Learning Gaussian Mixture Models (GMM) is a fundamental problem in machine learning with broadapplications.

We further transfer those PGNs into text which helps us build mixed game-language datasets from these sources.

In this paper, we introduce acertifiable defense against patch attacks that guarantees for agiven image and patch attack size, no patch adversarial examples exist.

Follo14,36], we alignments, outputand Ta, (y) whichreturnsY including T 1 : Y 7! Yisthecollapsing aandthen alignmenta=( , A, A,)iscollapsedy =( withamonotonic alignment logp(y|x, ) = log X Model BLEUMETEOR Speed Base Transformer 27.54 54.38 1.0 Vanilla-NAT 19.32 45.79 15.5

We propose a regularized pairwise pseudo-likelihood approach for matrix completion and provethat the proposed estimator can asymptotically recoverthe low-rank parameter matrix uptoanidentifiable equivalence class of aconstant shiftandscaling, atanear-optimal asymptotic convergencerateofthe standardwell-posed(non-informativemissing)setting,whileeffectivelymitigating the impact of informative missingness.