Density Deconvolution with Normalizing Flows
This addresses density estimation for noisy data, but it is incremental as it adapts existing normalizing flow methods to a specific problem.
The paper tackled density deconvolution by using normalizing flows to estimate probability densities from noise-corrupted samples, showing that flows outperform Gaussian mixtures on real data.
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but would like to exploit the superior density estimation performance of normalizing flows and allow for arbitrary noise distributions. Since both adjustments lead to an intractable likelihood, we resort to amortized variational inference. We demonstrate some problems involved in this approach, however, experiments on real data demonstrate that flows can already out-perform Gaussian mixtures for density deconvolution.