Joshua Cape
 |
Assistant Professor E-mail: joshua DOT cape AT pitt DOT edu 1802 Wesley W. Posvar Hall |
About
I am an Assistant Professor in the Department of Statistics at the University of Pittsburgh. 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 focuses on developing statistical theory for networks (graphs) and on examining 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, 2019
M.S.E. in Applied Mathematics and Statistics, Johns Hopkins University, 2016
B.A. in Mathematics and Economics, Rhodes College, 2014
Budapest Semesters in Mathematics study abroad program, Spring 2013
What's New
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.
September 2021 — Paper on sparse spiked covariance matrix estimation, to appear in Bayesian Analysis.
August 2021 — I am teaching the graduate course STAT 2221: Advanced Applied Multivariate Analysis.
June 2021 — Paper on asymptotically efficient estimators in network models, to appear in Bernoulli.
May 2021 — Paper on analyzing multiple heterogenous networks, to appear in Journal of Machine Learning Research.
April 2021 — Paper on modeling and inference for networks with latent space dynamics, published in the journal Stat.
Upcoming and Recent Talks
| 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.
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), in press.
[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), in press.
[pdf] [doi]
Bayesian sparse spiked covariance model with a continuous matrix shrinkage prior
Fangzheng Xie, Joshua Cape, Carey E. Priebe, and Yanxun Xu,
Bayesian Analysis (2022), in press.
[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), in press.
[advanced access] [preprint]
Eigenvalues of stochastic blockmodel graphs and random graphs with low-rank edge probability matrices
Avanti Athreya, Joshua Cape, and Minh Tang,
Sankhya A (2021), in press.
[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
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]
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,
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.
Spectral inference for large stochastic blockmodels with nodal covariates
Angelo Mele, Lingxin Hao, Joshua Cape, and Carey E. Priebe,
submitted.
[preprint]
A statistical interpretation of spectral embedding: the generalised random dot product graph
Patrick Rubin-Delanchy, Joshua Cape, Minh Tang, and Carey E. Priebe,
submitted.
[preprint]
Teaching
Spring 2022 — STAT 1632 / 2640: Intermediate Mathematical Statistics — Canvas site
Fall 2021 — STAT 2221: Advanced Applied Multivariate Analysis — Canvas site