If I understand correctly after skimming, one of the fundamental ideas behind this appears to be similar to the well-known Fast Multiple Method [1]. It’s also a tree-based approach where far away points are aggregated into larger chunks?
It’s exactly the same as the Barnes-Hut method from a quick glance, there’s nothing particularly new in this paper as far as I can see. There are various papers which have merit on releasing specific codes that support this, but people have been using it in spin systems and even in micromagnetics for years. I did my PhD in this area years ago and implemented it in Monte Carlo and dynamical simulations at the time… and I cited papers going back to the 80s and 90s when I wrote up my thesis!
While the spatial decomposition matches what is done in Barnes-Hut, the details of the underlying algorithm are somewhat different (they outline this in the introduction).
In particular, their scheme using exact bounds on energy differences (evaluated using a hierarchical tree as in BH) but in such a way that no approximation is being made. The tree is evaluated to whatever depth is needed to decide whether to accept/reject the MC move (which in worse case could be a brute-force sum over the whole lattice/system) -- this is different I think than BH or other multipole inspired methods (which have a kind of "truncation" or "tolerance" parameter).
[This also works well with systems where update are local and not global, which I think is a difference from some other spatial partitioning schemes -- but I'm less conversant with that aspect].
I imagine a similar scheme can be used for general inference if you have a way to cluster components of your model in a similar fashion even if the parameters are not spatial. Perhaps your model has some kind of natural tree structure.
This is a funny comment, not because it's so wrong, but because of the irony. Statisticians used to complain that neural net research was just badly reproducing statistics. As late as the early 2000s, I had a stats professor actually get angry when I expressed interest in ANN theory.
The relation between ANNs and statistics is a topic over which much ink was spilled in the 1990s. This is the most concise discussion I can think of:
Sarle, Warren S. (1994). Neural Networks and Statistical Models. Proceedings of the Nineteenth Annual SAS Users Group International Conference, April, 1994.
If you want an in-depth discussion, these books relate ANNs and statistical methods:
Schürmann, Jürgen. (1996). Pattern Classification: A Unified View of Statistical and Neural Approaches.
Raudys, Sarunas. (2001). Statistical and Neural Classifiers: An Integrated Approach to Design.
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If I understand correctly after skimming, one of the fundamental ideas behind this appears to be similar to the well-known Fast Multiple Method [1]. It’s also a tree-based approach where far away points are aggregated into larger chunks?
[1] https://en.m.wikipedia.org/wiki/Fast_multipole_method
In particular, their scheme using exact bounds on energy differences (evaluated using a hierarchical tree as in BH) but in such a way that no approximation is being made. The tree is evaluated to whatever depth is needed to decide whether to accept/reject the MC move (which in worse case could be a brute-force sum over the whole lattice/system) -- this is different I think than BH or other multipole inspired methods (which have a kind of "truncation" or "tolerance" parameter).
[This also works well with systems where update are local and not global, which I think is a difference from some other spatial partitioning schemes -- but I'm less conversant with that aspect].
Sarle, Warren S. (1994). Neural Networks and Statistical Models. Proceedings of the Nineteenth Annual SAS Users Group International Conference, April, 1994.
If you want an in-depth discussion, these books relate ANNs and statistical methods:
Schürmann, Jürgen. (1996). Pattern Classification: A Unified View of Statistical and Neural Approaches.
Raudys, Sarunas. (2001). Statistical and Neural Classifiers: An Integrated Approach to Design.