Bourbaki student M. Talagrand has some work on approximate independence. If I were trying to do something along the lines of Probabilistic Machine Learning: Ad

Bourbaki student M. Talagrand has some work on approximate independence. If I were trying to do something along the lines of Probabilistic Machine Learning: Advanced Topics I would look (1) carefully at the now classic L. Breiman, et al., Classification and Regression Trees (CART), and (2) at the classic Markov limiting results, e.g., as in E. Çinlar, Introduction to Stochastic Processes, at least to be sure are not missing something relevant and powerful, (3) at some of the work on sufficient statistics, of course, first via the classic Halmos and Savage paper and then at the interesting more recent work in Robert J. Serfling, Approximation Theorems of Mathematical Statistics, and then for the most promising (4) very carefully at Talagrand. (1) and (2) are old but a careful look along with more recent work may yield some directions for progress. What Serfling develops is a bit amazing. Then don't expect the Talagrand material to be trivial.