Sparse Regression with Multi-type Regularized Feature Modeling
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Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are of the same type, such as Lasso regression for continuous predictors. However, many predictive problems involve different predictor types. We propose a multi-type Lasso penalty that acts on the objective function as a sum of subpenalties, one for each predictor type. As such, we perform predictor selection and level fusion within a predictor in a data-driven way, simultaneous with the parameter estimation process. We develop a new estimation strategy for convex predictive models with this multi-type penalty. Using the theory of proximal operators, our estimation procedure is computationally efficient, partitioning the overall optimization problem into easier to solve subproblems, specific for each predictor type and its associated penalty. The proposed SMuRF algorithm improves on existing solvers in both accuracy and computational efficiency. This is demonstrated with an extensive simulation study and the analysis of a case-study on insurance pricing analytics.
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