The Elements of Statistical Learning

Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome H.

doi:10.1007/978-0-387-21606-5

Cited by 14,574 publications

(10,082 citation statements)

References 116 publications

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“…Additional simulations using small number of markers and pseudo-ancestors indicate that structure usually produces a slightly smaller sampling variance compared to the MLE, but at the expense of being substantially biased. The comparison of the RMSE for the two estimates therefore depends on the bias-variance trade-off (Hastie et al 2001). …”

Section: Discussionmentioning

confidence: 99%

Estimation of individual admixture: Analytical and study design considerations

Tang

Peng

Wang

et al. 2005

Genetic Epidemiology

630

642

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The genome of an admixed individual represents a mixture of alleles from different ancestries.In the United States, the two largest minority groups, African Americans and Hispanics, are both admixed. An understanding of the admixture proportion at an individual level (individual admixture, or IA) is valuable for both population geneticists and epidemiologists who conduct case-control association studies in these groups. Here we present an extension of a previously described frequentist (maximum likelihood or ML) approach to estimate individual admixture that allows for uncertainty in ancestral allele frequencies. We compare this approach both to prior partial likelihood based methods as well as more recently described Bayesian MCMC methods.Our full ML method demonstrates increased robustness when compared to an existing partial ML approach. Simulations also suggest that this frequentist estimator achieves similar efficiency, measured by the mean squared error criterion, as Bayesian methods but requires just a tiny fraction of the computational time to produce point estimates, allowing for extensive analysis (e.g. simulations) not possible by Bayesian methods. Our simulation results demonstrate that inclusion of ancestral populations or their surrogates in the analysis is required by any method of IA estimation to obtain reasonable results.keywords: admixture, EM algorithm, maximum likelihood estimate.

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Section: Discussionmentioning

confidence: 99%

Estimation of individual admixture: Analytical and study design considerations

Tang

Peng

Wang

et al. 2005

Genetic Epidemiology

630

642

View full text Add to dashboard Cite

show abstract

“…Accordingly, the kernel width of 10 is excessively large for these data. In any case, the statistical properties of the Nadaraya-Watson estimator can be found in Hastie et al (2001).…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, a way to quantify the representativeness of a region is to estimate the probability that the relative fit will fall within that region. One effective method is to use Gaussian kernels (e.g., Hastie, Tibshirani & Friedman, 2001), in which an unknown probability distribution is approximated by a mixture of a large number of normal distributions, one for each data set in the landscape (see Appendix B). The result is a distribution of fit representativeness, with each point in the landscape having an associated probability 4 .…”

Section: Defining Representativenessmentioning

confidence: 99%

Assessing the distinguishability of models and the informativeness of data

Navarro

Pitt

Myung

2004

Cognitive Psychology

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“…With dendrograms resulting from the analysis of tumor specimens, bio-medical knowledge is fundamental to select a proper "cut", but also in this case an "objective" and data-driven assessment of the reliability of the clusters may be useful to support bio-medical decisions. Even when clusters and cluster boundaries are univocally defined by the clustering algorithms, such as in K-means [21], or in Self-Organizing-Maps [22], the number of clusters must be chosen a priori and the results depend on the initial conditions. Other methods based on a Bayesian paradigm that combines a priori knowledge with observational data, can automatically select the "optimal" number of clusters, but their accuracy is decremented when small samples are used, due to their asymptotic assumptions [23,24].…”

Section: Introductionmentioning

confidence: 99%

Randomized maps for assessing the reliability of patients clusters in DNA microarray data analyses

Bertoni

Valentini

2006

Artificial Intelligence in Medicine

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Objective: Clustering algorithms may be applied to the analysis of DNA microarray data to identify novel subgroups that may lead to new taxonomies of diseases defined at bio-molecular level. A major problem related to the identification of biologically meaningful clusters is the assessment of their reliability, since clustering algorithms may find clusters even if no structure is present. Methodology:Recently, methods based on random "perturbations" of the data, such as bootstrapping, noise injections techniques and random subspace methods have been applied to the problem of cluster validity estimation. In this framework, we propose stability measures that exploits the high dimensionality of DNA microarray data and the redundancy of information stored in microarray chips. To this end we randomly project the original gene expression data into lower dimensional subspaces, approximately preserving the distance between the examples according to the Johnson-Lindenstrauss (JL) theory. The stability of the clusters discovered in the original high dimensional space is estimated by comparing them with the clusters discovered in randomly projected lower dimensional subspaces. The proposed cluster-stability measures may be applied to validate and to quantitatively assess the reliability of the clusters obtained by a large class of clustering algorithms. Results and conclusion:We tested the effectiveness of our approach with high dimensional synthetic data, whose distribution is a priori known, showing that the stability measures based on randomized maps correctly predict the number of clusters and the reliability of each individual cluster. Then we showed how to apply the proposed measures to the analysis of DNA microarray data, whose underlying distribution is unknown. We evaluated the validity of clusters discovered by hierarchical clustering algorithms in diffuse large B-cell lymphoma (DLBCL) and malignant melanoma patients, showing that the proposed reliability measures can support bio-medical researchers in the identification of stable clusters of patients and in the discovery of new subtypes of diseases characterized at bio-molecular level.

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The Elements of Statistical Learning

Cited by 14,574 publications

References 116 publications

Estimation of individual admixture: Analytical and study design considerations

Estimation of individual admixture: Analytical and study design considerations

Assessing the distinguishability of models and the informativeness of data

Randomized maps for assessing the reliability of patients clusters in DNA microarray data analyses

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