[HACK] NDEs for discrete (count) data

[justinalsing]

Flexible conditional density estimators for discrete data

Neural conditional density estimators such as MDNs and MAFs are great for continuous data, but often we run into discrete distributions (eg., for count/binned data). Can we build a flexible conditional density estimation framework for LFI in these situations?

Contacts: Justin Alsing Participants:

Goals and deliverable

Develop and implement (into eg. pydelfi) a flexible conditional density estimation framework for discrete densities.

Resources needed

Background knowledge of conditional density estimation + general enthusiasm! Tensorflow/pytorch probably useful for implementation

[EiffL]

That's a great hack,I have some ideas about this. What type of counts are you thinking about? We ran into similar problems when trying to model discrete obserables like galaxy number counts.

My first thought about this would be to use a mixture of quantized distributions, similar to what is done for wavenet, or pixelcnn++

https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/QuantizedDistribution

We can use this as part of a MADE for instance.

@justinalsing Have you tried something along these lines already ?

[justinalsing]

Great glad you're keen! I haven't had time to try anything in anger yet, but we've run into this issue a number of times already in the past few months when analyzing: photon counts in an array of photo-multiplier tubes, histogram of thermal SZ maps, histogram of Lyman-alpha transmission from high-z quasars. In all cases, multi-dimensional, correlated, positive semi-definite, discrete