5 papers
Remarks on a recent preprint of Chernikov and Towsner
Maryanthe Malliaris
In this brief note, we first give a counterexample to a theorem in Chernikov and Towsner, arXiv:2510.02420(1). In arXiv:2510.02420(2), the theorem has changed but as we explain the…
Sample completion, structured correlation, and Netflix problems
Leonardo N. Coregliano, Maryanthe Malliaris
We develop a new high-dimensional statistical learning model which can take advantage of structured correlation in data even in the presence of randomness. We completely characteri…
On ultrafilter construction
Maryanthe Malliaris
We give a model-theoretic perspective on regular ultrafilter construction in the twentieth and twenty-first century (so far), and explain the "canonical Boolean algebra" recently d…
A packing lemma for VCN-dimension and learning high-dimensional data
Leonardo N. Coregliano, Maryanthe Malliaris
Recently, the authors introduced the theory of high-arity PAC learning, which is well-suited for learning graphs, hypergraphs and relational structures. In the same initial work, t…
Model theory and ultraproducts
M. Malliaris
The article motivates recent work on saturation of ultrapowers from a general mathematical point of view.