Apriori-based mining algorithms enumerate frequent patterns efficiently, but the resulting large number of patterns makes it difficult to directly apply subsequent learning tasks. Recently, efficient iterative methods are proposed for mining discriminative patterns for classification and regression. These methods iteratively execute discriminative pattern mining algorithm and update example weights to emphasize on examples which received large errors in the previous iteration. In this paper, we study a family of loss functions that induces sparsity on example weights. Most of the resulting example weights become zeros, so we can eliminate those examples from discriminative pattern mining, leading to a significant decrease in search space and time. In computational experiments we compare and evaluate various loss functions in terms of the amount of sparsity induced and resulting speed-up obtained.