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R. Oliveira

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Preprint Sep 2026

Robust dimension-free estimation of simple random tensors: optimal guarantees under heavy tails and adversarial contamination

We study robust estimation of simple random tensors of arbitrary order $q\in\mathbb{N}$ under finite-moment assumptions and adversarial contamination. We propose the first robust estimator achieving near-optimal dimension-free statistical rates in this setting. The estimator attains the near-optimal corruption rate whenever $p\ge2q$ moments are finite and continues to provide nontrivial guarantees throughout the weak-moment regime $q\le p\le2q$. Being based on directional trimmed means and minimax aggregation, our estimator is adaptive to $p$ and upper bounds on hypercontractive constants without resorting to interval-intersection procedures. Our analysis extends the trimmed-mean framework underlying recent advances in robust mean and covariance estimation to arbitrary tensor order. In particular, we establish concentration inequalities for higher-order counting and truncated empirical multi-vector product processes. We believe these inequalities could be of independent interest beyond the present application, including algorithmic robust estimation.

R. Oliveira, Zoraida F. Rico, Philip Thompson · 0 citations

Preprint Aug 2026

Debiasing the Lasso under Weaker Tail Assumptions

We consider the problem of high-dimensional inference with the lasso estimator. Different methods including'double selection'techniques and multiple versions of the'debiased lasso'have been proposed for this task with noticeable success. However, most guarantees assume strong hypotheses on the underlying data process and the errors in the linear regression model, such as subgaussian designs and independence between errors and the data itself. We show that'standardizing'one's dataset -- a natural procedure in practical penalized regression -- leads to the same results under much weaker hypotheses, paying only a small price for not assuming light tails. The key technical point allowed by this step is exploiting the concentration properties of self-normalized processes. Importantly, we prove our results for two different methods closely related to the'debiased lasso'. The second method performs valid inference even for a misspecified linear model, under mild sparsity conditions similar to the'double selection'literature.

Leonardo Voltarelli, R. Oliveira · 0 citations