# A Statistical View of Column Subset Selection

arXiv: https://arxiv.org/abs/2307.12892 · HTML: https://mlsanity.com/paper/2307.12892/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 79 references that are in the map.
- First posted on arXiv 24 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Column subset selection is NP-complete](https://mlsanity.com/paper/1701.02764/) (2017)
- [A critical review of LASSO and its derivatives for variable selection under dependence among covariates](https://mlsanity.com/paper/2012.11470/) (2020)
- [Provably Correct Algorithms for Matrix Column Subset Selection with Selectively Sampled Data](https://mlsanity.com/paper/1505.04343/) (2015)
- [Greedy Column Subset Selection for Large-scale Data Sets](https://mlsanity.com/paper/1312.6838/) (2013)
- [Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations](https://mlsanity.com/paper/1511.01699/) (2015)
- [Regularized Greedy Column Subset Selection](https://mlsanity.com/paper/1804.04421/) (2018)

## Abstract (arXiv)

We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as Column Subset Selection (CSS). Meanwhile, the typical statistical formalization is to find an information-maximizing set of Principal Variables. This paper shows that these two approaches are equivalent, and moreover, both can be viewed as maximum likelihood estimation within a certain semi-parametric model. Within this model, we establish suitable conditions under which the CSS estimate is consistent in high dimensions, specifically in the proportional asymptotic regime where the number of variables over the sample size converges to a constant. Using these connections, we show how to efficiently (1) perform CSS using only summary statistics from the original dataset; (2) perform CSS in the presence of missing and/or censored data; and (3) select the subset size for CSS in a hypothesis testing framework.