Assistant Professor E-mail: joshua DOT cape AT pitt DOT edu 1826 Wesley W. Posvar Hall |

I am an Assistant Professor in the Department of Statistics at the University of Pittsburgh. 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 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.

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

August 2020 — New arXiv preprint “Multiple network embedding for anomaly detection in time series of graphs” with coauthors at Johns Hopkins University and Microsoft Research.

Fall 2020 — I'm teaching the graduate course STAT 2611: Theory of Multivariate Analysis I.

July 2020 — New arXiv preprint “On identifying unobserved heterogeneity in stochastic blockmodel graphs with vertex covariates” with Cong Mu, Angelo Mele, Lingxin Hao, Avanti Athreya, and Carey E. Priebe.

July 2020 — New working paper “Latent communities in employment relations and wage distributions: a network approach” with Lingxin Hao, Angelo Mele, Avanti Athreya, Cong Mu, and Carey E. Priebe.

July 2020 — Newly funded NSF proposal “Methods and Applications for Massive One-mode and Bipartite Social Networks” with Angelo Mele, Lingxin Hao, and Carey E. Priebe. Thanks, NSF!

March 2020 — New paper on orthogonal Procrustes problems and matrix norms published in

*Electronic Journal of Linear Algebra*.

Conference on Computational and Methodological Statistics | virtual | Dec. 2020 |

Biostatistics seminar, University of Pittsburgh | virtual | Nov. 2020 |

Statistics seminar, University of Delaware | virtual | Nov. 2020 |

Joint Statistical Meetings | virtual | Aug. 2020 |

SIAM Workshop on Network Science | virtual, poster | July 2020 |

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

**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*(2020), to appear.

[preprint]

**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.

[paper]

**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.

[paper] [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]

**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 identifying unobserved heterogeneity 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]

**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,**Joshua Cape**, Minh Tang, and Carey E. Priebe,

*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]

Spring 2021 — STAT 2221: Advanced Applied Multivariate Analysis

Fall 2020 — STAT 2611: Theory of Multivariate Analysis I — (Canvas site)