Near-optimal Sample Complexity Bounds for Robust Learning of Gaussian Mixtures via Compression Schemes

We introduce a novel technique for distribution learning based on a notion of sample compression . Any class of distributions that allows such a compression scheme can be learned with few samples. Moreover, if a class of distributions has such a compression scheme, then so do the classes of products and mixtures of those distributions. As an application of this technique, we prove that ˜Θ( kd 2 /ε 2 ) samples are necessary and sufficient for …