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Distributed Linear Regression with Compositional Covariates

arXiv 2310.13969 ↗First posted 21 Oct 2023stat.ML cs.LGcited by 0

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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.

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References · 23

  1. 2019Advances and Open Problems in Federated Learningcited by 3,021
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  10. 2019Distributed High-dimensional Regression Under a Quantile Loss Functioncited by 12
  11. 2017Distributed inference for quantile regression processescited by 11
  12. 2019Least Squares Approximation for a Distributed Systemcited by 8
11 more
  1. 2021Communication-Constrained Distributed Quantile Regression with Optimal Statistical Guaranteescited by 8
  2. 2020Communication Efficient Distributed Learning with Censored, Quantized, and Generalized Group ADMMcited by 6
  3. 2016Distributed Convex Optimization with Many Convex Constraintscited by 5
  4. 2022Network Gradient Descent Algorithm for Decentralized Federated Learningcited by 5
  5. 2016Large Covariance Estimation for Compositional Data via Composition-Adjusted Thresholdingcited by 4
  6. 2018Generalized Linear Models with Linear Constraints for Microbiome Compositional Datacited by 4
  7. 2021Distributed Bootstrap for Simultaneous Inference Under High Dimensionalitycited by 4
  8. 2019Robust Regression with Compositional Covariatescited by 1
  9. 2020Communication-Efficient Distributed Estimator for Generalized Linear Models with a Diverging Number of Covariatescited by 1
  10. 2020Statistical inference in massive datasets by empirical likelihoodcited by 1
  11. 2022CoDGraD: A Code-based Distributed Gradient Descent Scheme for Decentralized Convex Optimizationcited by 1

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