6 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…