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Asymptotic equivalence for nonparametric generalized linear models
Nonparametric regression Statistical experiment De® - ciency distance Global white noise approximation Exponential family Variance stabilizing transformation
2015/8/25
We establish that a non-Gaussian nonparametric regression model is asymptotically equivalent to a regression model with Gaussian noise. The approximation is in the sense of Le Cam's de®- ciency d...
Linear Bandits in High Dimension and Recommendation Systems
Services automation browsing space
2015/8/21
A large number of online services provide automated recommendations to help users to navigate through a large collection of items. New items (products, videos, songs, advertisements) are suggested on ...
Analysis of Belief Propagation for Non-Linear Problems: The Example of CDMA (or: How to Prove Tanaka’s Formula)
Binary signal and white gaussian noise spread sequence scheme of linear time
2015/8/21
We consider the CDMA (code-division multipleaccess) multi-user detection problem for binary signals and additive white gaussian noise. We propose a spreading sequences scheme based on random sparse si...
Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit
compressed sensing decoding error-correcting codes
2015/8/21
Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard
in general. We show here that for systems with ‘typical’/‘random’ Φ, a good approximation to the
sparse...
Sparse Nonnegative Solution of Underdetermined Linear Equations by Linear Programming
Neighborly Polytopes Cyclic Polytopes
2015/8/21
Consider an underdetermined system of linear equations y = Ax with known d×n matrix
A and known y. We seek the sparsest nonnegative solution, i.e. the nonnegative x with fewest
nonzeros satisfying y...
Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations
Centrosymetric Polytopes Centrally-Neighborly Polytopes
2015/8/21
Consider a d × n matrix A, with d < n. The problem of solving for x in y = Ax is
underdetermined, and has many possible solutions (if there are any). In several fields it is
of interest to ...
For Most Large Underdetermined Systems of Linear Equations the Minimal ` 1 -norm Solution is also the Sparsest Solution
Solution of Underdetermined Linear Systems Overcomplete Representations
2015/8/21
We consider linear equations y = Φα where y is a given vector in R
n
, Φ is a given n by m
matrix with n < m ≤ An, and we wish to solve for α ∈ Rm. We suppose that the columns
of Φ are normalized ...
Functional Linear Discriminant Analysis for Irregularly Sampled Curves
Classification Filtering Functional data Linear discriminant analysis Low dimensional representation Reduced rank Regularized discriminant analysis Sparse curves
2015/8/21
We introduce a technique for extending the classical method of Linear Discriminant Analysis to data sets where the predictor variables are curves or functions. This procedure, which we call functional...
We study linear smoothers and their use in building nonparametric regression models. In the first part of this paper we examine certain aspects of linear smoothers for scatterplots; examples of these ...
Generalized linear and generalized additive models in studies of species distributions:setting the scene
Statistical modeling Generalized linear model Generalized additive model Species distribution Predictive modeling
2015/8/21
An important statistical development of the last 30 years has been the advance in regression analysis provided by generalized linear models (GLMs) and generalized additive models (GAMs). Here we intro...
L1-regularization path algorithm for generalized linear models
Generalized linear model Lasso Path algorithm Predictor–corrector method Regularization Variable selection
2015/8/21
We introduce a path following algorithm for L1-regularized generalized linear models. The L 1-regularization procedure is useful especially because it, in effect, selects variables according to the am...
Regularized linear discriminant analysis and its application in microarrays
Regularized linear discriminant analysis microarrays
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...
PROPER FORCING,CARDINAL ARITHMETIC,AND UNCOUNTABLE LINEAR ORDERS
PROPER FORCING CARDINAL ARITHMETIC UNCOUNTABLE LINEAR ORDERS
2015/8/17
In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ1-definable in (H(ω2), ...
A FIVE ELEMENT BASIS FOR THE UNCOUNTABLE LINEAR ORDERS
FIVE ELEMENT BASIS UNCOUNTABLE LINEAR ORDERS
2015/8/17
In this paper I will show that it is relatively consistent with the usual axioms of mathematics (ZFC) together with a strong form of the axiom of infinity (the existence of a supercompact cardinal) th...
ω1 and −ω1 May Be the Only Minimal Uncountable Linear Orders
ω1 and − ω1 May Only Minimal Uncountable Linear Orders
2015/8/17
In 1971 Laver proved the following result, confirming a long-standing conjecture of Fraïssé. Theorem 1.1 [10]. If Li (i < ω) is a sequence of σ-scattered linear orders, then there exist i < j suc...