Motivated by learning theory, Aaronson et al. introduced many (weaker) learning models: the

We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated learning, crowdsourcing, and sensor networks, yet existing robust estimators typically assume uniform or worst-case corruption, ignoring structural heterogeneity. For mean estimation for multivariate bounded distributions and univariate gaussian distributions, we give tight minimax rates for all heterogeneous corruption patterns. For multivariate gaussian mean estimation and linear regression, we establish the minimax rate for squared error up to a factor of $\sqrt{d}$, where $d$ is the dimension. Roughly, our findings suggest that samples beyond a certain corruption threshold may be discarded by the optimal estimators -- this threshold is determined by the empirical distribution of the corruption rates given.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Thank you all for your thoughtful comments; we address your concerns below. The MDL principle formalizes Occam's razor and is a We will add the discussion of such relevant studies to section 1. We will add these results and accompanying visualizations to appendix. Model (solver) MAC DAFT MAC (euler) DAFT MAC (rk4) DAFT MAC (dopri5; used in training)Time (ms) 153. We found that during evaluation, rk4 solves all the dynamics generated from CLEVR dataset.