  We study Sinkhorn EM (sEM), a variant of the expectation maximization (EM)
algorithm for mixtures based on entropic optimal transport. sEM differs from
the classic EM algorithm in the way responsibilities are computed during the
expectation step: rather than assign data points to clusters independently, sEM
uses optimal transport to compute responsibilities by incorporating prior
information about mixing weights. Like EM, sEM has a natural interpretation as
a coordinate ascent procedure, which iteratively constructs and optimizes a
lower bound on the log-likelihood. However, we show theoretically and
empirically that sEM has better behavior than EM: it possesses better global
convergence guarantees and is less prone to getting stuck in bad local optima.
We complement these findings with experiments on simulated data as well as in
an inference task involving C. elegans neurons and show that sEM learns cell
labels significantly better than other approaches.
