High-Dimensional Adaptive Minimax Sparse Estimation With Interactions

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Adaptive Minimax Estimation over Sparse q-Hulls

Given a dictionary of Mn initial estimates of the unknown true regression function, we aim to construct linearly aggregated estimators that target the best performance among all the linear combinations under a sparse q-norm (0 ≤ q ≤ 1) constraint on the linear coefficients. Besides identifying the optimal rates of aggregation for these lq-aggregation problems, our multi-directional (or adaptive...

متن کامل

Minimax Bounds for Sparse Pca with Noisy High-dimensional Data.

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the l2 loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the ris...

متن کامل

Adaptive minimax regression estimation over sparse lq-hulls

Given a dictionary of Mn predictors, in a random design regression setting with n observations, we construct estimators that target the best performance among all the linear combinations of the predictors under a sparse `q-norm (0 ≤ q ≤ 1) constraint on the linear coefficients. Besides identifying the optimal rates of convergence, our universal aggregation strategies by model mixing achieve the...

متن کامل

Nearly Optimal Minimax Estimator for High Dimensional Sparse Linear Regression

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints (`q constraint with 0 < q ≤ 1) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic ...

متن کامل

Minimax risks for sparse regressions: Ultra-high dimensional phenomenons

Abstract: Consider the standard Gaussian linear regression model Y = Xθ0 + ǫ, where Y ∈ R is a response vector and X ∈ R is a design matrix. Numerous work have been devoted to building efficient estimators of θ0 when p is much larger than n. In such a situation, a classical approach amounts to assume that θ0 is approximately sparse. This paper studies the minimax risks of estimation and testing...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: IEEE Transactions on Information Theory

سال: 2019

ISSN: 0018-9448,1557-9654

DOI: 10.1109/tit.2019.2913417