Gaussian determinantal processes: A new model for directionality in data
Abstract
The increasingly complex nature of data has led statisticians to rethinking even the most basic of modeling assumptions. In this context, a determinantal point process (DPP) modeling paradigm promotes diversity in the sample at hand. In this work, we introduce a simple and flexible Gaussian DPP model to capture directionality in the data. Using the Gaussian DPP as an ansatz, we obtain an approach for dimensionality reduction that produces a better and more readable representation of the original data than standard principal component analysis (PCA). These findings are supported by a finite sample analysis of the performance of our estimator, in particular in a spiked model similar to the one employed to analyze PCA.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 01, 2020
- Source ID
- 10.1073/pnas.1917151117
Entities
People
- Philippe Rigollet
- Subhroshekhar Ghosh
Organizations
- Division of Computing and Communication Foundations
- Division of Information and Intelligent Systems
- Massachusetts Institute of Technology
- Ministry of Education
- National Science Foundation Division of Mathematical Sciences
- Office of Naval Research