7 papers
Some model-theoretic consequences of high-arity uniform convergence, part I
Leonardo N. Coregliano, Maryanthe Malliaris
We show that certain families of sets in (or ) which are neither definable nor have bounded VC-dimension are nonetheless uniformly approximately defina…
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…
High-arity PAC learning via exchangeability
Leonardo N. Coregliano, Maryanthe Malliaris
We develop a theory of high-arity PAC learning, which is statistical learning in the presence of "structured correlation". In this theory, hypotheses are either graphs, hypergraphs…
Model theory and ultraproducts
M. Malliaris
The article motivates recent work on saturation of ultrapowers from a general mathematical point of view.