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Although various distributed machine learning schemes have been proposedrecently for pure linear models and fully nonparametric models, littleattention has been paid on distributed optimization for semi-paramemetricmodels with multiple-level structures (e.g. sparsity, linearity andnonlinearity). To address these issues, the current paper proposes a newcommunication-efficient distributed learning algorithm for partially sparselinear models with an increasing number of features. The proposed method isbased on the classical divide and conquer strategy for handing big data andeach sub-method defined on each subsample consists of a debiased estimation ofthe double-regularized least squares approach. With the proposed method, wetheoretically prove that our global parametric estimator can achieve optimalparametric rate in our semi-parametric model given an appropriate partition onthe total data. Specially, the choice of data partition relies on theunderlying smoothness of the nonparametric component, but it is adaptive to thesparsity parameter. Even under the non-distributed setting, we develop a newand easily-read proof for optimal estimation of the parametric error in highdimensional partial linear model. Finally, several simulated experiments areimplemented to indicate comparable empirical performance of our debiasedtechnique under the distributed setting.

Debiased distributed learning for sparse partial linear models in high dimensions