  By utilizing recently developed tools for constructing gradient flows on
Wasserstein spaces, we extend an analysis technique commonly employed to
understand alternating minimization algorithms on Euclidean space to the
Expectation Maximization (EM) algorithm via its representation as
coordinate-wise minimization on the product of a Euclidean space and a space of
probability distributions due to Neal and Hinton (1998). In so doing we obtain
finite sample error bounds and exponential convergence of the EM algorithm
under a natural generalisation of a log-Sobolev inequality. We further
demonstrate that the analysis technique is sufficiently flexible to allow also
the analysis of several variants of the EM algorithm.
