Gradient Boosted Normalizing Flows
This provides an incremental improvement for researchers and practitioners in machine learning by offering a wider, more flexible approach to normalizing flows without requiring deeper or more complex transformations.
The paper tackles the problem of improving normalizing flows for density estimation and generative modeling by proposing Gradient Boosted Normalizing Flows (GBNF), which uses gradient boosting to add components sequentially, resulting in a mixture model that outperforms non-boosted analogs and sometimes achieves better results with smaller, simpler flows.
By chaining a sequence of differentiable invertible transformations, normalizing flows (NF) provide an expressive method of posterior approximation, exact density evaluation, and sampling. The trend in normalizing flow literature has been to devise deeper, more complex transformations to achieve greater flexibility. We propose an alternative: Gradient Boosted Normalizing Flows (GBNF) model a density by successively adding new NF components with gradient boosting. Under the boosting framework, each new NF component optimizes a sample weighted likelihood objective, resulting in new components that are fit to the residuals of the previously trained components. The GBNF formulation results in a mixture model structure, whose flexibility increases as more components are added. Moreover, GBNFs offer a wider, as opposed to strictly deeper, approach that improves existing NFs at the cost of additional training---not more complex transformations. We demonstrate the effectiveness of this technique for density estimation and, by coupling GBNF with a variational autoencoder, generative modeling of images. Our results show that GBNFs outperform their non-boosted analog, and, in some cases, produce better results with smaller, simpler flows.