Robust dimension-free estimation of simple random tensors: optimal guarantees under heavy tails and adversarial contamination
Abstract
We study robust estimation of simple random tensors of arbitrary order q∈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≥2q moments are finite and continues to provide nontrivial guarantees throughout the weak-moment regime q≤ p≤2q. 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.
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BibTeX
@misc{oliveira2026robust,
title = {{Robust dimension-free estimation of simple random tensors: optimal guarantees under heavy tails and adversarial contamination}},
author = {Roberto I. Oliveira and Zoraida F. Rico and Philip Thompson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00675},
eprint = {2609.00675},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00675},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Robust dimension-free estimation of simple random tensors: optimal guarantees under heavy tails and adversarial contamination
AU - Roberto I. Oliveira
AU - Zoraida F. Rico
AU - Philip Thompson
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.00675
UR - https://arxiv.org/abs/2609.00675
AB - We study robust estimation of simple random tensors of arbitrary order q∈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≥2q moments are finite and continues to provide nontrivial guarantees throughout the weak-moment regime q≤ p≤2q. 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.
ER -