  Mixture models serve as one fundamental tool with versatile applications.
However, their training techniques, like the popular Expectation Maximization
(EM) algorithm, are notoriously sensitive to parameter initialization and often
suffer from bad local optima that could be arbitrarily worse than the optimal.
To address the long-lasting bad-local-optima challenge, we draw inspiration
from the recent ground-breaking foundation models and propose to leverage their
underlying big learning principle to upgrade the EM. Specifically, we present
the Big Learning EM (BigLearn-EM), an EM upgrade that simultaneously performs
joint, marginal, and orthogonally transformed marginal matchings between data
and model distributions. Through simulated experiments, we empirically show
that the BigLearn-EM is capable of delivering the optimal with high
probability; comparisons on benchmark clustering datasets further demonstrate
its effectiveness and advantages over existing techniques. The code is
available at
https://github.com/YulaiCong/Big-Learning-Expectation-Maximization.
