5 papers
High-arity Sample Compression
Leonardo N. Coregliano, William Opich
Recently, a series of works have started studying variations of concepts from learning theory for product spaces, which can be collected under the name high-arity learning theory.…
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…
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…
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…
Higher-order Delsarte Dual LPs: Lifting, Constructions and Completeness
Leonardo Nagami Coregliano, Fernando Granha Jeronimo, Chris Jones +2
A central and longstanding open problem in coding theory is the rate-versus-distance trade-off for binary error-correcting codes. In a seminal work, Delsarte introduced a family of…