Painless Embeddings of Distributions: the Function Space View (Part 1)

whereK is the (fixed) number of mixture component, π is a vector ofmixing weights, andp(x|k) are the densities for each component. We consider some examples below. 2 Gaussian mixture models Consider the dataset of height and weight in Figure 1. It is cl ear that there are two subpopulations in this data set, and in this case they are easy to interpret: one represents ma le and the other females. Within each class or cluster, the data is fairly well represented by a 2D Gaussian (as can be seen from the fitted ellipses), but to model the data as a whole, we need to use a mixture of Gaussians (MoG)or aGaussian mixture model (GMM). This is defined as follows: p(x|θ) = K