Philip Thompson

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20172022

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math.ST2022

A spectral least-squares-type method for heavy-tailed corrupted regression with unknown covariance \& heterogeneous noise

Roberto I. Oliveira, Zoraida F. Rico, Philip Thompson

We revisit heavy-tailed corrupted least-squares linear regression assuming to have a corrupted $n$ -sized label-feature sample of at most $ε n$ arbitrary outliers. We wish to estimat…

math.ST2019

Outlier-robust estimation of a sparse linear model using $ℓ_{1}$ -penalized Huber's $M$ -estimator

Arnak S. Dalalyan, Philip Thompson

We study the problem of estimating a $p$ -dimensional $s$ -sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by a…

math.ST2018

Restricted eigenvalue property for corrupted Gaussian designs

Philip Thompson, Arnak S. Dalalyan

Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eige…

A spectral least-squares-type method for heavy-tailed corrupted regression with unknown covariance \& heterogeneous noise

Outlier-robust estimation of a sparse linear model using ℓ1​-penalized Huber's M-estimator

Restricted eigenvalue property for corrupted Gaussian designs

Outlier-robust estimation of a sparse linear model using $ℓ_{1}$ -penalized Huber's $M$ -estimator