Assistant Professor Department of Statistics University of Pittsburgh E-mail: joshua DOT cape AT pitt DOT edu 1802 Wesley W. Posvar Hall 230 South Bouquet Street Pittsburgh, PA 15260 [Google Scholar] [arXiv ID] [GitHub]

About

In addition to being an Assistant Professor of Statistics, I currently serve as an Associate Editor for the Journal of Statistical Planning and Inference. Previously, I spent one year as a National Science Foundation Mathematical Sciences Postdoctoral Research Fellow in the Department of Statistics at the University of Michigan. I completed my Ph.D. in Applied Mathematics and Statistics at Johns Hopkins University in Baltimore, Maryland.

My current research interests include:

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

On the theoretical side, my research develops statistical theory for complex data problems, often involving networks and graphs. My work also examines the mathematical foundations of data science via the study of matrices. On the applied side, I work on problems arising in the natural sciences (currently, neuroscience and biology) and in the social sciences (currently, economics and sociology) that involve dimensionality reduction, inference, and structure discovery.

My research is supported by NSF grants DMS-1902755 and SES-1951005. I am grateful for past research support during my studies from the NSF, NIH, DARPA, and JHU. Any opinions, findings, and conclusions or recommendations are those of the author(s) and do not necessarily reflect the views of funding agencies.

Education

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

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

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

• Budapest Semesters in Mathematics study abroad program

What's New

• May 2022  —  Commentary on discussion paper by Rohe and Zeng, to appear in Journal of the Royal Statistical Society, Series B.

• May 2022  —  Two papers on network inference with covariates, to appear in Journal of Business and Economic Statistics and IEEE Transactions on Network Science and Engineering.

• March 2022  —  Paper on generalized random dot product graphs, to appear in Journal of the Royal Statistical Society, Series B.

• February 2022  —  New preprint on spectral embedding of multipartite networks, with collaborators at the University of Bristol.

• January 2022  —  I am teaching the undergraduate course STAT 1632: Intermediate Mathematical Statistics.

• December 2021  —  Review papers (Parts I and II) with Pitt collaborators on structural covariance networks, to appear in Schizophrenia Research.

• November 2021  —  Paper on eigenvalue asymptotics for random graphs (e.g., stochastic blockmodels), published in Sankhya A.

• October 2021  —  New preprint on threshold selection in MRI network data, with Pitt collaborators in psychiatry, statistics, and mathematics.

Upcoming and Recent Talks

Conference on Computational and Methodological Statistics	virtual	Dec. 2022
Joint Statistical Meetings	TBD	Aug. 2022
Conference on Computational and Methodological Statistics	virtual	Dec. 2021
Joint Statistical Meetings	virtual	Aug. 2021
International Conference on Econometrics and Statistics	virtual	June 2021

Publications

Preprints may differ from published papers in terms of content and formatting.

• Discussion of “Vintage factor analysis with varimax performs statistical inference” by Rohe and Zeng
  Joshua Cape,
  Journal of the Royal Statistical Society, Series B (2022+), to appear.

• On spectral algorithms for community detection in stochastic blockmodel graphs with vertex covariates
  Cong Mu, Angelo Mele, Lingxin Hao, Joshua Cape, Avanti Athreya, and Carey E. Priebe,
  IEEE Transactions on Network Science and Engineering (2022+), to appear.
  [preprint]

• Spectral inference for large stochastic blockmodels with nodal covariates
  Angelo Mele, Lingxin Hao, Joshua Cape, and Carey E. Priebe,
  Journal of Business and Economic Statistics (2022+), to appear.
  [preprint]

• A statistical interpretation of spectral embedding: the generalised random dot product graph
  Patrick Rubin-Delanchy, Joshua Cape, Minh Tang, and Carey E. Priebe,
  Journal of the Royal Statistical Society, Series B (2022+), to appear.
  [preprint]

• Bayesian sparse spiked covariance model with a continuous matrix shrinkage prior
  Fangzheng Xie, Joshua Cape, Carey E. Priebe, and Yanxun Xu,
  Bayesian Analysis (2022+), to appear.
  [advanced access] [preprint]

• Asymptotically efficient estimators for stochastic blockmodels: the naive MLE, the rank-constrained MLE, and the spectral estimator
  Minh Tang, Joshua Cape, and Carey E. Priebe,
  Bernoulli (2022), vol. 28, no. 2, pp. 1049–1073.
  [pdf] [suppl] [doi] [preprint]

• Structural covariance networks in schizophrenia: a systematic review (Part II)
  Konasale Prasad, Jonathan Rubin, Anirban Mitra, Madison Lewis, Nicholas Theis, Brendan Muldoon, Satish Iyengar, and Joshua Cape,
  Schizophrenia Research (2022), vol. 239, pp. 176–191.
  [pdf] [doi]

• Structural covariance networks in schizophrenia: a systematic review (Part I)
  Konasale Prasad, Jonathan Rubin, Anirban Mitra, Madison Lewis, Nicholas Theis, Brendan Muldoon, Satish Iyengar, and Joshua Cape,
  Schizophrenia Research (2022), vol. 240, pp. 1–21.
  [pdf] [doi]

• Eigenvalues of stochastic blockmodel graphs and random graphs with low-rank edge probability matrices
  Avanti Athreya, Joshua Cape, and Minh Tang,
  Sankhya A (2022), vol. 84m no. 1, pp. 36–63.
  In special issue on Network Analysis.
  [pdf] [doi]

• 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,
  Journal of Machine Learning Research (2021), vol. 22, no. 142, pp. 1–49.
  [pdf] [doi] [preprint]

• Spectral analysis of networks with latent space dynamics and signs
  Joshua Cape,
  Stat (2021), vol. 11, no. 1, e381.
  In special issue on Statistical Network Analysis.
  [pdf] [doi]

• A note on the orthogonal Procrustes problem and norm-dependent optimality
  Joshua Cape,
  Electronic Journal of Linear Algebra (2020), vol. 36, no. 36, pp. 158–168.
  [pdf] [doi]

• On spectral embedding performance and elucidating network structure in stochastic blockmodel graphs
  Joshua Cape, Minh Tang, and Carey E. Priebe,
  Network Science (2019), vol. 7, no. 3, pp. 269–291.
  [pdf] [doi] [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.
  [pdf] [doi] [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.
  [pdf] [doi] [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.
  [pdf] [suppl] [doi] [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.
  [pdf] [doi] [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.
  [pdf] [doi]

• 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.
  [pdf] [doi] [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.
  [pdf] [doi]

Preprints

• Spectral embedding and the latent geometry of multipartite networks
  Alexander Modell, Ian Gallagher, Joshua Cape, and Patrick Rubin-Delanchy,
  submitted.
  [preprint]

• Evaluating network threshold selection for structural and functional brain connectomes
  Nicholas Theis, Jonathan Rubin, Joshua Cape, Satish Iyengar, Raquel Gur, Ruben Gur, David Roalf, Michael Pogue-Geile, Laura Almasy, Vishwajit Nimgaonkar, and Konasale Prasad,
  submitted.
  [preprint]

• Multiple network embedding for anomaly detection in time series of graphs
  Guodong Chen, Jesús Arroyo, Avanti Athreya, Joshua Cape, Joshua T. Vogelstein, Youngser Park, Christopher White, Jonathan Larson, Weiwei Yang, and Carey E. Priebe,
  submitted.
  [preprint]

• Latent communities in employment relations and wage distributions: a network approach
  Lingxin Hao, Angelo Mele, Joshua Cape, Avanti Athreya, Cong Mu, and Carey E. Priebe,
  submitted.

Teaching

Spring 2022  —  STAT 1632 / 2640: Intermediate Mathematical Statistics  —  Canvas site

Fall 2021  —  STAT 2221: Advanced Applied Multivariate Analysis  —  Canvas site