<p>This paper introduced a novel variable importance measure within the framework of maximum mean discrepancy (MMD). The proposed method assigns weights to each variable and optimizes these weights through a regularized MMD criterion, allowing them to adapt to the signal strength of each variable. These optimized weights quantify the contribution of each variable to the discrepancy between two distributions, thereby serving as a measure of variable importance. We further develop an object-oriented variable selection approach, where the selected variables–determined by the optimized weights–are tailored to minimize a task-specific loss function. Focusing on two common scenarios–two-sample testing and classification–we demonstrate that the proposed method enhances the power of MMD-based tests and improves classification accuracy. We establish consistency of the estimated weights, and extensive simulations and real-data applications confirm the practical effectiveness of our approach.</p>