start work on gmm

[ezhang94]

Adding in GaussianMixture distribution with E-M fitting functionality, tests, and notebook demonstrations.

Maximum likelihood estimation of MVN distribution

• Unweighted ML estimation of MVN full-covariance distribution
• Weighted ML estimation of MVN full-covariance distribution
• Unweighted and weighted ML estimation of MVN diagonal cov distribution
• Unweighted and weighted ML estimation of MVN spherical cov distribution

Expectation maximization inference

• Create barebones GaussianMixture distribution and sample
• Test EM inference with full-covariance MVN distribution
• + diagonal-covariance MVN components distribution
• + spherical-covariance MVN components distribution

Sidequests

• Compare home-brewed k-means implementation (see gimbal-refactor repo) with sklearn.cluster.KMeans (additional benefits: does not require reshaping dataset. perhaps can generalize to different distances, i.e. cosine distance to permit generalization to spherical k-means)
• Propose simpler one_hot implementation

[schlagercollin]

Nice!