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Distributed Sparse Linear Regression under Communication Constraints

arXiv 2301.04022 ↗First posted 9 Jan 2023cs.LG math.ST stat.THcited by 0

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Abstract (arXiv)

In multiple domains, statistical tasks are performed in distributed settings, with data split among several end machines that are connected to a fusion center. In various applications, the end machines have limited bandwidth and power, and thus a tight communication budget. In this work we focus on distributed learning of a sparse linear regression model, under severe communication constraints. We propose several two round distributed schemes, whose communication per machine is sublinear in the data dimension. In our schemes, individual machines compute debiased lasso estimators, but send to the fusion center only very few values. On the theoretical front, we analyze one of these schemes and prove that with high probability it achieves exact support recovery at low signal to noise ratios, where individual machines fail to recover the support. We show in simulations that our scheme works as well as, and in some cases better, than more communication intensive approaches.

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References · 19

  1. 2019Advances and Open Problems in Federated Learningcited by 3,021
  2. 2019Towards Federated Learning at Scale: System Designcited by 826
  3. 2013Confidence Intervals and Hypothesis Testing for High-Dimensional Regressioncited by 78
  4. 2015Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequalitycited by 50
  5. 2015De-biasing the Lasso: Optimal Sample Size for Gaussian Designscited by 35
  6. 2018Distributed linear regression by averagingcited by 21
  7. 2013Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theorycited by 18
  8. 2014On the Optimality of Averaging in Distributed Statistical Learningcited by 14
  9. 2019Distributed High-dimensional Regression Under a Quantile Loss Functioncited by 12
  10. 2018Adaptive distributed methods under communication constraintscited by 9
  11. 2019Distributed Learning with Sublinear Communicationcited by 9
  12. 2019Least Squares Approximation for a Distributed Systemcited by 8
7 more
  1. 2015DUAL-LOCO: Distributing Statistical Estimation Using Random Projectionscited by 7
  2. 2020Integrative High Dimensional Multiple Testing with Heterogeneity under Data Sharing Constraintscited by 5
  3. 2014LOCO: Distributing Ridge Regression with Random Projectionscited by 3
  4. 2021Distributed Sparse Normal Means Estimation with Sublinear Communicationcited by 3
  5. 2017Debiased distributed learning for sparse partial linear models in high dimensionscited by 2
  6. 2021Distributed Sparse Feature Selection in Communication-Restricted Networkscited by 2
  7. 2021Distributed Sparse Regression via Penalizationcited by 1

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