We are pleased to share that faculty member, Dr. Dena Asta was promoted to Associate Professor this year.
Dena is interested in bringing geometric methods to bear on non-parametric non-Euclidean methods, network inference and subsequent applications. Data often collectively lives in a space with interesting geometry or describes objects, like networks, with interesting geometry. Her interest is in importing tools from differential geometry and analysis to extend non-parametric inference for both kinds of data. She is interested in applications ranging from imaging to social network analysis.
Her relatively recent theoretical work may be partly characterized by the abstract of a department seminar that Dena delivered in February of 2022:
Graph Laplacians are certain matrices defined in terms of samples of random vectors drawn from a latent, unknown subspace of Euclidean space. The use of graph Laplacians to partially learn the geometry of a latent manifold is one of the dominant paradigms in machine learning. However, graph Laplacians as they are currently used can never completely recover the latent manifold in a non-parametric setting.
The goal of this talk is to show how graph Laplacians can actually be used to obtain a consistent estimator for intrinsic latent manifold distances between sample points, and in particular, a non-parametric but computable method of completely recovering the manifold. There are two main insights behind this method: 1) graph Laplacians can be regarded not just as linear operators but something we might call quadratic operators; and 2) a fundamental result from non-commutative geometry reformulates manifold distance purely in terms of such quadratic operators. This latter reformulation is a special case of the Kontorovich dual reformulation of Wasserstein distances known as Connes' Distance Formula.
Dena joined the department in 2015 after receiving a dual PhD in Engineering and Public Policy and Statistics at Carnegie Mellon University. She is also core faculty in the Translational Data Analytics Institute (TDAI).
Please join us in congratulating Dena on this momentous achievement!