About

Dena Asta is an Associate Professor of Statistics at The Ohio State University, having joined the faculty in 2015. Her research focuses on bringing geometric methods to non-parametric and non-Euclidean statistical inference, particularly in the context of network analysis and applications involving data with interesting geometric properties. She is interested in applying tools from differential geometry and analysis to extend non-parametric inference for data that either resides in spaces with complex geometry or describes objects like networks with inherent geometric structure. Her work spans a range of applications, including imaging and social network analysis. Dena Asta holds a PhD from Carnegie Mellon University, earned in 2015. Her research has been funded by the NSF. She is also a member of the Translational Data Analytics group. Her professional contact information includes her office at Cockins Hall, her email (dasta@stat.osu.edu), and her phone number (614-292-8112). She is actively involved in the academic community at Ohio State, contributing to the Department of Statistics and its related initiatives.

Research topics

• Statistics
• Computer Science
• Mathematics
• Mathematical analysis
• Artificial Intelligence
• Pure mathematics
• Geometry
• Applied mathematics
• Medicine
• Clinical psychology
• Internal medicine
• Psychiatry
• Psychology

Selected publications

• Lower bounds for density estimation on symmetric spaces

  Statistics & Probability Letters · 2025-04-01 · 1 citations

  articleOpen access1st authorCorresponding

  We prove that kernel density estimation on symmetric spaces of non-compact type, whose L 2 -risk was bounded above in previous work (Asta, 2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density estimation on all symmetric spaces is completed. The idea in adapting the proof for Euclidean space is to suitably abstract vector space operations on Euclidean space to both actions of symmetric groups and reparametrizations of Helgason–Fourier transforms and to use the fact that the exponential map for symmetric spaces of non-compact type defines a diffeomorphism.

  PublisherDOI

• Consistency of maximum likelihood for continuous-space network models I

  Electronic Journal of Statistics · 2024-01-01 · 1 citations

  articleOpen accessSenior author

  A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent space. We study the embedding problem for these models, of recovering the latent positions from the observed graph. Assuming certain natural symmetry and smoothness properties, we establish the uniform convergence of the log-likelihood of latent positions as the number of nodes grows. A consequence is that the maximum likelihood embedding converges on the true positions in a certain information-theoretic sense. Extensions of these results, to recovering distributions in the latent space, and so distributions over arbitrarily large graphs, will be treated in the sequel.

  PublisherOA PDFDOI

• Lower Bounds for Kernel Density Estimation on Symmetric Spaces

  arXiv (Cornell University) · 2024-03-15

  preprintOpen access1st authorCorresponding

  We prove that kernel density estimation on symmetric spaces of non-compact type, whose L2-risk was bounded above in previous work (Asta,2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density estimation on all symmetric spaces is completed. The idea in adapting the proof for Euclidean space is to suitably abstract vector space operations on Euclidean space to both actions of symmetric groups and reparametrizations of Helgason-Fourier transforms and to use the fact that the exponential map for symmetric spaces of non-compact type defines a diffeomorphism.

  PublisherOA PDFDOI

• Non-parametric manifold learning

  Electronic Journal of Statistics · 2024-01-01

  articleOpen access1st authorCorresponding

  We introduce an estimator for distances in a compact Riemannian manifold based on graph Laplacian estimates of the Laplace-Beltrami operator. We upper bound the error in the estimate of manifold distances, or more precisely an estimate of a spectrally truncated variant of manifold distance of interest in non-commutative geometry (cf. [Connes and Suijelekom, 2020]), in terms of spectral errors in the graph Laplacian estimates and, implicitly, several geometric properties of the manifold. A consequence is a proof of consistency for (untruncated) manifold distances. The estimator resembles, and in fact its convergence properties are derived from, a special case of the Kontorovic dual reformulation of Wasserstein distance known as Connes’ Distance Formula.

  PublisherOA PDFDOI

• Lower Bounds for Density Estimation on Symmetric Spaces

  SSRN Electronic Journal · 2024-01-01

  preprintOpen access1st authorCorresponding
  PublisherDOI

• The influence of social relationships on substance use behaviors among pregnant women with opioid use disorder

  Drug and Alcohol Dependence · 2021 · 20 citations

  1st authorCorresponding
  • Psychology
  • Psychiatry
  • Clinical psychology
  PublisherOA PDFDOI

• Non-Parametric Manifold Learning

  arXiv (Cornell University) · 2021

  1st authorCorresponding
  • Computer Science
  • Artificial Intelligence
  • Mathematics

  We introduce an estimator for distances in a compact Riemannian manifold based on graph Laplacian estimates of the Laplace-Beltrami operator. We upper bound the error in the estimate of manifold distances, or more precisely an estimate of a spectrally truncated variant of manifold distance of interest in non-commutative geometry (cf. [Connes and Suijelekom, 2020]), in terms of spectral errors in the graph Laplacian estimates and, implicitly, several geometric properties of the manifold. A consequence is a proof of consistency for (untruncated) manifold distances. The estimator resembles, and in fact its convergence properties are derived from, a special case of the Kontorovic dual reformulation of Wasserstein distance known as Connes' Distance Formula.

  PublisherOA PDFDOI

• Kernel density estimation on symmetric spaces of non-compact type

  Journal of Multivariate Analysis · 2020 · 10 citations

  1st authorCorresponding
  • Mathematics
  • Mathematical analysis
  • Pure mathematics
  PublisherDOI

• The Geometry of Continuous Latent Space Models for Network Data

  Statistical Science · 2019-08-01 · 9 citations

  preprintOpen access

  We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to be conditionally independent given the dyads' unobserved positions in a latent space. In this way, these models provide a probabilistic framework for embedding network nodes in a continuous space equipped with a geometry that facilitates the description of dependence between random dyadic ties. Specifically, these models naturally capture homophilous tendencies and triadic clustering, among other common properties of observed networks. In addition to reviewing the literature on continuous latent space models from a geometric perspective, we highlight the important role the geometry of the latent space plays on properties of networks arising from these models via intuition and simulation. Finally, we discuss results from spectral graph theory that allow us to explore the role of the geometry of the latent space, independent of network size. We conclude with conjectures about how these results might be used to infer the appropriate latent space geometry from observed networks.

  PublisherOA PDFDOI

• Consistency of Maximum Likelihood for Continuous-Space Network Models.

  arXiv (Cornell University) · 2017-11-06 · 7 citations

  preprintOpen accessSenior author

  Network analysis needs tools to infer distributions over graphs of arbitrary size from a single graph. Assuming the distribution is generated by a continuous latent space model which obeys certain natural symmetry and smoothness properties, we establish three levels of consistency for non-parametric maximum likelihood inference as the number of nodes grows: (i) the estimated locations of all nodes converge in probability on their true locations; (ii) the distribution over locations in the latent space converges on the true distribution; and (iii) the distribution over graphs of arbitrary size converges.

  Publisher

Frequent coauthors

• Catherine A. Calder

  The University of Texas at Austin

  11 shared

• Anna L. Smith

  University of Kentucky

  10 shared

• Cosma Rohilla Shalizi

  7 shared

• Elizabeth E. Krans

  Magee-Womens Research Institute

  3 shared

• Leah C. Klocke

  Magee-Womens Research Institute

  2 shared

• Walitta Abdullah

  University of Pittsburgh

  2 shared

• Alex Davis

  Jet Propulsion Laboratory

  1 shared

• Tamar Krishnamurti

  1 shared

Labs

• Dena AstaPI