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

Tags

Fields of Study

  • Computer science

Readers

  • Calculus or Mathematical Analysis
  • Operations Research
  • Statistical inference.