  We consider the problem of estimating means of two Gaussians in a 2-Gaussian
mixture, which is not balanced and is corrupted by noise of an arbitrary
distribution. We present a robust algorithm to estimate the parameters,
together with upper bounds on the numbers of samples required for the estimate
to be correct, where the bounds are parametrised by the dimension, ratio of the
mixing coefficients, a measure of the separation of the two Gaussians, related
to Mahalanobis distance, and a condition number of the covariance matrix. In
theory, this is the first sample-complexity result for imbalanced mixtures
corrupted by adversarial noise. In practice, our algorithm outperforms the
vanilla Expectation-Maximisation (EM) algorithm in terms of estimation error.
