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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...
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...
Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates
Divide and Conquer Kernel Ridge Regression A Distributed Algorithm Minimax Optimal Rates
2013/6/14
We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subse...
Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions
Noisy matrix decomposition via convex relaxation high dimensions
2011/3/24
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are the noisy realizations of the sum of an (appproximately) lo...
Optimal rates of convergence for estimating the null density and proportion of nonnull effects in large-scale multiple testing
Optimal rates convergence null density proportion nonnull effects large-scale multiple testing
2010/3/9
An important estimation problem that is closely related to largescale
multiple testing is that of estimating the null density and the
proportion of nonnull effects. A few estimators have been introd...
Optimal rates and adaptation in the single-index model using aggregation
Nonparametric regression single-index aggregation adaptation minimax random design oracle inequality
2010/4/27
We want to recover the regression function in the single-index
model. Using an aggregation algorithm with local polynomial estimators,
we answer in particular to the second part of Question 2 from S...