1 research outputs found
Boosted Density Estimation Remastered
There has recently been a steady increase in the number iterative approaches
to density estimation. However, an accompanying burst of formal convergence
guarantees has not followed; all results pay the price of heavy assumptions
which are often unrealistic or hard to check. The Generative Adversarial
Network (GAN) literature --- seemingly orthogonal to the aforementioned pursuit
--- has had the side effect of a renewed interest in variational divergence
minimisation (notably -GAN). We show that by introducing a weak learning
assumption (in the sense of the classical boosting framework) we are able to
import some recent results from the GAN literature to develop an iterative
boosted density estimation algorithm, including formal convergence results with
rates, that does not suffer the shortcomings other approaches. We show that the
density fit is an exponential family, and as part of our analysis obtain an
improved variational characterisation of -GAN.Comment: Contains lots of essential inf