MapFromSamples

[dannys4]

An easy wrapper that performs the following steps

1. Standardize the samples
2. Reorder the dimensions to maximize conditional independence *
3. Estimate conditional independence structure in the map *
   4a) Train a map according to a specific total order OR
   4b) Adaptively learn a map using ATM or something
4. compose the standardization, reordering, and learnt map somehow
5. return that composition
   The steps with * are optional. Related to Refine TrainMap #334 Overhaul to MapObjective #317 StandardizedMap #312

[mparno]

@dannys4 How were you thinking of tackling (2)? Something like the sparse Cholesky approach of [Raskutti and Uhler, 2018]?

[dannys4]

My original idea was something super simple, actually, which is ordering by variance; intuitively, things with higher variance "generally" need more variables to explain (qualified by the fact that there is any number of pathological scenarios that this isn't the case). However, it's computationally super cheap.

For a more complicated case, I've thought about sparse cholesky (especially florian's work), but the "second easiest" and "first principled" approach is an unpublished algorithm Max has for doing this (I still need to get it exactly), but it's pretty intuitively based on the Cuthill-Mckee algorithm.