Review for NeurIPS paper: A Stochastic Path Integral Differential EstimatoR Expectation Maximization Algorithm

Summary and Contributions: This paper proposes SPIDER-EM algorithm, which is the combination of recently developed SPIDER estimator with Expectation Maximization (EM) algorithm. The paper also provides a unified framework of stochastic approximation (SA) within EM. The results of SPIDER-EM match the typical results of SPIDER in nonconvex optimization, i.e., O(\sqrt(n)) and improves the previous result on EM with SVRG O(n {2/3}). Since it matches the typical results of SPIDER in nonconvex optimization, the obtained results should be correct. It is interesting that the SPIDER estimator can be applied to EM algorithms. On the other hand, since other variance reduction techniques (such as SVRG) have already been applied in the EM setting in the literature, the idea of SPIDER-EM is a combination of recent popular variance reduction algorithm SPIDER and the previous variance reduction EM algorithms, which is incremental.