Joshua Cape
University of Wisconsin-Madison, WI·Mathematics & Statistics·Early-career
Many modern datasets come as huge tables of numbers (matrices) or as networks of connections, such as brain wiring maps measured in many people. A common way to make sense of them is to compress them into a few key patterns, called a low-dimensional embedding.
- Fields
Mathematics & Statistics
Computer Science
Neuroscience
- Topics
spectral methods
matrix factorization
data embedding
- Grants
- 2 known grants, through Jul 2031
What they work on
- Develop nonparametric spectral clustering and dimension-reduction methods that tolerate messy, mixed data, and apply them to brain network studies of schizophrenia with psychiatry collaborators.
- Create uncertainty-quantification tools for spectral hypothesis tests, so that statistically significant signal can be separated from noise in large matrix datasets.
- Model dependent relational data by combining stochastic processes, multilayer graphs and optimization, and apply these models to metabolomics data on small molecules in biological systems.
- Build latent space models that separate brain-network features shared across subjects from features unique to individuals, using multi-subject functional and diffusion MRI networks.
- Derive eigenvector perturbation and concentration-inequality theory for spectral network-integration methods, and develop cross-validation for choosing models across multiple networks.
More about the research
Spectral techniques do this by factoring, truncating and perturbing large matrices. They sit underneath much of data science, but their statistical foundations are not fully understood. This work develops spectral methods that are robust, come with measures of uncertainty, and can handle data from many sources. It pairs mathematical theory with applications in neuroscience, psychiatry and biology.
Why it matters
Researchers studying the brain, mental illness and metabolism increasingly rely on large network and matrix datasets. This work could give them more reliable ways to find groups, combine brain scans from many subjects, and judge whether a detected pattern is real. Potential uses include brain network studies of schizophrenia and metabolomics research. Public software and a monograph would make the methods available to other analysts.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Yinqiu He
University of Wisconsin-Madison, WI·Mathematics & Statistics
Develop methods with theoretical guarantees for estimating low-dimensional network embeddings and quantifying their uncertainty under general network models with relaxed assumptions.
Marianna Pensky
University of Central Florida, FL·Mathematics & Statistics
Extend the multiplex Generalized Dot Product Graph model so that groups of network layers can have different underlying structures. This would allow layers to be clustered by condition.
Sreekalyani Bhamidi
University of North Carolina at Chapel Hill, NC·Mathematics & Statistics
Develop statistically principled methods for summarizing, clustering, and extracting principal directions of variation in multilayer network data, using Gaussian process optimal transport and Procrustes metrics on covariance operators expressed via Wasserstein distance.
The school
University of Wisconsin-Madison: 91 labs on PI Pages, $1.9B a year on research, 854 research doctorates a year.
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