Learning in Riemannian Orbifolds
This work addresses a foundational problem in machine learning for researchers and practitioners dealing with structured data, though it appears incremental as it extends existing theoretical frameworks.
The paper tackles the lack of statistical justification for machine learning algorithms on finite combinatorial structures like point patterns, trees, and graphs by deriving consistency results for learning in Riemannian orbifolds, generalizing learning from vector spaces and manifolds.
Learning in Riemannian orbifolds is motivated by existing machine learning algorithms that directly operate on finite combinatorial structures such as point patterns, trees, and graphs. These methods, however, lack statistical justification. This contribution derives consistency results for learning problems in structured domains and thereby generalizes learning in vector spaces and manifolds.