# Minimax and Communication-Efficient Distributed Best Subset Selection with Oracle Property

arXiv: https://arxiv.org/abs/2408.17276 · HTML: https://mlsanity.com/paper/2408.17276/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 7 of 7)

- [Communication Efficient Distributed Optimization using an Approximate Newton-type Method](https://mlsanity.com/paper/1312.7853/) (2013)
- [Efficient Distributed Learning with Sparsity](https://mlsanity.com/paper/1605.07991/) (2016)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [First-order Newton-type Estimator for Distributed Estimation and Inference](https://mlsanity.com/paper/1811.11368/) (2018)
- [Tuning parameter selection in high dimensional penalized likelihood](https://mlsanity.com/paper/1605.03321/) (2016)
- [A Distributed One-Step Estimator](https://mlsanity.com/paper/1511.01443/) (2015)
- [Distributed Estimation, Information Loss and Exponential Families](https://mlsanity.com/paper/1410.2653/) (2014)

## Abstract (arXiv)

The explosion of large-scale data in fields such as finance, e-commerce, and social media has outstripped the processing capabilities of single-machine systems, driving the need for distributed statistical inference methods. Traditional approaches to distributed inference often struggle with achieving true sparsity in high-dimensional datasets and involve high computational costs. We propose a novel, two-stage, distributed best subset selection algorithm to address these issues. Our approach starts by efficiently estimating the active set while adhering to the ℓ0 norm-constrained surrogate likelihood function, effectively reducing dimensionality and isolating key variables. A refined estimation within the active set follows, ensuring sparse estimates and matching the minimax ℓ2 error bound. We introduce a new splicing technique for adaptive parameter selection to tackle subproblems under ℓ0 constraints and a Generalized Information Criterion (GIC). Our theoretical and numerical studies show that the proposed algorithm correctly finds the true sparsity pattern, has the oracle property, and greatly lowers communication costs. This is a big step forward in distributed sparse estimation.