English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper introduces a simple principle for robust statistical inference via appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the distributional conditions from sub-exponential or sub-Gaussian to more relaxed bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix Θ * from the trace regression model Y = Tr( Θ * ⊤  X ) + ϵ . It encompasses four popular problems: sparse linear model, compressed sensing, matrix completion and multi-task learning. We propose to apply the penalized least-squares approach to the appropriately truncated or shrunk data. Under only bounded 2+ δ moment condition on the response, the proposed robust methodology yields an estimator that possesses the same statistical error rates as previous literature with sub-Gaussian errors. For sparse linear model and multi-task regression, we further allow the design to have only bounded fourth moment and obtain the same statistical rates. As a byproduct, we give a robust covariance estimator with concentration inequality and optimal rate of convergence in terms of the spectral norm, when the samples only bear bounded fourth moment. This result is of its own interest and importance. We reveal that under high dimensions, the sample covariance matrix is not optimal whereas our proposed robust covariance can achieve optimality. Extensive simulations are carried out to support the theories.

A shrinkage principle for heavy-tailed data: High-dimensional robust low-rank matrix recovery