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Distributed Stochastic Smoothing ADMM for Penalized Quantile Regression — arXiv:2608.09220

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.09220
License (as archived): CC0-1.0
Archived: 2026-10-19T09:04:43.349Z
SHA-256 of the archived text: 6281debcec20ac4c8c170db3e8ef9a23bf10bdae5c603989c24c7bc596c1c5c8
Stable URL of this page: https://metraipolis.com/documento/dc_0544e81978ea

How to cite

Distributed Stochastic Smoothing ADMM for Penalized Quantile Regression — arXiv:2608.09220 — arXiv (en), https://arxiv.org/abs/2608.09220 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0544e81978ea (Metraipolis archive dc_0544e81978ea, sha256 6281debcec20ac4c8c170db3e8ef9a23bf10bdae5c603989c24c7bc596c1c5c8)

BibTeX

@misc{dc0544e81978ea,
  title = {Distributed Stochastic Smoothing ADMM for Penalized Quantile Regression — arXiv:2608.09220},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.09220},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0544e81978ea; sha256 6281debcec20ac4c8c170db3e8ef9a23bf10bdae5c603989c24c7bc596c1c5c8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.09220. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Quantile regression is well suited to heterogeneous and heavy-tailed data, but computation becomes challenging for large, distributed data sets because the check loss is nonsmooth. We propose a distributed stochastic smoothing alternating direction method of multipliers (DSS-ADMM) for horizontally partitioned penalized quantile regression. Each worker computes a mini-batch gradient of a Huber-smoothed check loss, and a coordinator performs a single proximal aggregation step for the regularizer. Raw observations remain local, worker updates run in parallel, and the method requires no matrix inversion. For proper, closed, and convex penalties, stacking the local coefficient vectors yields a standard two-block stochastic ADMM formulation. With fixed smoothing, we establish an expected $O(\log K/\sqrt K)$ joint objective-feasibility bound and an explicit $\eps/4$ approximation term for the original check-loss objective; when the smooth block is strongly convex, the bound improves to $O(\log K/K)$. We also characterize the scope of an extension to the minimax concave penalty and the smoothly clipped absolute deviation penalty. Reproducible simulations consider both homogeneous worker partitions, in which observations are independently and identically distributed across workers, and heterogeneous partitions, in which worker-specific covariate distributions differ. Sensitivity studies and analyses of the diabetes and Engel data illustrate the trade-offs among per-observation gradient evaluations, communication, consensus, sparsity, and prediction.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-11 in stat.CO).
Categorie arXiv: Computation (stat.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.09220 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T09:03:00.141Z dalla pagina https://arxiv.org/catchup/stat.CO/2026-08-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).