Expectation-Maximisation

a single gaussian is a committed statement: one bump, symmetric, thin tails. real data is usually several stories overlaid — different regimes, different subpopulations — and a gaussian mixture says so explicitly: each point was generated by one of \(k\) gaussians, we just don’t get told which. 𐃏 fitting one is the canonical latent-variable problem, and the algorithm that fits it — expectation-maximisation — is one of the great workhorses of statistics.