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Contrastive dimension estimation

Abstract Number:

2535 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Speed 

Participants:

Sam Hawke (1), Didong Li (1)

Institutions:

(1) University of North Carolina, Chapel Hill, NC

Co-Author:

Didong Li  
University of North Carolina

First Author:

Sam Hawke  
University of North Carolina

Presenting Author:

Sam Hawke  
N/A

Abstract Text:

Contrastive dimension reduction methods have been used to uncover the low-dimensional structure that distinguishes one dataset (foreground) from another (background). However, current contrastive dimension reduction techniques do not estimate the number of unique dimensions, denoted as d_c, within the foreground data. Instead, they require this quantity as an input and proceed to estimate the dimensions themselves. In this paper, we formally define the contrastive dimension, d_c, and present what we believe to be the first estimator for this parameter. Under a linear model, we demonstrate the consistency of this estimator, establish a finite-sample error bound, and develop a hypothesis test for d_c = 0. This test is valuable for determining the suitability of a contrastive method for a given dataset. Furthermore, we provide a detailed analysis of our findings, supported by simulations using both synthetic and real-world datasets.

Keywords:

Dimension reduction|Contrastive dimension| | | |

Sponsors:

Section on Statistical Learning and Data Science

Tracks:

Dimension Reduction

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