最大似然估计等价于带熵正则的最优传输问题。
A note on the relations between mixture models, maximum-likelihood and entropic optimal transport
- 用熵正则化最优传输视角重看混合模型最大似然
- 高斯混合模型中EM算法是特定坐标下降法
- 适合对优化与概率建模交叉感兴趣的读者
本文旨在阐明：对混合模型进行最大似然估计，等价于在参数空间上最小化一个带有熵正则化的最优传输问题。文章以教学为目的，力求简洁清晰地呈现这一已知结果。通过高斯混合模型的实例说明，标准EM算法本质上是作用于最优传输损失上的特定块坐标下降过程。
原文摘要 · Abstract (English)
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek to present this already known result in a concise and hopefully simple manner. We give an illustration with Gaussian mixture models by showing that the standard EM algorithm is a specific block-coordinate descent on an optimal transport loss.
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