Gaussian determinantal processes: A new model for directionality in data
Name
13207.full.pdf
Description
Published version
Size
1.07 MB
Format
Adobe PDF
Checksum (MD5)
b7241f74773257d7eebf99ba77617a68
Author(s)
Ghosh, Subhroshekhar
Rigollet, Philippe
Date Issued
2020
Journal
Proceedings of the National Academy of Sciences of the United States of America
Publisher
Proceedings of the National Academy of Sciences
Version
Final published version
Abstract
© 2020 National Academy of Sciences. All rights reserved. Determinantal point processes (DPPs) have recently become popular tools for modeling the phenomenon of negative dependence, or repulsion, in data. However, our understanding of an analogue of a classical parametric statistical theory is rather limited for this class of models. In this work, we investigate a parametric family of Gaussian DPPs with a clearly interpretable effect of parametric modulation on the observed points. We show that parameter modulation impacts the observed points by introducing directionality in their repulsion structure, and the principal directions correspond to the directions of maximal (i.e., the most longranged) dependency. This model readily yields a viable alternative to principal component analysis (PCA) as a dimension reduction tool that favors directions along which the data are most spread out. This methodological contribution is complemented by a statistical analysis of a spiked model similar to that employed for covariance matrices as a framework to study PCA. These theoretical investigations unveil intriguing questions for further examination in random matrix theory, stochastic geometry, and related topics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1073/pnas.1917151117
