Ridge regression for two dimensional locality preserving projection

Two Dimensional Locality Preserving Projection (2D-LPP) is a recent extension of LPP, a popular face recognition algorithm. It has been shown that 2D-LPP performs better than PCA, 2D-PCA and LPP. However, the computational cost of 2D-LPP is high. This paper proposes a novel algorithm called Ridge Regression for Two Dimensional Locality Preserving Projection (RR- 2DLPP), which is an extension of 2D-LPP with the use of ridge regression. RR-2DLPP is comparable to 2DLPP in performance whilst having a lower computational cost. The experimental results on three benchmark face data sets - the ORL, Yale and FERET databases - demonstrate the effectiveness and efficiency of RR-2DLPP compared with other face recognition algorithms such as PCA, LPP, SR, 2D-PCA and 2D-LPP.

Face recognition using kernel ridge regression

In this paper, we present novel ridge regression (RR) and kernel ridge regression (KRR) techniques for multivariate labels and apply the methods to the problem of face recognition. Motivated by the fact that the regular simplex vertices are separate points with highest degree of symmetry, we choose such vertices as the targets for the distinct individuals in recognition and apply RR or KRR to map the training face images into a face subspace where the training images from each individual will locate near their individual targets. We identify the new face image by mapping it into this face subspace and comparing its distance to all individual targets. An efficient cross-validation algorithm is also provided for selecting the regularization and kernel parameters. Experiments were conducted on two face databases and the results demonstrate that the proposed algorithm significantly outperforms the three popular linear face recognition techniques (Eigenfaces, Fisherfaces and Laplacianfaces) and also performs comparably with the recently developed Orthogonal Laplacianfaces with the advantage of computational speed. Experimental results also demonstrate that KRR outperforms RR as expected since KRR can utilize the nonlinear structure of the face images. Although we concentrate on face recognition in this paper, the proposed method is general and may be applied for general multi-category classification problems.

Use of ridge regression for the prediction of early growth performance in crossbred calves

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Multicollinearity and financial constraint in investment decisions: a bayesian generalized ridge regression

This paper addresses the investment decisions considering the presence of financial constraints of 373 large Brazilian firms from 1997 to 2004, using panel data. A Bayesian econometric model was used considering ridge regression for multicollinearity problems among the variables in the model. Prior distributions are assumed for the parameters, classifying the model into random or fixed effects. We used a Bayesian approach to estimate the parameters, considering normal and Student t distributions for the error and assumed that the initial values for the lagged dependent variable are not fixed, but generated by a random process. The recursive predictive density criterion was used for model comparisons. Twenty models were tested and the results indicated that multicollinearity does influence the value of the estimated parameters. Controlling for capital intensity, financial constraints are found to be more important for capital-intensive firms, probably due to their lower profitability indexes, higher fixed costs and higher degree of property diversification.

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

THE IMPROVEMENT REGION IN RIDGE REGRESSION

One of the difficulties in the practical application of ridge regression is that, for a given data set, it is unknown whether a selected ridge estimator has smaller squared error than the least squares estimator. The concept of the improvement region is defined, and a technique is developed which obtains approximate confidence intervals for the value of ridge k which produces the maximum reduction in mean squared error. Two simulation experiments were conducted to investigate how accurate these approximate confidence intervals might be. ^

MSC-clustering and forward stepwise regression for virtual metrology in highly correlated input spaces

Increasingly semiconductor manufacturers are exploring opportunities for virtual metrology (VM) enabled process monitoring and control as a means of reducing non-value added metrology and achieving ever more demanding wafer fabrication tolerances. However, developing robust, reliable and interpretable VM models can be very challenging due to the highly correlated input space often associated with the underpinning data sets. A particularly pertinent example is etch rate prediction of plasma etch processes from multichannel optical emission spectroscopy data. This paper proposes a novel input-clustering based forward stepwise regression methodology for VM model building in such highly correlated input spaces. Max Separation Clustering (MSC) is employed as a pre-processing step to identify a reduced srt of well-conditioned, representative variables that can then be used as inputs to state-of-the-art model building techniques such as Forward Selection Regression (FSR), Ridge regression, LASSO and Forward Selection Ridge Regression (FCRR). The methodology is validated on a benchmark semiconductor plasma etch dataset and the results obtained are compared with those achieved when the state-of-art approaches are applied directly to the data without the MSC pre-processing step. Significant performance improvements are observed when MSC is combined with FSR (13%) and FSRR (8.5%), but not with Ridge Regression (-1%) or LASSO (-32%). The optimal VM results are obtained using the MSC-FSR and MSC-FSRR generated models. © 2012 IEEE.

Boosting performance for 2D linear discriminant analysis via regression

Two Dimensional Linear Discriminant Analysis (2DLDA) has received much interest in recent years. However, 2DLDA could make pairwise distances between any two classes become significantly unbalanced, which may affect its performance. Moreover 2DLDA could also suffer from the small sample size problem. Based on these observations, we propose two novel algorithms called Regularized 2DLDA and Ridge Regression for 2DLDA (RR-2DLDA). Regularized 2DLDA is an extension of 2DLDA with the introduction of a regularization parameter to deal with the small sample size problem. RR-2DLDA integrates ridge regression into Regularized 2DLDA to balance the distances among different classes after the transformation. These proposed algorithms overcome the limitations of 2DLDA and boost recognition accuracy. The experimental results on the Yale, PIE and FERET databases showed that RR-2DLDA is superior not only to 2DLDA but also other state-of-the-art algorithms.

Prevendo inflação usando ridge regressions

Este estudo tem como objetivo analisar o desempenho de vários modelos econométricos ao prever Inflação . Iniciamos o trabalho utilizando como base de comparação para todos os modelos a tradicional curva de Phillips que usa a taxa de desemprego como variável explicativa para diferenças de preço. Dentre os modelos analisados temos univariados e bivariados, sendo estes últimos uma curva de Phillips alternativa já que apenas sustitui a variável desemprego por outra variável macroeconômica. Além destes modelos também comparamos o desempenho de previsão de modelos que usam como covariadas uma combinação das previsões dos modelos anteriores (univariados e bivariados). O resultado deste estudo aponta a combinação de modelos por "ridge regression" como uma técnica - dentre as analisadas para combinação de previsões - de menor erro de previsão sempre; sendo alcançado pela combinação da média em apenas um dos casos analisados. No entanto, a combinação de previsões não apresentou melhor resultado que algumas das covariadas testadas em modelos bivariados

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

High subsoil chloride concentrations reduce soil water extraction and crop yield on Vertosols in north-eastern Australia

Salinity, sodicity, acidity, and phytotoxic levels of chloride (Cl) in subsoils are major constraints to crop production in many soils of north-eastern Australia because they reduce the ability of crop roots to extract water and nutrients from the soil. The complex interactions and correlations among soil properties result in multi-colinearity between soil properties and crop yield that makes it difficult to determine which constraint is the major limitation. We used ridge-regression analysis to overcome colinearity to evaluate the contribution of soil factors and water supply to the variation in the yields of 5 winter crops on soils with various levels and combinations of subsoil constraints in the region. Subsoil constraints measured were soil Cl, electrical conductivity of the saturation extract (ECse), and exchangeable sodium percentage (ESP). The ridge regression procedure selected several of the variables used in a descriptive model, which included in-crop rainfall, plant-available soil water at sowing in the 0.90-1.10 m soil layer, and soil Cl in the 0.90-1.10 m soil layer, and accounted for 77-85% of the variation in the grain yields of the 5 winter crops. Inclusion of ESP of the top soil (0.0-0.10 m soil layer) marginally increased the descriptive capability of the models for bread wheat, barley and durum wheat. Subsoil Cl concentration was found to be an effective substitute for subsoil water extraction. The estimates of the critical levels of subsoil Cl for a 10% reduction in the grain yield were 492 mg cl/kg for chickpea, 662 mg Cl/kg for durum wheat, 854 mg Cl/kg for bread wheat, 980 mg Cl/kg for canola, and 1012 mg Cl/kg for barley, thus suggesting that chickpea and durum wheat were more sensitive to subsoil Cl than bread wheat, barley, and canola.

Effects of environmental heat on conception rates in lactating dairy cows: Critical periods of exposure

Environmental heat can reduce conception rates (the proportion of services that result in pregnancy) in lactating dairy cows. The study objectives were to identify periods of exposure relative to the service date in which environmental heat is most closely associated with conception rates, and to assess whether the total time cows are exposed to high environmental heat within each 24-h period is more closely associated with conception rates than is the maximum environmental heat for each 24-h period. A retrospective observational study was conducted in 25 predominantly Holstein-Friesian commercial dairy herds located in Australia. Associations between weather and conception rates were assessed using 16,878 services performed over a 21-mo period. Services were classified as successful based on rectal palpation. Two measures of heat load were defined for each 24-h period: the maximum temperature-humidity index (THI) for the period, and the number of hours in the 24-h period when the THI was >72. Conception rates were reduced when cows were exposed to a high heat load from the day of service to 6 d after service, and in wk -1. Heat loads in wk -3 to -5 were also associated with reduced conception rates. Thus, management interventions to ameliorate the effects of heat load on conception rates should be implemented at least 5 wk before anticipated service and should continue until at least 1 wk after service. High autocorrelations existed between successive daily values in both measures, and associations between day of heat load relative to service day and conception rates differed substantially when ridge regression was used to account for this autocorrelation. This indicates that when assessing the effects of heat load on conception rates, the autocorrelation in heat load between days should be accounted for in analyses. The results suggest that either weekly averages or totals summarizing the daily heat load are adequate to describe heat load when assessing effects on conception rates in lactating dairy cows.

Computação da Seleção Genômica Ampla (GWS).

Métodos para GWS; Teoria dos métodos de regressão; Computação do método Random (Ridge) Regression BLUP (RR-BLUP/GWS); Fenótipos corrigidos; Frequências alélicas, variância dos marcadores e herdabilidade; Marcadores codominantes (SNP) ? Modelo genotípico; Marcadores dominantes (DArT) - Modelo genotípico; Marcadores codominantes (SNP) ? Modelo gamético ou alélico; Número de marcadores com efeitos significativos; Populações de estimação, validação e seleção; População de validação e Jacknife; Correlação e regressão entre valores genéticos preditos e fenótipos na população de validação; Análise de associação na GWAS; Software Selegen Genômica: Random (Ridge) Regression BLUP: RR-BLUP/GWS; Exemplo aplicado ao melhoramento do eucalipto.