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Regularized linear discriminant analysis and its application in microarrays
Regularized linear discriminant analysis microarrays
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2015/8/21
In this paper, we introduce a modified version of linear discriminant analysis, called the “shrunken centroids regularized discriminant analysis” (SCRDA). This method generalizes the idea of the “near...
Sparse Discriminant Analysis
Sparse Discriminant Analysis
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2015/8/21
We consider the problem of performing interpretable classification in the high-dimensional setting, in which the number of features is very large and the number of observations is limited. This settin...
Genomewide Association Analysis by Lasso Penalized Logistic Regression
Genomewide Association Analysis Lasso Penalized Logistic Regression
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2015/8/21
In ordinary regression, imposition of a lasso penalty makes continuous model selection straightforward. Lasso penalized regression is particularly advantageous when the number of predictors far exceed...
Bi-cross-validation for factor analysis
analysis i-cross-validation
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2015/8/21
Factor analysis is over a century old, but it is still problematic to choose
the number of factors for a given data set. The scree test is popular but subjective. The best performing objective method...
Sparse Principal Components Analysis
Components Analysis Contemporary data
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2015/8/20
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of
data in the form of n observations (or cases) of a vector with p variables. Contemporary data sets
of...
ON THE DISTRIBUTION OF THE LARGEST EIGENVALUE IN PRINCIPAL COMPONENTS ANALYSIS
LARGEST EIGENVALUE PRINCIPAL COMPONENTS
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2015/8/20
Let x1 denote the square of the largest singular value of an n × p
matrix X, all of whose entries are independent standard Gaussian varates. Equivalently, x1 is the largest principal component vari...
Exact Risk Analysis of Wavelet Regression
Orthogonal series denoising Squared error
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2015/8/20
Wavelets have motivated development of a host of new ideas in nonparametric
regression smoothing. Here we apply the tool of exact risk analysis, to understand the
small sample behavior of wavelet es...
MULTISCALE MAXIMUM LIKELIHOOD ANALYSIS OF A SEMIPARAMETRIC MODEL, WITH APPLICATIONS
LIKELIHOOD ANALYSIS SEMIPARAMETRIC MODEL WITH APPLICATIONS
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2015/8/20
A special semiparametric model for a univariate density is introduced
that allows analyzing a number of problems via appropriate transformations. Two problems treated in some detail are testing for t...
Constrained ordination analysis with flexible response functions
Canonical correspondence analysis Density estimation
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2015/8/20
Canonical correspondence analysis (CCA) is perhaps the most popular multivariate technique used by environmental ecologists
for constrained ordination; it is an approximation to the maximum likelihoo...
STRUCTURAL ANALYSIS OF ARONSZAJN TREES
STRUCTURAL ANALYSIS ARONSZAJN TREES
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2015/8/17
In this paper I will survey some recent developments in the combinatorics of Aronszajn trees. I will cover work on coherent and Lipschitz trees, the basis problem for uncountable linear orderings, sub...
Closed-loop convex analysis of performance limits for linear control systems
Linear control system computer aided control system and design a linear controller convex optimization digital signal processor
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2015/8/12
In closed-loop convex analysis and design, the linear controller design problem is reformulated as a convex optimization problem, which may be more easily solved than the problems resulting from conve...
Control systems analysis and synthesis via linear matrix inequalities
Control theory and linear matrix inequality the numerical algebraic riccati inequality lyapunov
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2015/8/12
A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are “analytical sol...
CRCD program: convex optimization for engineering analysis and design
Convex optimization engineering analysis the numerical values
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2015/8/11
The focus of this NSF-supported combined research and curriculum development (CRCD) project is convex optimization applied to engineering analysis and design. The basic idea is that many analysis and ...
Analysis of linear systems with saturation using convex optimization
Linear matrix inequality linear system the lyapunov function space area half plan
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2015/8/11
We show how linear matrix inequalities (LMI) can be used to perform local stability and performance analysis of linear systems with saturating elements. This leads to conservative information on stabi...
Symmetry analysis of reversible Markov chains
Reversible markov chain orbital diagram characteristic vector；the mixture of markov chain an arbitrary number
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2015/8/11
We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools invo...