We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport followed by a clustering technique leads to principled estimators at a reasonable computational cost. Also, robustness, sparsity and stability properties of the optimal transport plan arguably make the regularised self-transport a statistical tool of choice for the GMM.

翻译：我们研究了正则化自输运问题与高斯混合模型（GMM）中最大似然估计之间的关联。这种关联表明，自输运结合聚类技术能以合理的计算代价得到具有理论依据的估计量。此外，最优输运计划的鲁棒性、稀疏性和稳定性特性，使正则化自输运成为GMM统计工具的理想选择。