pyGMMis is a mixtures-of-Gaussians density estimation method that accounts for arbitrary incompleteness in the process that creates the samples as long as the incompleteness is known over the entire feature space and does not depend on the sample density (missing at random). pyGMMis uses the Expectation-Maximization procedure and generates its best guess of the unobserved samples on the fly. It can also incorporate an uniform "background" distribution as well as independent multivariate normal measurement errors for each of the observed samples, and then recovers an estimate of the error-free distribution from which both observed and unobserved samples are drawn. The code automatically segments the data into localized neighborhoods, and is capable of performing density estimation with millions of samples and thousands of model components on machines with sufficient memory.

Spender establishes a restframe for galaxy spectra that has higher resolution and larger wavelength range than the spectra from which it is trained. The model can be trained from spectra at different redshifts or even from different instruments without the need to standardize the observations. Spender also has an explicit, differentiable redshift dependence, which can be coupled with a redshift estimator for a fully data-driven spectrum analysis pipeline. The code describes the restframe spectrum by an autoencoder and transforms the restframe model to the observed redshift; it also matches the spectral resolution and line spread function of the instrument.