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Optimal Rates of Convergence of Transelliptical Component Analysis
Transelliptical component analysis Optimal rates of convergence Double asymptotics Minimax lower bound Elliptical copula
2013/6/14
Han and Liu (2012) proposed a method named transelliptical component analysis (TCA) for conducting scale-invariant principal component analysis on high dimensional data with transelliptical distributi...
When uniform weak convergence fails: empirical processes for dependence functions via epi- and hypographs
bootstrap copula epigraph hypograph stable tail dependence function minimum distance estimation weak convergence
2013/6/14
For copulas whose partial derivatives are not continuous everywhere on the interior of the unit cube, the empirical copula process does not converge weakly with respect to the supremum distance. This ...
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
Optimal rates convergence persistence diagrams Topological Data Analysis
2013/6/14
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appear...
On the Convergence and Consistency of the Blurring Mean-Shift Process
Mean-shift Convergence Consistency Clustering,γ-divergence Super robustness
2013/6/13
The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shi...
Convergence rate of Markov chain methods for genomic motif discovery
Gibbs sampler DNA slow mixing spectral gap multimodal
2013/4/27
We analyze the convergence rate of a simplified version of a popular Gibbs sampling method used for statistical discovery of gene regulatory binding motifs in DNA sequences. This sampler satisfies a v...
The Convergence Rate of Majority Vote under Exchangeability
Convergence Rate Majority Vote Exchangeability
2013/4/28
Majority vote plays a fundamental role in many applications of statistics, such as ensemble classifiers, crowdsourcing, and elections. When using majority vote as a prediction rule, it is of basic int...
On the convergence of the IRLS algorithm in Non-Local Patch Regression
Non-local means non-local patch regression,ℓ p minimization non-convex optimization iteratively reweighted least-squares majorize-minimize stationary point relaxation sequence linear convergence
2013/4/28
Recently, it was demonstrated in [CS2012,CS2013] that the robustness of the classical Non-Local Means (NLM) algorithm [BCM2005] can be improved by incorporating $\ell^p (0 < p \leq 2)$ regression into...
Convergence and asymptotic normality of variational Bayesian approximations for exponential family models with missing values
Convergence asymptotic normality variational Bayesian approximations exponential family models missing values
2012/9/19
We study the properties of variational Bayes approximations for exponential family mod-els with missing values. It is shown that the iterative algorithm for obtaining the varia-tional Bayesian estimat...
On the Linear Convergence of the Alternating Direction Method of Multipliers
Linear convergence alternating directions of multipliers error bound relaxation dual ascent.
2012/9/18
We analyze the convergence of the alternating direction method ofmultipliers (ADMM) for solving the problem of minimizing a nonsmooth convex separable function subject to linear constraints. Previous ...
An Upper Bound on the Convergence Time for Quantized Consensus
Distributed quantized consensus gossip conver-gence time
2012/9/17
We analyze a class of distributed quantized consen-sus algorithms for arbitrary networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate o...
Adaptive Equi-Energy Sampler : Convergence and Illustration
interacting Markov chain Monte Carlo adaptive sampler equi-energy sampler ergod-icity law of large numbers motif sampling.
2012/9/18
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The Rate of Convergence of AdaBoost
AdaBoost optimization coordinate descent convergence rate.
2011/7/7
The AdaBoost algorithm was designed to combine many "weak" hypotheses that perform slightly better than random guessing into a "strong" hypothesis that has very low error.
Nonparametric Regression Estimation with Incomplete Data: Minimax Global Convergence Rates and Adaptivity
Adaptivity Besov spaces inhomogeneous data minimax estimation
2011/7/6
We consider the nonparametric regression estimation problem of recovering an unknown response function $f$ on the basis of incomplete data when the design points follow a known density $g$ with a fini...
Convergence rate for predictive recursion estimation of finite mixtures
Density estimation Kullback–Leibler divergence
2011/7/6
Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models.
Almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case
Kesten's stochastic approximation algorithm multidimensional
2011/6/20
It is shown the almost sure convergence and asymptotical normality of a generalization of
Kesten's stochastic approximation algorithm for multidimensional case.
In this generalization, the step incr...