Formixtures of axis-aligned Gaussians, we show thateO(kd/ε2)samples suffice, matching a knownlowerbound.

For additional motivation, it is reasonable to consider Massart noise to be a more realistic model of real-life noise (even when benign) when compared to the RCN model, as it allows for some amount of non-uniformity. This made Definition 1 a possibly tractable way to relax the noise assumption, without running intotheaforementioned computational barriers foragnostic learning.

We give the first polynomial-time algorithm for robust regression in the listdecodable setting where an adversary can corrupt a greater than1/2 fraction ofexamples.

Given 2 (0,12] and 2 (0,1), letT bethesamplesetgiventothe learner.

Lastly, [orkdoesnot heavy-tailedsetting. and Notations thespectralnormof( trace.