Joshua Cape

NSF Mathematical Sciences Postdoctoral Research Fellow Department of Statistics University of Michigan E-mail: jrcape AT umich DOT edu 323 West Hall 1085 South University Avenue Ann Arbor, MI 48109–1107 [arXiv ID] [Google Scholar]

About

I am currently a National Science Foundation Mathematical Sciences Postdoctoral Research Fellow in the Department of Statistics at the University of Michigan, hosted by Elizaveta (Liza) Levina. Previously, I completed my Ph.D. in Applied Mathematics and Statistics at Johns Hopkins University, advised by Carey E. Priebe and Minh Tang. In the fall of 2020 I will join the Department of Statistics at the University of Pittsburgh as a tenure-track Assistant Professor. My current research interests include:

— Network Analysis
— Statistical Machine Learning
— Multivariate Statistics
— Matrix Analysis

On the theoretical side, my research focuses on developing statistical theory for networks (graphs) and on examining the mathematical foundations of data science. On the applied side, I work on problems arising in neuroscience and biology that involve dimensionality reduction, inference, and structure discovery.

Education

• 2019, Ph.D. in Applied Mathematics and Statistics, Johns Hopkins University

• 2016, M.S.E. in Applied Mathematics and Statistics, Johns Hopkins University

• 2014, B.A. in Mathematics and Economics, Rhodes College

• 2013 (spring), Budapest Semesters in Mathematics study abroad program

Selected Publications

• On spectral embedding performance and elucidating network structure in stochastic blockmodel graphs
  Joshua Cape, Minh Tang, and Carey E. Priebe,
  Network Science (2019+), to appear.
  [preprint]

• The two-to-infinity norm and singular subspace geometry with applications to high-dimensional statistics
  Joshua Cape, Minh Tang, and Carey E. Priebe,
  Annals of Statistics (2019), vol. 47, no. 5, pp. 2405–2439.
  One of four selected papers presented in the Annals of Statistics Special Invited Session at JSM 2019.
  [paper] [preprint]

• On a ‘two truths’ phenomenon in spectral graph clustering
  Carey E. Priebe, Youngser Park, Joshua T. Vogelstein, John M. Conroy, Vince Lyzinski, Minh Tang, Avanti Athreya, Joshua Cape, and Eric Bridgeford,
  Proceedings of the National Academy of Sciences (2019), vol. 116, no. 13, pp. 5995–6000.
  [paper] [preprint]

• Signal-plus-noise matrix models: eigenvector deviations and fluctuations
  Joshua Cape, Minh Tang, and Carey E. Priebe,
  Biometrika (2019), vol. 106, no. 1, pp. 243–250.
  [paper] [preprint]

• The Kato–Temple inequality and eigenvalue concentration with applications to graph inference
  Joshua Cape, Minh Tang, and Carey E. Priebe,
  Electronic Journal of Statistics (2017), vol. 11, no. 2, pp. 3954–3978.
  [paper] [preprint]

• A Bayesian framework for the classification of microbial gene activity states
  Craig Disselkoen, Brian Greco, Kaitlyn Cook, Kristin Koch, Reginald Lerebours, Chase Viss, Joshua Cape, Elizabeth Held, Yonatan Ashenafi, Karen Fischer, Aaron Best, Matthew DeJongh, and Nathan Tintle,
  Frontiers in Microbiology (2016), vol. 7, no. 1191, pp. 1–15.
  [paper]

• Symplectic reduction at zero angular momentum
  Joshua Cape, Hans-Christian Herbig, and Christopher Seaton,
  Journal of Geometric Mechanics (2016), vol. 8, no. 1, pp. 13–34.
  [paper] [preprint]

• Comparing machine learning and logistic regression methods for predicting hypertension using a combination of gene expression and next-generation sequencing data
  Elizabeth Held, Joshua Cape, and Nathan Tintle,
  BMC Proceedings for Genetic Analysis Workshop 19 (2016), vol. 10, Suppl. 7:34, pp. 141–145.
  [paper]

Preprints

• Spectral inference for large stochastic blockmodels with nodal covariates
  Angelo Mele, Lingxin Hao, Joshua Cape, and Carey E. Priebe
  submitted.
  [preprint]

• Inference for multiple heterogeneous networks with a common invariant subspace
  Jesús Arroyo, Avanti Athreya, Joshua Cape, Guodong Chen, Carey E. Priebe, and Joshua T. Vogelstein,
  submitted.
  [preprint]

• Bayesian estimation of sparse spiked covariance matrices in high dimensions
  Fangzheng Xie, Yanxun Xu, Carey E. Priebe, and Joshua Cape,
  submitted.
  [preprint]

• A statistical interpretation of spectral embedding: the generalised random dot product graph
  Patrick Rubin-Delanchy, Carey E. Priebe, Minh Tang, and Joshua Cape,
  submitted.
  [preprint]

• Asymptotically efficient estimators for stochastic blockmodels: the naive MLE, the rank-constrained MLE, and the spectral
  Minh Tang, Joshua Cape, and Carey E. Priebe,
  submitted.
  [preprint]

• A note on the orthogonal Procrustes problem and norm-dependent optimality
  Joshua Cape,
  submitted.

Upcoming and Recent Talks

Teaching

I am not teaching during this academic year (2019–20).