Fast convergence of the expectation-maximization algorithm under a logarithmic Sobolev inequality
利用欧几里得-瓦瑟斯坦空间上的梯度流理论，将欧氏空间中的交替最小化技术扩展到EM算法，在广义对数Sobolev不等式下得到有限样本误差界和指数收敛速度，并统一分析多种EM变体。
Summary We present a new framework for analysing the expectation-maximization (em) algorithm. Drawing on recent advances in the theory of gradient flows over Euclidean–Wasserstein spaces, we extend techniques from alternating minimization in Euclidean spaces to the em algorithm, via its representation as coordinatewise minimization of the free energy. In so doing, we obtain finite-sample error bounds and exponential convergence of the em algorithm under a natural generalization of the log-Sobolev inequality. We further show that this framework naturally extends to several variants of the em algorithm, offering a unified approach for studying such algorithms.