biological anthropology, bio-archaeology and paleoanthropology, in order to gain biological insights into the individuals/populations studied. The most accurate stature estimation method is based on anatomical reconstruction (i.e., the Fully method), followed by type I regression equations (e.g., ordinary least squares – OLS) based on long bones, preferably from the lower limb. In some cases, due to the fragmentary nature of the osseous material recovered, stature estimates have to rely on other elements, such as foot remains. In this study, we explore stature estimation based on different foot bones: the talus, calcaneus, and metatarsals 1–4 in Afro- and Euroamericans of both sexes. The approach undertaken in this study is novel for two reasons. First, individual estimates for each bone are provided, and tarsals and metatarsals are combined in order to obtain more accurate estimates. Second, robust statistical methods based on type I regression equations are used, namely least trimmed squares (LTS). Our results show that the best individual bones for estimating stature are the first and second metatarsal and both the talus and the calcaneus. The combination of a tarsal and a metatarsal bone slightly improves the accuracy of the stature estimate.

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.

A Study on Fuzzy Robust Regression and Its Application to Insurance

In this study, a fuzzy robust regression method is proposed to construct a model that describes the relation between dependent and independent variables in insurance. Fuzzy robust regression suggested as an alternative to not only ordinary least squares but also classical robust regression. Fuzzy robust regression is finally investigated and discussed by an example with real data arose from a well-known insurance company in Turkey.

TELBS robust linear regression method

TELBS robust linear regression method MA Tabatabai,1 WM Eby,1 H Li,1 S Bae,2 KP Singh21Department of Mathematical Sciences, Cameron University, Lawton, OK, 2Department of Medicine, University of Alabama, Birmingham, AL, USAAbstract: Ordinary least squares estimates can behave badly when outliers are present. An alternative is to use a robust regression technique that can handle outliers and influential observations. We introduce a new robust estimation method called TELBS robust regression method. We also introduce a new measurement called Sh(i) for detecting influential observations. In addition, a new measure for goodness of fit, called R2RFPR, is introduced. We provide an algorithm to perform the TELBS estimation of regression parameters. Real and simulated data sets are used to assess the performance of this new estimator. In simulated data with outliers, the TELBS estimator of regression parameters performs better in comparison with least squares, M and MM estimators, with respect to both bias and mean squared error. For rat liver weights data, none of the estimators (least squares, M, and MM) are able to estimate the parameters accurately. However, TELBS does give an accurate estimate. Using real data for brain imaging, the TELBS and MM methods were equally accurate. In both of these real data sets, the Sh(i) measure was very effective in identifying influential observations. The robustness and simplicity of computations of TELBS model parameters make this method an appropriate one for analysis of linear regression. Algorithms and programs have been provided for ease in implementation, including all relevant statistics necessary to perform a complete analysis of linear regression.Keywords: robust linear regression, least squares estimator, M and MM estimators, magnetic resonance imaging, Cook's distance, detection of influential observations, Studentized residual

Robust Support Vector Regression for Uncertain Input and Output Data

In this paper, a robust support vector regression (RSVR) method with uncertain input and output data is studied. First, the data uncertainties are investigated under a stochastic framework and two linear robust formulations are derived. Linear formulations robust to ellipsoidal uncertainties are also considered from a geometric perspective. Second, kernelized RSVR formulations are established for nonlinear regression problems. Both linear and nonlinear formulations are converted to second-order cone programming problems, which can be solved efficiently by the interior point method. Simulation demonstrates that the proposed method outperforms existing RSVRs in the presence of both input and output data uncertainties.

A Least Trimmed Square Regression Method for Second Level fMRI Effective Connectivity Analysis

We present a least trimmed square (LTS) robust regression method to combine different runs/subjects for second/high level effective connectivity analysis. The basic idea of this method is to treat the extreme nonlinear model variability as outliers if they exceed a certain threshold. A bootstrap method for the LTS estimation is employed to detect model outliers. We compared the LTS robust method with a non-robust method using simulated and real datasets. The difference between LTS and the non-robust method for second level effective connectivity analysis is significant, suggesting the conventional non-robust method is easily affected by the model variability from the first level analysis. In addition, after these outliers are detected and excluded for the high level analysis, the model coefficients of the second level are combined within the framework of a mixed model. The variance of the mixed model is estimated using the Newton-Raphson (NR) type Levenberg-Marquardt algorithm. Three sets of real data are adopted to compare conventional methods which do not include random effects in the analysis with a mixed model for second level effective connectivity analysis. The results show that the conventional method is significantly different from the mixed model when greater model variability exists, suggesting there is a strong random effect, and the mixed model should be employed for the second level effective connectivity analysis.

An inferential modeling method using enumerative PLS based nonnegative garrote regression

In this paper a robust linear regression method with variable selection is proposed for predicting desirable end-of-line quality variables in complex industrial processes. The development of such prediction models is challenging because there is usually a large pool of candidate explanatory variables, limited sample data, and multicollinearity among explanatory variables. The proposed method is named as the enumerative partial least square based nonnegative garrote regression. It employs partial least square regression in enumerative manner to generate initial model coefficients and then uses a nonnegative garrote method to shrink original coefficients so that irrelevant variables can be eliminated implicitly. Analysis about the advantages of the proposed method is provided compared to existing state-of-art model construction methods. Two simulation examples as well as an industrial application in a local semiconductor factory unit are used to validate the proposed method. These examples witness substantial improvement in terms of accuracy and robustness in variable selection compared to existing methods. Specifically, for the industrial case the percentages of improvement in terms of root mean squared error is up to 24.3% compared with the previous work.