In the absence of sufficiently large samples, due to expensive sampling costs or other constraints, statisticians can gain power for statistical inference by pooling the information of multiple available samples. If the underlying distributions of the samples being pooled are assumed to share some latent characteristics, one option at the statisticians’ disposal is the semi-parametric Density Ratio Model (DRM). An area of interest concerning DRM inference is determining the pre-specified basis function of the model prior to estimating the model parameters. It has been shown that misspecification of this function can have adverse effects with respect to bias and mean-squared error of the estimates. This paper investigates the application of a Group Lasso penalty to the parameter estimation problem in order to obtain sparse solutions and simplify an overspecified basis function. Simulated results of this novel estimator, computed with multiple algorithms, will be presented.