Multivariate Discriminant Analysis and Maximum Penalized Likelihood Density Estimation

Granville, V.; Rasson, Jean‐Paul

doi:10.1111/j.2517-6161.1995.tb02044.x

Cited by 9 publications

(3 citation statements)

References 27 publications

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“…This problem is more severe when higher-density SNP panels are used, which are expected to convey more accurate information on the animals. Another well-known disadvantage of linear regression is that it is too flexible in cases with an enormous number of (highly) correlated covariates that are used for prediction [ 22 , 23 ]. To overcome this problem, a regularization parameter is added to the model, which in the case of genomic prediction includes the variances attributed to each SNP, e.g.…”

Section: Methodsmentioning

confidence: 99%

Genomic prediction based on data from three layer lines: a comparison between linear methods

et al. 2014

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BackgroundThe prediction accuracy of several linear genomic prediction models, which have previously been used for within-line genomic prediction, was evaluated for multi-line genomic prediction.MethodsCompared to a conventional BLUP (best linear unbiased prediction) model using pedigree data, we evaluated the following genomic prediction models: genome-enabled BLUP (GBLUP), ridge regression BLUP (RRBLUP), principal component analysis followed by ridge regression (RRPCA), BayesC and Bayesian stochastic search variable selection. Prediction accuracy was measured as the correlation between predicted breeding values and observed phenotypes divided by the square root of the heritability. The data used concerned laying hens with phenotypes for number of eggs in the first production period and known genotypes. The hens were from two closely-related brown layer lines (B1 and B2), and a third distantly-related white layer line (W1). Lines had 1004 to 1023 training animals and 238 to 240 validation animals. Training datasets consisted of animals of either single lines, or a combination of two or all three lines, and had 30 508 to 45 974 segregating single nucleotide polymorphisms.ResultsGenomic prediction models yielded 0.13 to 0.16 higher accuracies than pedigree-based BLUP. When excluding the line itself from the training dataset, genomic predictions were generally inaccurate. Use of multiple lines marginally improved prediction accuracy for B2 but did not affect or slightly decreased prediction accuracy for B1 and W1. Differences between models were generally small except for RRPCA which gave considerably higher accuracies for B2. Correlations between genomic predictions from different methods were higher than 0.96 for W1 and higher than 0.88 for B1 and B2. The greater differences between methods for B1 and B2 were probably due to the lower accuracy of predictions for B1 (~0.45) and B2 (~0.40) compared to W1 (~0.76).ConclusionsMulti-line genomic prediction did not affect or slightly improved prediction accuracy for closely-related lines. For distantly-related lines, multi-line genomic prediction yielded similar or slightly lower accuracies than single-line genomic prediction. Bayesian variable selection and GBLUP generally gave similar accuracies. Overall, RRPCA yielded the greatest accuracies for two lines, suggesting that using PCA helps to alleviate the “n ≪ p” problem in genomic prediction.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-014-0057-5) contains supplementary material, which is available to authorized users.

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Section: Methodsmentioning

confidence: 99%

Genomic prediction based on data from three layer lines: a comparison between linear methods

et al. 2014

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“…To estimate the prior joint probabilities , we propose to use an iterative fixed-point EM-like algorithm [38], which is a specific version of the EM algorithm and is suited to evaluating only the proportions of a set of parameters. In our case, we estimate only the joint probabilities of classes, assuming no need to update the estimates of the posterior probabilities and of the a priori probabilities of classes (such estimations are performed as described in Section III) during the successive iterations.…”

Section: B Estimation Of Prior Joint Probabilitiesmentioning

confidence: 99%

“…The temporal correlation between the multisource images acquired at two dates is captured by using the joint class probabilities related to possible land-cover changes. A technique based on a specific formulation of the expectation-maximization (EM) algorithm [38] is applied to estimate such joint probabilities. As it represents the main innovative aspect of this paper, special attention will be given to this technique.…”

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A neural-statistical approach to multitemporal and multisource remote-sensing image classification

Bruzzone

Prieto

Serpico

1999

IEEE Trans. Geosci. Remote Sensing

210

111

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A data fusion approach to the classification of multisource and multitemporal remote-sensing images is proposed. The method is based on the application of the Bayes rule for minimum error to the "compound" classification of pairs of multisource images acquired at two different dates. In particular, the fusion of multisource data is obtained by using multilayer perceptron neural networks for a nonparametric estimation of posterior class probabilities. The temporal correlation between images is taken into account by the prior joint probabilities of classes at the two dates. As a novel contribution of this paper, such joint probabilities are automatically estimated by applying a specific formulation of the expectation-maximization (EM) algorithm to the data to be classified. Experiments carried out on a multisource and multitemporal data set confirmed the effectiveness of the proposed approach.

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Penalized Maximum Likelihood

Simonoff¹

2014

Wiley StatsRef: Statistics Reference Online

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Nonparametric density estimation methods are designed to estimate the density function f that generates a sample of observations, without assuming a parametric form for f . Rather, f is only assumed to be smooth, where smoothness is defined as the condition that at least a specified number of derivatives are square integrable. Penalized maximum likelihood estimators accomplish this by maximizing a penalized form of the log‐likelihood, where the penalty discourages roughness in the final estimate. The estimator has a Bayesian interpretation, with the penalty function corresponding to the logged prior for the density. The resultant estimator often takes the form of a polynomial spline with knots at the order statistics, and asymptotically is approximately a local‐bandwidth kernel estimator. The method can be adapted to large sparse contingency tables, resulting in cell probability estimators that are consistent under asymptotics that approximate such tables.

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Multivariate Discriminant Analysis and Maximum Penalized Likelihood Density Estimation

Cited by 9 publications

References 27 publications

Genomic prediction based on data from three layer lines: a comparison between linear methods

Genomic prediction based on data from three layer lines: a comparison between linear methods

A neural-statistical approach to multitemporal and multisource remote-sensing image classification

Penalized Maximum Likelihood

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