Goal: we need to find a model that is “expressive enough”: we need to have enough parameters to help match the shape of the data we collect. to help match the shape of the data we collect. constituents requirements additional information selecting parameters see model fitting increasing expressiveness mixure model We could mix distributions into a . See Gaussian mixture model. transforming distributions Suppose you start with:

we can sample k points k \sim Z, and then transform them across a function x_{j}=f(k_{j}). We now want to know the destruction of x_{j}. Turns out, if f is invertible and differential, we have:

where g(x) = f^{-1}\left(x\right). This new p_{x} is now the PDF of our transformed distribution. …but how do you pick f Normalizing Flow! generative model see generative model