Aprendizagem de má quina robusta e privativa: o e o de estimadores em alta dimensão

This report presents a two-stage PIBIC research trajectory from robust mean estimation to robust covariance estimation under adversarial contamination. The first stage was deliberately designed to build the theoretical, computational and experimental foundation required for the second stage. The student implemented and compared a broad collection of robust estimators, data generators, contamination mechanisms and evaluation routines. PGDMean and Median-of-Means appear here as two widely known reference methods within that broader set; they are illustrative examples, not a complete account of the work carried out during this preparatory phase. The second stage became the central focus of the project: implementing and testing a new robust covariance algorithm conceived by the advisor, whose technical formulation is confidential. To support its validation, the student built robcov, a reproducible test suite that expands deterministic trials, balances them by estimated cost, executes them in isolated worker processes, checkpoints results and can distribute independent batches across cloud instances. One completed comparison comprises 60 trials at dimensions 20 and 50 under 10% eigenvector-inflation contamination; the proposed method obtained the lowest mean Mahalanobis operator error at both dimensions. A second comparison adds 120 trials under AR(1) and equicorrelation structures and shows that the method remained among the three best alternatives in all four scenarios, at a higher computational cost. The project also studied Propose-Test-Release, reductions from robustness to privacy, robust-and-private mean estimation and privacy–accuracy lower bounds. These privacy results are theoretical foundations: the documented code does not yet implement a differentially private mechanism or privacy-budget experiment.