Download Statistical Analysis for High-Dimensional Data: The Abel PDF
This ebook positive aspects study contributions from The Abel Symposium on Statistical research for top Dimensional information, held in Nyvagar, Lofoten, Norway, in may possibly 2014.
The concentration of the symposium used to be on statistical and laptop studying methodologies in particular constructed for inference in colossal facts events, with specific connection with genomic functions. The individuals, who're one of the so much trendy researchers at the idea of statistics for prime dimensional inference, current new theories and techniques, in addition to hard purposes and computational strategies. particular subject matters comprise, between others, variable choice and screening, penalised regression, sparsity, thresholding, low dimensional constructions, computational demanding situations, non-convex events, studying graphical types, sparse covariance and precision matrices, semi- and non-parametric formulations, a number of checking out, category, issue types, clustering, and preselection.
Highlighting state-of-the-art study and casting gentle on destiny examine instructions, the contributions will profit graduate scholars and researchers in computational biology, facts and the desktop studying community."
Read Online or Download Statistical Analysis for High-Dimensional Data: The Abel Symposium 2014 (Abel Symposia, Volume 11) PDF
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Additional info for Statistical Analysis for High-Dimensional Data: The Abel Symposium 2014 (Abel Symposia, Volume 11)
Example text
Xij /j2J denotes the subset of covariates for model J. 0; 1/ coordinates. As in previous section, we denote the resulting prior density by fJ . J/ D B bD1 B where we use B D 50;000 in all of our simulations. 1=2 ; where ˇOJ is the maximum likelihood estimator in model J. J/ j : We consider n 2 f50; 60; 70; 80; 90; 100g in our experiment. Since we wish to compute the Laplace approximation error of every q-sparse model, and the number of possible models is on the order of pq , we consider p D n=2 and q 2 f1; 2; 3g.
1a that preselection of variables based on the univariate ranking may lead to a completely different and smaller optimal value of and hence to a model of higher dimensionality. In this particular example, lasso based on the top 200 preselected variables selects 98 variables, while the number of variables selected in the optimal lasso solution based on all variables is only 33. However, when we fit several lasso models, for a suitable grid of , using subsets with an increasing number p of covariates ordered on the basis of univariate analyses, an interesting feature appears.
N/ jJj @1 ˙ cLaplace A: n Proof (i) Bounded MLEs. It follows from Sect. , J Ã J0 and jJj Ä 2q) are bounded by a constant. The result makes reference to an event for which all the claims we make subsequently are true. The bound on the norm of an MLE of a true model was obtained by comparing the maximal likelihood to the likelihood at the true parameter ˇ0 . As we show now, for false sparse models, we may argue similarly but comparing to the likelihood at 0. Recall that a0 is the bound on the norm of ˇ0 assumed in (A1) and that the functions clower and cupper in (A2) are decreasing and increasing in the norm of ˇ0 , respectively.