# Distributed Linear Regression with Compositional Covariates

arXiv: https://arxiv.org/abs/2310.13969 · HTML: https://mlsanity.com/paper/2310.13969/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 58 references that are in the map.
- First posted on arXiv 21 Oct 2023.

## Builds on (most cited first, 23 of 23)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization](https://mlsanity.com/paper/1709.08765/) (2017)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [GADMM: Fast and Communication Efficient Framework for Distributed Machine Learning](https://mlsanity.com/paper/1909.00047/) (2019)
- [Q-GADMM: Quantized Group ADMM for Communication Efficient Decentralized Machine Learning](https://mlsanity.com/paper/1910.10453/) (2019)
- [Heterogeneity-aware and communication-efficient distributed statistical inference](https://mlsanity.com/paper/1912.09623/) (2019)
- [Tuning parameter selection in high dimensional penalized likelihood](https://mlsanity.com/paper/1605.03321/) (2016)
- [Distributed High-dimensional Regression Under a Quantile Loss Function](https://mlsanity.com/paper/1906.05741/) (2019)
- [Distributed inference for quantile regression processes](https://mlsanity.com/paper/1701.06088/) (2017)
- [Least Squares Approximation for a Distributed System](https://mlsanity.com/paper/1908.04904/) (2019)
- [Communication-Constrained Distributed Quantile Regression with Optimal Statistical Guarantees](https://mlsanity.com/paper/2110.13113/) (2021)
- [Communication Efficient Distributed Learning with Censored, Quantized, and Generalized Group ADMM](https://mlsanity.com/paper/2009.06459/) (2020)
- [Distributed Convex Optimization with Many Convex Constraints](https://mlsanity.com/paper/1610.02967/) (2016)
- [Network Gradient Descent Algorithm for Decentralized Federated Learning](https://mlsanity.com/paper/2205.08364/) (2022)
- [Large Covariance Estimation for Compositional Data via Composition-Adjusted Thresholding](https://mlsanity.com/paper/1601.04397/) (2016)
- [Generalized Linear Models with Linear Constraints for Microbiome Compositional Data](https://mlsanity.com/paper/1801.03238/) (2018)
- [Distributed Bootstrap for Simultaneous Inference Under High Dimensionality](https://mlsanity.com/paper/2102.10080/) (2021)
- [Robust Regression with Compositional Covariates](https://mlsanity.com/paper/1909.04990/) (2019)
- [Communication-Efficient Distributed Estimator for Generalized Linear Models with a Diverging Number of Covariates](https://mlsanity.com/paper/2001.06194/) (2020)
- [Statistical inference in massive datasets by empirical likelihood](https://mlsanity.com/paper/2004.08580/) (2020)
- [CoDGraD: A Code-based Distributed Gradient Descent Scheme for Decentralized Convex Optimization](https://mlsanity.com/paper/2204.06344/) (2022)

## Abstract (arXiv)

With the availability of extraordinarily huge data sets, solving the problems of distributed statistical methodology and computing for such data sets has become increasingly crucial in the big data area. In this paper, we focus on the distributed sparse penalized linear log-contrast model in massive compositional data. In particular, two distributed optimization techniques under centralized and decentralized topologies are proposed for solving the two different constrained convex optimization problems. Both two proposed algorithms are based on the frameworks of Alternating Direction Method of Multipliers (ADMM) and Coordinate Descent Method of Multipliers(CDMM, Lin et al., 2014, Biometrika). It is worth emphasizing that, in the decentralized topology, we introduce a distributed coordinate-wise descent algorithm based on Group ADMM(GADMM, Elgabli et al., 2020, Journal of Machine Learning Research) for obtaining a communication-efficient regularized estimation. Correspondingly, the convergence theories of the proposed algorithms are rigorously established under some regularity conditions. Numerical experiments on both synthetic and real data are conducted to evaluate our proposed algorithms.