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Achieving robust regression of general ReLUs with a dramatically reduced query complexity could redefine the efficiency of active learning strategies.
Even with a realizable missing data model, estimating the mean of a high-dimensional Gaussian provably requires either exponentially more samples or exponential runtime, revealing a fundamental information-computation tradeoff.
Mean estimation is possible even when an adversary shifts a fraction of your data, provided the base distribution's characteristic function meets certain spectral conditions.
Forget faster algorithms: learning halfspaces agnostically under smoothed distributions hits a fundamental complexity wall at $d^{Ω(1/σ^{2}+\log(1/ε))}$, suggesting current upper bounds are nearly tight.
