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M J Carabano - One of the best experts on this subject based on the ideXlab platform.
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Bayesian comparison of test‐day models under different assumptions of heterogeneity for the Residual Variance: the change point technique versus arbitrary intervals
Journal of Animal Breeding and Genetics, 2004Co-Authors: P. López-romero, Romdhane Rekaya, M J CarabanoAbstract:Summary Test-day milk yields from Spanish Holstein cows were analysed with two random regression models based on Legendre polynomials under two different assumptions of heterogeneity of Residual Variance which aim to describe the variability of temporary measurement errors along days in milk with a reduced number of parameters, such as (i) the change point identification technique with two unknown change points and (ii) using 10 arbitrary intervals of Residual Variance. Both implementations were based on a previous study where the trajectory of the Residual Variance was estimated using 30 intervals. The change point technique has been previously implemented in the analysis of the heterogeneity of the Residual Variance in the Spanish population, yet no comparisons with other methods have been reported so far. This study aims to compare the change point technique identification versus the use of arbitrary intervals as two possible techniques to deal with the characterization of the Residual Variance in random regression test-day models. The Bayes factor and the cross-validation predictive densities were employed for the model assessment. The two model-selecting tools revealed a strong consistency between them. Both specifications for the Residual Variance were close to each other. The 10 intervals modelling showed a slightly better performance probably because the change point function overestimates the Residual Variance values at the very early lactation. Zusammenfassung Testtagsgemelke von Spanischen Holstein-Kuhen wurden mittels zweier zufalliger Regressionsmodelle, basierend auf Legendre Polynomen, unter zwei unterschiedlichen Voraussetzungen von Heterogenitat der Residualvarianz, untersucht, um die Variabilitat der Restvarianz der Milchleistung der Testtage durch so wenig Parameter wie moglich beschreiben zu konnen: 1) dem Verfahren des Wechsel-Identifikationspunktes mit zwei unbekannten Anderungspunkten und 2) der Verwendung von 10 frei gewahlten Intervallen der Residualvarianz. Beide Anwendungen beruhen auf einer vorherigen Untersuchung, in der der Verlauf der Residualvarianz durch die Verwendung von 30 Intervallen geschatzt wurde. Das Wechsel-Identifikationspunkt Verfahren wurde bereits bei der Untersuchung der Residualvarianz in der spanischen Population verwendet, aber das Verfahren wurde noch nicht mit anderen Methoden verglichen. Das Ziel dieser Studie war der Vergleich des Wechsel-Identifikationspunkt Verfahrens mit dem Gebrauch von frei wahlbaren Intervallen als zwei Moglichkeiten zur Charakterisierung der Residualvarianz in zufalligen Testtags-Regressionsmodellen. Der Bayes'sche Faktor und die Vorhersage der Vergleichsprufungsdichten wurden zur Bewertung der Modelle verwandt. Beide Verfahren zeigten eine uberzeugende Konsistenz der Modelle und die Beschreibung der Residualvarianzen stimmte in beiden Fallen uberein. Die Modellierung mit 10 Intervallen zeigte eine etwas bessere Leistung, moglicherweise weil die Wechsel-Identifikationspunkt Funktion die Residualvarianz in der sehr fruhen Laktation uberbewertet.
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bayesian comparison of test day models under different assumptions of heterogeneity for the Residual Variance the change point technique versus arbitrary intervals
Journal of Animal Breeding and Genetics, 2004Co-Authors: P Lopezromero, Romdhane Rekaya, M J CarabanoAbstract:Summary Test-day milk yields from Spanish Holstein cows were analysed with two random regression models based on Legendre polynomials under two different assumptions of heterogeneity of Residual Variance which aim to describe the variability of temporary measurement errors along days in milk with a reduced number of parameters, such as (i) the change point identification technique with two unknown change points and (ii) using 10 arbitrary intervals of Residual Variance. Both implementations were based on a previous study where the trajectory of the Residual Variance was estimated using 30 intervals. The change point technique has been previously implemented in the analysis of the heterogeneity of the Residual Variance in the Spanish population, yet no comparisons with other methods have been reported so far. This study aims to compare the change point technique identification versus the use of arbitrary intervals as two possible techniques to deal with the characterization of the Residual Variance in random regression test-day models. The Bayes factor and the cross-validation predictive densities were employed for the model assessment. The two model-selecting tools revealed a strong consistency between them. Both specifications for the Residual Variance were close to each other. The 10 intervals modelling showed a slightly better performance probably because the change point function overestimates the Residual Variance values at the very early lactation. Zusammenfassung Testtagsgemelke von Spanischen Holstein-Kuhen wurden mittels zweier zufalliger Regressionsmodelle, basierend auf Legendre Polynomen, unter zwei unterschiedlichen Voraussetzungen von Heterogenitat der Residualvarianz, untersucht, um die Variabilitat der Restvarianz der Milchleistung der Testtage durch so wenig Parameter wie moglich beschreiben zu konnen: 1) dem Verfahren des Wechsel-Identifikationspunktes mit zwei unbekannten Anderungspunkten und 2) der Verwendung von 10 frei gewahlten Intervallen der Residualvarianz. Beide Anwendungen beruhen auf einer vorherigen Untersuchung, in der der Verlauf der Residualvarianz durch die Verwendung von 30 Intervallen geschatzt wurde. Das Wechsel-Identifikationspunkt Verfahren wurde bereits bei der Untersuchung der Residualvarianz in der spanischen Population verwendet, aber das Verfahren wurde noch nicht mit anderen Methoden verglichen. Das Ziel dieser Studie war der Vergleich des Wechsel-Identifikationspunkt Verfahrens mit dem Gebrauch von frei wahlbaren Intervallen als zwei Moglichkeiten zur Charakterisierung der Residualvarianz in zufalligen Testtags-Regressionsmodellen. Der Bayes'sche Faktor und die Vorhersage der Vergleichsprufungsdichten wurden zur Bewertung der Modelle verwandt. Beide Verfahren zeigten eine uberzeugende Konsistenz der Modelle und die Beschreibung der Residualvarianzen stimmte in beiden Fallen uberein. Die Modellierung mit 10 Intervallen zeigte eine etwas bessere Leistung, moglicherweise weil die Wechsel-Identifikationspunkt Funktion die Residualvarianz in der sehr fruhen Laktation uberbewertet.
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assessment of homogeneity vs heterogeneity of Residual Variance in random regression test day models in a bayesian analysis
Journal of Dairy Science, 2003Co-Authors: P Lopezromero, Romdhane Rekaya, M J CarabanoAbstract:Test-day first-lactation milk yields from Holstein cows were analyzed with a set of random regression models based on Legendre polynomials of varying order on additive genetic and permanent environmental effects. Homogeneity and heterogeneity of Residual Variance, assuming three and 30 arbitrary measurement error classes of different length were considered. Unknown parameters were estimated within a Bayesian framework. Bayes factors and a checking function for the cross-validation predictive densities of the data were the tools chosen for selecting among competing models. Residual Variances obtained from 30 arbitrary intervals were nearly constant between d 70 and 300 and tended to increase towards the extremes of the lactation, especially at the onset. In early lactation, the temporary measurement errors were found to be larger and highly variable. A high order of the regression submodels employed for modeling the permanent environmental deviations tended to strongly correct the heterogeneity of the Residual Variance. Accordingly, the assumption of homogeneity of Residual Variance was the most plausible specification under both comparison criteria when the number of random regression coefficients was set to five. Otherwise, the heterogeneity assumption, using three or 30 error classes, was better supported, depending on the criterion and on the order of the submodel fitted for the permanent environmental effect.
Amaury Lendasse - One of the best experts on this subject based on the ideXlab platform.
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Residual Variance estimation in machine learning
Neurocomputing, 2020Co-Authors: Elia Liitiainen, Michel Verleysen, Francesco Corona, Amaury LendasseAbstract:The problem of Residual Variance estimation consists of estimating the best possible generalization error obtainable by any model based on a finite sample of data. Even though it is a natural generalization of linear correlation, Residual Variance estimation in its general form has attracted relatively little attention in machine learning. In this paper, we examine four different Residual Variance estimators and analyze their properties both theoretically and experimentally to understand better their applicability in machine learning problems. The theoretical treatment differs from previous work by being based on a general formulation of the problem covering also heteroscedastic noise in contrary to previous work, which concentrates on homoscedastic and additive noise. In the second part of the paper, we demonstrate practical applications in input and model structure selection. The experimental results show that using Residual Variance estimators in these tasks gives good results often with a reduced computational complexity, while the nearest neighbor estimators are simple and easy to implement. (C) 2009 Elsevier B.V. All rights reserved
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Residual Variance estimation using a nearest neighbor statistic
Journal of Multivariate Analysis, 2010Co-Authors: Elia Liitiainen, Francesco Corona, Amaury LendasseAbstract:In this paper we consider the problem of estimating E[(Y-E[Y|X])^2] based on a finite sample of independent, but not necessarily identically distributed, random variables (X"i,Y"i)"i"="1^M. We analyze the theoretical properties of a recently developed estimator. It is shown that the estimator has many theoretically interesting properties, while the practical implementation is simple.
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autoregressive time series prediction by means of fuzzy inference systems using nonparametric Residual Variance estimation
Fuzzy Sets and Systems, 2010Co-Authors: Federico Montesino Pouzols, Amaury Lendasse, Angel Barriga BarrosAbstract:We propose an automatic methodology framework for short- and long-term prediction of time series by means of fuzzy inference systems. In this methodology, fuzzy techniques and statistical techniques for nonparametric Residual Variance estimation are combined in order to build autoregressive predictive models implemented as fuzzy inference systems. Nonparametric Residual Variance estimation plays a key role in driving the identification and learning procedures. Concrete criteria and procedures within the proposed methodology framework are applied to a number of time series prediction problems. The learn from examples method introduced by Wang and Mendel (W&M) is used for identification. The Levenberg-Marquardt (L-M) optimization method is then applied for tuning. The W&M method produces compact and potentially accurate inference systems when applied after a proper variable selection stage. The L-M method yields the best compromise between accuracy and interpretability of results, among a set of alternatives. Delta test based Residual Variance estimations are used in order to select the best subset of inputs to the fuzzy inference systems as well as the number of linguistic labels for the inputs. Experiments on a diverse set of time series prediction benchmarks are compared against least-squares support vector machines (LS-SVM), optimally pruned extreme learning machine (OP-ELM), and k-NN based autoregressors. The advantages of the proposed methodology are shown in terms of linguistic interpretability, generalization capability and computational cost. Furthermore, fuzzy models are shown to be consistently more accurate for prediction in the case of time series coming from real-world applications.
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Residual Variance estimation in machine learning
Neurocomputing, 2009Co-Authors: Elia Liitiainen, Michel Verleysen, Francesco Corona, Amaury LendasseAbstract:The problem of Residual Variance estimation consists of estimating the best possible generalization error obtainable by any model based on a finite sample of data. Even though it is a natural generalization of linear correlation, Residual Variance estimation in its general form has attracted relatively little attention in machine learning. In this paper, we examine four different Residual Variance estimators and analyze their properties both theoretically and experimentally to understand better their applicability in machine learning problems. The theoretical treatment differs from previous work by being based on a general formulation of the problem covering also heteroscedastic noise in contrary to previous work, which concentrates on homoscedastic and additive noise. In the second part of the paper, we demonstrate practical applications in input and model structure selection. The experimental results show that using Residual Variance estimators in these tasks gives good results often with a reduced computational complexity, while the nearest neighbor estimators are simple and easy to implement.
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on nonparametric Residual Variance estimation
Neural Processing Letters, 2008Co-Authors: Elia Liitiainen, Francesco Corona, Amaury LendasseAbstract:In this paper, the problem of Residual Variance estimation is examined. The problem is analyzed in a general setting which covers non-additive heteroscedastic noise under non-iid sampling. To address the estimation problem, we suggest a method based on nearest neighbor graphs and we discuss its convergence properties under the assumption of a Holder continuous regression function. The universality of the estimator makes it an ideal tool in problems with only little prior knowledge available.
William G Hill - One of the best experts on this subject based on the ideXlab platform.
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estimation of genetic variation in Residual Variance in female and male broiler chickens
Animal, 2009Co-Authors: H A Mulder, William G Hill, A Vereijken, R F VeerkampAbstract:In breeding programs, robustness of animals and uniformity of end product can be improved by exploiting genetic variation in Residual Variance. Residual Variance can be defined as environmental Variance after accounting for all identifiable effects. The aims of this study were to estimate genetic Variance in Residual Variance of body weight, and to estimate genetic correlations between body weight itself and its Residual Variance and between female and male Residual Variance for broilers. The data sets comprised 26 972 female and 24 407 male body weight records. Variance components were estimated with ASREML. Estimates of the heritability of Residual Variance were in the range 0.029 (s.e.50.003) to 0.047 (s.e.50.004). The genetic coefficients of variation were high, between 0.35 and 0.57. Heritabilities were higher in females than in males. Accounting for heterogeneous Residual Variance increased the heritabilities for body weight as well. Genetic correlations between body weight and its Residual Variance were 20.41 (s.e.50.032) and 20.45 (s.e.50.040), respectively, in females and males. The genetic correlation between female and male Residual Variance was 0.11 (s.e.50.089), indicating that female and male Residual Variance are different traits. Results indicate good opportunities to simultaneously increase the mean and improve uniformity of body weight of broilers by selection.
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selection for uniformity in livestock by exploiting genetic heterogeneity of Residual Variance
Genetics Selection Evolution, 2008Co-Authors: H A Mulder, P Bijma, William G HillAbstract:In some situations, it is worthwhile to change not only the mean, but also the variability of traits by selection. Genetic variation in Residual Variance may be utilised to improve uniformity in livestock populations by selection. The objective was to investigate the effects of genetic parameters, breeding goal, number of progeny per sire and breeding scheme on selection responses in mean and Variance when applying index selection. Genetic parameters were obtained from the literature. Economic values for the mean and Variance were derived for some standard non-linear profit equations, e.g. for traits with an intermediate optimum. The economic value of Variance was in most situations negative, indicating that selection for reduced Variance increases profit. Predicted responses in Residual Variance after one generation of selection were large, in some cases when the number of progeny per sire was at least 50, by more than 10% of the current Residual Variance. Progeny testing schemes were more efficient than sib-testing schemes in decreasing Residual Variance. With optimum traits, selection pressure shifts gradually from the mean to the Variance when approaching the optimum. Genetic improvement of uniformity is particularly interesting for traits where the current population mean is near an intermediate optimum.
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Selection for uniformity in livestock by exploiting genetic heterogeneity of environmental Variance
Genetics Selection Evolution, 2007Co-Authors: Han A. Mulder, P Bijma, William G HillAbstract:In some situations, it is worthwhile to change not only the mean, but also the variability of traits by selection. Genetic variation in Residual Variance may be utilised to improve uniformity in livestock populations by selection. The objective was to investigate the effects of genetic parameters, breeding goal, number of progeny per sire and breeding scheme on selection responses in mean and Variance when applying index selection. Genetic parameters were obtained from the literature. Economic values for the mean and Variance were derived for some standard non-linear profit equations, e.g. for traits with an intermediate optimum. The economic value of Variance was in most situations negative, indicating that selection for reduced Variance increases profit. Predicted responses in Residual Variance after one generation of selection were large, in some cases when the number of progeny per sire was at least 50, by more than 10% of the current Residual Variance. Progeny testing schemes were more efficient than sib-testing schemes in decreasing Residual Variance. With optimum traits, selection pressure shifts gradually from the mean to the Variance when approaching the optimum. Genetic improvement of uniformity is particularly interesting for traits where the current population mean is near an intermediate optimum.
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genetic heterogeneity of Residual Variance in broiler chickens
Genetics Selection Evolution, 2006Co-Authors: Suzanne Rowe, I M S White, S Avendano, William G HillAbstract:Aims were to estimate the extent of genetic heterogeneity in environmental Variance. Data comprised 99 535 records of 35-day body weights from broiler chickens reared in a controlled environment. Residual Variance within dam families was estimated using ASREML, after fitting fixed effects such as genetic groups and hatches, for each of 377 genetically contemporary sires with a large number of progeny (> 100 males or females each). Residual Variance was computed separately for male and female offspring, and after correction for sampling, strong evidence for heterogeneity was found, the standard deviation between sires in within Variance amounting to 15–18% of its mean. Reanalysis using log-transformed data gave similar results, and elimination of 2–3% of outlier data reduced the heterogeneity but it was still over 10%. The correlation between estimates for males and females was low, however. The correlation between sire effects on progeny mean and Residual Variance for body weight was small and negative (-0.1). Using a data set bigger than any yet presented and on a trait measurable in both sexes, this study has shown evidence for heterogeneity in the Residual Variance, which could not be explained by segregation of major genes unless very few determined the trait.
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A Link Function Approach to Model Heterogeneity of Residual Variances Over Time in Lactation Curve Analyses
Journal of Dairy Science, 2000Co-Authors: Florence Jaffrézic, R Thompson, I M S White, William G HillAbstract:Several studies with test-day models for the lactation curve show heterogeneity of Residual Variance over time. The most common approach is to divide the lactation length into subclasses, assuming homogeneity within these classes and heterogeneity between them. The main drawbacks of this approach are that it can lead to many parameters being estimated and that classes have to be arbitrarily defined, whereas the Residual Variance changes continuously over time. A methodology that overcomes these drawbacks is proposed here. A structural model on the Residual Variance is assumed in which the covariates are parametric functions of time. In this model, only a few parameters need to be estimated, and the Residual Variance is then a continuous function of time. The analysis of a sample data set illustrates this methodology.
Majbritt Felleki - One of the best experts on this subject based on the ideXlab platform.
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Genetic heteroscedasticity of teat count in pigs
Journal of Animal Breeding and Genetics, 2015Co-Authors: Majbritt Felleki, Nils LundeheimAbstract:The genetic improvement in pig litter size has been substantial. The number of teats on the sowmust thus increase as well to meet the needs of the piglets, because each piglet needs access to itsown teat. We applied a genetic heterogeneity model to teat counts in pigs, and estimated a mediumheritability for teat counts (0.35), but found a low heritability for Residual Variance (0.06),indicating that selection for reduced Residual Variance might have a limited effect. A numericallypositive correlation (0.8) was estimated between the breeding values for the mean and the ResidualVariance. However, because of the low heritability of the Residual Variance, the Residual Variance will probably increase very slowly with the mean.
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Variance component and breeding value estimation for genetic heterogeneity of Residual Variance in swedish holstein dairy cattle
Journal of Dairy Science, 2013Co-Authors: H A Mulder, Lars Ronnegard, Majbritt Felleki, W F Fikse, E StrandbergAbstract:Trait uniformity, or micro-environmental sensitivity, may be studied through individual differences in Residual Variance. These differences appear to be heritable, and the need exists, therefore, to fit models to predict breeding values explaining differences in Residual Variance. The aim of this paper is to estimate breeding values for micro-environmental sensitivity (vEBV) in milk yield and somatic cell score, and their associated Variance components, on a large dairy cattle data set having more than 1.6 million records. Estimation of Variance components, ordinary breeding values, and vEBV was performed using standard Variance component estimation software (ASReml), applying the methodology for double hierarchical generalized linear models. Estimation using ASReml took less than 7 d on a Linux server. The genetic standard deviations for Residual Variance were 0.21 and 0.22 for somatic cell score and milk yield, respectively, which indicate moderate genetic Variance for Residual Variance and imply that a standard deviation change in vEBV for one of these traits would alter the Residual Variance by 20%. This study shows that estimation of Variance components, estimated breeding values and vEBV, is feasible for large dairy cattle data sets using standard Variance component estimation software. The possibility to select for uniformity in Holstein dairy cattle based on these estimates is discussed.
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genetic control of Residual Variance for teat number in pigs
Proceedings of the Twentieth Conference of the Association for the Advancement of Animal Breeding and Genetics Translating Science into Action Napier , 2013Co-Authors: Majbritt Felleki, Nils LundeheimAbstract:The genetic improvement in litter size in pigs has been substantial during the last 10-15 years. The number of teats on the sow must increase as well to meet the needs of the piglets, because each ...
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genetic heterogeneity of Residual Variance estimation of Variance components using double hierarchical generalized linear models
Genetics Selection Evolution, 2010Co-Authors: Lars Ronnegard, Majbritt Felleki, Freddy Fikse, Herman A Mulder, E StrandbergAbstract:Background: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the Residual Variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. Results: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared Residuals are assumed to be gamma distributed and the Residual Variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of Variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the Variance components in the Residual Variance part of the model. Conclusions: We have shown that Variance components in the Residual Variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and Residual Variance parts of the model as a parameter of the DHGLM.
Lars Ronnegard - One of the best experts on this subject based on the ideXlab platform.
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Variance component and breeding value estimation for genetic heterogeneity of Residual Variance in swedish holstein dairy cattle
Journal of Dairy Science, 2013Co-Authors: H A Mulder, Lars Ronnegard, Majbritt Felleki, W F Fikse, E StrandbergAbstract:Trait uniformity, or micro-environmental sensitivity, may be studied through individual differences in Residual Variance. These differences appear to be heritable, and the need exists, therefore, to fit models to predict breeding values explaining differences in Residual Variance. The aim of this paper is to estimate breeding values for micro-environmental sensitivity (vEBV) in milk yield and somatic cell score, and their associated Variance components, on a large dairy cattle data set having more than 1.6 million records. Estimation of Variance components, ordinary breeding values, and vEBV was performed using standard Variance component estimation software (ASReml), applying the methodology for double hierarchical generalized linear models. Estimation using ASReml took less than 7 d on a Linux server. The genetic standard deviations for Residual Variance were 0.21 and 0.22 for somatic cell score and milk yield, respectively, which indicate moderate genetic Variance for Residual Variance and imply that a standard deviation change in vEBV for one of these traits would alter the Residual Variance by 20%. This study shows that estimation of Variance components, estimated breeding values and vEBV, is feasible for large dairy cattle data sets using standard Variance component estimation software. The possibility to select for uniformity in Holstein dairy cattle based on these estimates is discussed.
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genetic heterogeneity of Residual Variance estimation of Variance components using double hierarchical generalized linear models
Genetics Selection Evolution, 2010Co-Authors: Lars Ronnegard, Majbritt Felleki, Freddy Fikse, Herman A Mulder, E StrandbergAbstract:Background: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the Residual Variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. Results: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared Residuals are assumed to be gamma distributed and the Residual Variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of Variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the Variance components in the Residual Variance part of the model. Conclusions: We have shown that Variance components in the Residual Variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and Residual Variance parts of the model as a parameter of the DHGLM.
