Joshua Cape
 |
Assistant Professor Email: jrcape AT wisc DOT edu 1250A Medical Sciences Center |
About
I am an Assistant Professor of Statistics at the University of Wisconsin–Madison. Previously, I was a faculty member at the University of Pittsburgh, and I spent one year as a National Science Foundation Mathematical Sciences Postdoctoral Research Fellow in the Department of Statistics at the University of Michigan, Ann Arbor. I completed my Ph.D. in Applied Mathematics and Statistics at Johns Hopkins University in Baltimore, Maryland.
— Associate Editor for Journal of Business and Economic Statistics (JBES) since Sept. 2024
— Associate Editor for Computational Statistics and Data Analysis (CSDA) since June 2024
— Associate Editor for Journal of Statistical Planning and Inference (JSPI) since Jan. 2021
— Member of the Math Alliance since Mar. 2021
My current research interests include:
— Statistical Machine Learning
— Multivariate Statistics
— Network Analysis
— Spectral Methods
— Matrix Analysis
On the theoretical side, my research develops statistical methods and 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 grants NSF DMS 2413552, NSF SES 1951005, NSF DMS 1902755, and I am a consultant for 1R01MH137090-01. 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.
I am actively recruiting self-motivated graduate students who have a strong background in the mathematical and statistical sciences.
I ignore email inquiries that appear to be generated or heavily edited by AI.
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
Join us for the IMSI workshop “Recent advances in random networks: theory and applications” in January 2026
Summer 2025 — Accepted paper in Journal of Nonparametric Statistics on spectral embedding geometry of multipartite networks
Summer 2025 — Congrats on your summer research fellowship, Jun!
Summer 2025 — Congrats on your summer internship, Jonquil!
May 2025 — Welcome to the research group, Xiaoyu!
May 2025 — Congrats on your graduation and upcoming Ph.D. journey, Yuqi!
March 2025 — Congrats on your successful dissertation defense, Dr. Wenlong Jiang!
January 2025 — New manuscript on estimation, inference, and asymptotics for latent position graphs
January 2025 — Accepted paper in Statistical Science surveying statistical guarantees for stochastic blockmodel random graphs
January 2025 — Accepted paper in Neural Networks on GCNs and network neuroscience applications in psychiatry
January 2025 — Accepted paper in Computational Statistics and Data Analysis on multiple network analysis in graph time series
Teaching
Fall 2025 — STAT 992 / STAT 679: Spectral Methods in Statistical Machine Learning [Canvas site]
Upcoming and Recent Talks
| Joint Statistical Meetings | |
| 8th International Conference on Econometrics and Statistics | |
| 19th International Joint Conference CFE-CMStatistics | |
Research Group
| Xiaoyu Lei | Ph.D. in Statistics (Wisc) | 2024–present | |
| Jun Hyung Chang | Ph.D. in Statistics (Wisc) | 2022–present | |
| Yancheng Li | Ph.D. in Statistics (Wisc) | 2022–present | |
| Jonquil Zhongling Liao | Ph.D. in Statistics (Wisc) | 2022–present | |
| Weiqiong Huang | Ph.D. in Statistics (Pitt), joint with Prof. Chris McKennan | 2021–present | |
| Wenlong Jiang | Ph.D. in Statistics (Pitt), joint with Prof. Chris McKennan | 2021–2025 | First position: Senior Machine Learning Engineer at LinkedIn (USA) |
| Anirban Mitra | Ph.D. in Statistics (Pitt) | 2020–2023 | First position: Senior Statistician at Johnson & Johnson (India) |
| Bill Zekun Wang | M.S. in Statistics and Data Science (Wisc) | 2022–2024 | First position: Ph.D. student at Johns Hopkins University (USA) |
| Yuqi Tu | B.S. in Mathematics and Computer Science (Wisc) | 2024–2025 | First position: Ph.D. student at Boston University (USA) |
Preprints
Eigenvector fluctuations and limit results for random graphs with infinite rank kernels
Minh Tang and Joshua Cape,
submitted.
[preprint]
Diagnostically distinct resting state fMRI energy distributions: a subject-specific maximum entropy modeling study
Nicholas Theis, Jyotika Bahuguna, Jonathan Rubin, Joshua Cape, Satish Iyengar, and Konasale Prasad,
manuscript.
[preprint]
A statistical framework for GWAS of high dimensional phenotypes using summary statistics, with application to metabolite GWAS
Weiqiong Huang, Emily Hector, Joshua Cape, and Chris McKennan,
submitted.
[preprint]
Publications
Preprints may differ from published papers in terms of content and formatting.
Spectral embedding and the latent geometry of multipartite networks
Alexander Modell, Ian Gallagher, Joshua Cape, and Patrick Rubin-Delanchy,
Journal of Nonparametric Statistics (2025+), to appear.
[preprint]
An overview of asymptotic normality in stochastic blockmodels: cluster analysis and inference
Joshua Agterberg and Joshua Cape,
Statistical Science (2025+), to appear.
[preprint]
Classification of psychosis spectrum disorders using graph convolutional networks with structurally constrained functional connectomes
Madison Lewis, Wenlong Jiang, Nicholas Theis, Joshua Cape, and Konasale Prasad,
Neural Networks (2025), vol. 181, 106771.
[doi] [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,
Computational Statistics and Data Analysis (2025), vol. 203, 108070.
[doi] [preprint]
Robust spectral clustering with rank statistics
Joshua Cape, Xianshi Yu, and Jonquil Zhongling Liao,
Journal of Machine Learning Research (2024), vol. 25, no. 398, pp. 1–81.
[pdf] [preprint] [code]
On inference for modularity statistics in structured networks
Anirban Mitra, Konasale Prasad, and Joshua Cape,
Journal of Computational and Graphical Statistics (2024), vol. 33, no. 4, pp. 1370–1382.
[pdf] [doi] [preprint] [code]
On varimax asymptotics in network models and spectral methods for dimensionality reduction
Joshua Cape,
Biometrika (2024), vol. 111, no. 2, pp. 609–623.
[pdf] [doi] [preprint] [code]
Discussion of “Vintage factor analysis with varimax performs statistical inference” by Rohe and Zeng
Joshua Cape,
Journal of the Royal Statistical Society, Series B (2023), vol. 85, no. 4, pp. 1066–1067.
[pdf] [doi]
Spectral estimation of large stochastic blockmodels with discrete nodal covariates
Angelo Mele, Lingxin Hao, Joshua Cape, and Carey E. Priebe,
Journal of Business and Economic Statistics (2023), vol. 41, no. 4, pp. 1364–1376.
[pdf] [doi] [preprint]
Threshold selection for brain connectomes
Nicholas Theis, Jonathan Rubin, Joshua Cape, Satish Iyengar, and Konasale Prasad,
Brain Connectivity (2023), vol. 13, no. 7, pp. 383–393.
[pdf] [doi] [preprint]
Invited commentary: Global network disorganization underlying psychosis high risk states
Konasale Prasad, Jonathan Rubin, Satish Iyengar, and Joshua Cape,
Schizophrenia Research (2023), vol. 255, pp. 67–68.
[pdf] [doi]
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), vol. 9, no. 5, pp. 3373–3384.
[pdf] [doi] [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), vol. 84, no. 4, pp. 1446–1473.
[pdf] [suppl] [doi] [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), vol. 17, no. 4, pp. 1193–1217.
[pdf] [suppl] [doi] [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. 84, 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]
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]
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]