List-decodeable Linear Regression

We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than 1/2 fraction of examples. For any alpha < 1, our algorithm takes as input a sample {(x(i), y(i))}(i <= n) of n linear equations where alpha n of the equations satisfy y(i) = < x(i), l*> + zeta for s...More