97,476 research outputs found
Design of Experiments for Screening
The aim of this paper is to review methods of designing screening
experiments, ranging from designs originally developed for physical experiments
to those especially tailored to experiments on numerical models. The strengths
and weaknesses of the various designs for screening variables in numerical
models are discussed. First, classes of factorial designs for experiments to
estimate main effects and interactions through a linear statistical model are
described, specifically regular and nonregular fractional factorial designs,
supersaturated designs and systematic fractional replicate designs. Generic
issues of aliasing, bias and cancellation of factorial effects are discussed.
Second, group screening experiments are considered including factorial group
screening and sequential bifurcation. Third, random sampling plans are
discussed including Latin hypercube sampling and sampling plans to estimate
elementary effects. Fourth, a variety of modelling methods commonly employed
with screening designs are briefly described. Finally, a novel study
demonstrates six screening methods on two frequently-used exemplars, and their
performances are compared
A Selective Review of Group Selection in High-Dimensional Models
Grouping structures arise naturally in many statistical modeling problems.
Several methods have been proposed for variable selection that respect grouping
structure in variables. Examples include the group LASSO and several concave
group selection methods. In this article, we give a selective review of group
selection concerning methodological developments, theoretical properties and
computational algorithms. We pay particular attention to group selection
methods involving concave penalties. We address both group selection and
bi-level selection methods. We describe several applications of these methods
in nonparametric additive models, semiparametric regression, seemingly
unrelated regressions, genomic data analysis and genome wide association
studies. We also highlight some issues that require further study.Comment: Published in at http://dx.doi.org/10.1214/12-STS392 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Normal-Mixture-of-Inverse-Gamma Priors for Bayesian Regularization and Model Selection in Structured Additive Regression Models
In regression models with many potential predictors, choosing an appropriate subset of covariates and their interactions at the same time as determining whether linear or more flexible functional forms are required is a challenging and important task. We propose a spike-and-slab prior structure in order to include or exclude single coefficients as well as blocks of coefficients associated
with factor variables, random effects or basis expansions
of smooth functions. Structured additive models with this prior structure are estimated with Markov Chain Monte Carlo using a redundant multiplicative parameter expansion. We discuss shrinkage properties of the novel prior induced by the redundant parameterization, investigate its sensitivity to hyperparameter settings and compare performance of the proposed method in terms of model selection, sparsity recovery, and estimation error for Gaussian, binomial and Poisson responses on real and simulated data sets with that of component-wise boosting and other approaches
Spectral Sequence Motif Discovery
Sequence discovery tools play a central role in several fields of
computational biology. In the framework of Transcription Factor binding
studies, motif finding algorithms of increasingly high performance are required
to process the big datasets produced by new high-throughput sequencing
technologies. Most existing algorithms are computationally demanding and often
cannot support the large size of new experimental data. We present a new motif
discovery algorithm that is built on a recent machine learning technique,
referred to as Method of Moments. Based on spectral decompositions, this method
is robust under model misspecification and is not prone to locally optimal
solutions. We obtain an algorithm that is extremely fast and designed for the
analysis of big sequencing data. In a few minutes, we can process datasets of
hundreds of thousand sequences and extract motif profiles that match those
computed by various state-of-the-art algorithms.Comment: 20 pages, 3 figures, 1 tabl
A General Family of Penalties for Combining Differing Types of Penalties in Generalized Structured Models
Penalized estimation has become an established tool for regularization and model selection in regression models.
A variety of penalties with specific features are available
and effective algorithms for specific penalties have been proposed.
But not much is available to fit models that call for a combination of different penalties.
When modeling rent data, which will be considered as an example, various types of predictors call for a combination of a Ridge, a grouped Lasso and a Lasso-type penalty within one model.
Algorithms that can deal with such problems, are in demand.
We propose to approximate penalties that are (semi-)norms of scalar linear transformations of the coefficient vector in generalized structured models.
The penalty is very general such that the Lasso, the fused Lasso, the Ridge, the smoothly clipped absolute deviation penalty (SCAD), the elastic net and many more penalties are embedded.
The approximation allows to combine all these penalties within one model.
The computation is based on conventional penalized iteratively re-weighted least squares (PIRLS) algorithms and hence, easy to implement.
Moreover, new penalties can be incorporated quickly.
The approach is also extended to penalties with vector based arguments; that is, to penalties with norms of linear transformations of the coefficient vector.
Some illustrative examples and the model for the Munich rent data show promising results
Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors
Penalized regression is an attractive framework for variable selection
problems. Often, variables possess a grouping structure, and the relevant
selection problem is that of selecting groups, not individual variables. The
group lasso has been proposed as a way of extending the ideas of the lasso to
the problem of group selection. Nonconvex penalties such as SCAD and MCP have
been proposed and shown to have several advantages over the lasso; these
penalties may also be extended to the group selection problem, giving rise to
group SCAD and group MCP methods. Here, we describe algorithms for fitting
these models stably and efficiently. In addition, we present simulation results
and real data examples comparing and contrasting the statistical properties of
these methods
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