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In caret package of R, there is a method 'xgblinear'. What is the working algorithm behind this method.

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I am not sure if this is helpful or not but here is a link to an academic paper detailing both the algorithm behind XGBoost and some use cases.

http://dmlc.cs.washington.edu/data/pdf/XGBoostArxiv.pdf

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It's the usual XGBoost boosting, but with linear models instead of decision trees as the base learner.

There are several questions about this over at stats.SE; here's a quick sampling:
What exactly is the gblinear booster in XGBoost?
How does linear base learner works in boosting? And how does it works in the xgboost library?
Difference in regression coefficients of sklearn's LinearRegression and XGBRegressor

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