Josh Tenenbaum sent me a link to a paper, The discovery of structural form, by C. Kemp and himself. Also commentary by Keith Holyoak and some supporting information. Code and datasets are here.
For my own thoughts on this work, see here. Josh’s talk at Columbia made me realize that all these years I’d been thinking of life as part of a “great chain of being” without realizing it.
Interesting papers. I love to see all the new models out there for analyzing structural properties of relational data, although I wish there was a good reference to compare them (especially in terms of their use).
Speaking of which, I was a little surprised that the linked papers didn't compare their method (at least in terms of purpose and capabilities) to any of the random graph models (p*, ERGM, whatever they are calling it nowadays) that are out there, especially since they both seem to be based on some idea of lower-level graph "configurations" to explain the observed network. Reading the paper, it didn't sound as flexible, but the models definitely sounded much more directly interpretable.
One thing that seemed a little unclear to me after reading the articles is how the model results are interpreted (perhaps I missed something, or misunderstood the models): is there meant to be only one best structural model estimates (tree structures, rings, etc.), or are the results meant to be interpreted simultaneously in terms of the relative magnitude of effects (e.g., if a tree structure was most likely, but a ring structure was slightly less likely, does that mean the model is "rejecting" a ring-based structure entirely, or does it mean that there is a dominant tree-like structure with some regions or aspects that are ring-like?