We demonstrate the first algorithms for the problem of regression for generalized linear models

(GLMs) in the presence of additive oblivious noise. We assume we have sample access to examples

(x, y) where y is a noisy measurement of g(w∗ · x). In particular, y = g(w∗ · x) + ξ + ϵ where ξ is

the oblivious noise drawn independently of x, satisfying Pr[ξ = 0] ≥ o(1), and ϵ ∼ N(0, σ2). Our

goal is to accurately recover a function g(w · x) with arbitrarily small error when compared to the

true values g(w∗ · x), rather than the noisy measurements y.

We present an algorithm that tackles the problem in its most general distribution-independent

setting, where the solution may not be identifiable. The algorithm is designed to return the solution

if it is identifiable, and otherwise return a small list of candidates, one of which is close to the true

solution. Furthermore, we characterize a necessary and sufficient condition for identifiability, which

holds in broad settings. The problem is identifiable when the quantile at which ξ + ϵ = 0 is known,

or when the family of hypotheses does not contain candidates that are nearly equal to a translated

g(w∗ · x) + A for some real number A, while also having large error when compared to g(w∗ · x).

This is the first result for GLM regression which can handle more than half the samples being

arbitrarily corrupted. Prior work focused largely on the setting of linear regression with oblivious

noise, and giving algorithms under more restrictive assumptions.