Simple one-pass algorithm for penalized linear regression with cross-validation on MapReduce
This work addresses the need for scalable and accurate regression modeling in big data contexts, though it is incremental as it builds on existing penalized regression methods with a focus on computational efficiency.
The paper tackles the problem of efficiently performing penalized linear regression with cross-validation on MapReduce by proposing a one-pass algorithm that achieves huge performance improvement over iterative distributed methods and is exact compared to approximate algorithms like parallel stochastic gradient descent.
In this paper, we propose a one-pass algorithm on MapReduce for penalized linear regression \[f_λ(α, β) = \|Y - α\mathbf{1} - Xβ\|_2^2 + p_λ(β)\] where $α$ is the intercept which can be omitted depending on application; $β$ is the coefficients and $p_λ$ is the penalized function with penalizing parameter $λ$. $f_λ(α, β)$ includes interesting classes such as Lasso, Ridge regression and Elastic-net. Compared to latest iterative distributed algorithms requiring multiple MapReduce jobs, our algorithm achieves huge performance improvement; moreover, our algorithm is exact compared to the approximate algorithms such as parallel stochastic gradient decent. Moreover, what our algorithm distinguishes with others is that it trains the model with cross validation to choose optimal $λ$ instead of user specified one. Key words: penalized linear regression, lasso, elastic-net, ridge, MapReduce