Another idea that's been intriguing me lately is applied sheaf theory. Robinson, Ghrist, and Curry are the only people I see working on this but I don't know what I'm not seeing. The "big idea" is taking local data and seeing if it patches together to a global coherent whole or not. Sometimes it doesn't (old Russian example: arbitrage in currency exchange networks). Or sometimes it's about using interpolation to fill in missing data, if you know that it's something for which there is a global function (temperatures across ocean surfaces), or providing a probability distribution for the missing parts. Category theory has something to offer here as well.
Anyone know more about any of these things?
What's your background, out of curiosity?
I wonder if those new techniques are different from the usually used like: weighted averages of random forest, cross entropy of density estimation, minimization of variance between local estimations and the like.
Any chance you have some references? All their examples in the UMAP paper and in this talk look very toy-like.
UMAP has already demonstrated its efficacy as a tool in any data scientist’s belt. Ayasdi and Gunnar Carlson’s work is certainly interesting, but unsure how much business value it can actually unlock. Seems like there is also opportunity to draw inspiration from the applied category theory crew (Spivak, Fong etc) to use some CT tools to approach data science from a fresh perspective.
Some of the research coming out is interesting, but as a practitioner I’m more interested in seeing how TDA can add differentiated value in a business context. Interested to hear where people see the field moving next.