437 research outputs found
Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models
A variable screening procedure via correlation learning was proposed Fan and
Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models.
Even when the true model is linear, the marginal regression can be highly
nonlinear. To address this issue, we further extend the correlation learning to
marginal nonparametric learning. Our nonparametric independence screening is
called NIS, a specific member of the sure independence screening. Several
closely related variable screening procedures are proposed. Under the
nonparametric additive models, it is shown that under some mild technical
conditions, the proposed independence screening methods enjoy a sure screening
property. The extent to which the dimensionality can be reduced by independence
screening is also explicitly quantified. As a methodological extension, an
iterative nonparametric independence screening (INIS) is also proposed to
enhance the finite sample performance for fitting sparse additive models. The
simulation results and a real data analysis demonstrate that the proposed
procedure works well with moderate sample size and large dimension and performs
better than competing methods.Comment: 48 page
Nonparametric estimation of genewise variance for microarray data
Estimation of genewise variance arises from two important applications in
microarray data analysis: selecting significantly differentially expressed
genes and validation tests for normalization of microarray data. We approach
the problem by introducing a two-way nonparametric model, which is an extension
of the famous Neyman--Scott model and is applicable beyond microarray data. The
problem itself poses interesting challenges because the number of nuisance
parameters is proportional to the sample size and it is not obvious how the
variance function can be estimated when measurements are correlated. In such a
high-dimensional nonparametric problem, we proposed two novel nonparametric
estimators for genewise variance function and semiparametric estimators for
measurement correlation, via solving a system of nonlinear equations. Their
asymptotic normality is established. The finite sample property is demonstrated
by simulation studies. The estimators also improve the power of the tests for
detecting statistically differentially expressed genes. The methodology is
illustrated by the data from microarray quality control (MAQC) project.Comment: Published in at http://dx.doi.org/10.1214/10-AOS802 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification
We propose a high dimensional classification method that involves
nonparametric feature augmentation. Knowing that marginal density ratios are
the most powerful univariate classifiers, we use the ratio estimates to
transform the original feature measurements. Subsequently, penalized logistic
regression is invoked, taking as input the newly transformed or augmented
features. This procedure trains models equipped with local complexity and
global simplicity, thereby avoiding the curse of dimensionality while creating
a flexible nonlinear decision boundary. The resulting method is called Feature
Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by
generalizing the Naive Bayes model, writing the log ratio of joint densities as
a linear combination of those of marginal densities. It is related to
generalized additive models, but has better interpretability and computability.
Risk bounds are developed for FANS. In numerical analysis, FANS is compared
with competing methods, so as to provide a guideline on its best application
domain. Real data analysis demonstrates that FANS performs very competitively
on benchmark email spam and gene expression data sets. Moreover, FANS is
implemented by an extremely fast algorithm through parallel computing.Comment: 30 pages, 2 figure
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