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In modern data analysis, sparse model selection becomes inevitable once the number of predictors variables is very high. It is well-known that model selection procedures like the Lasso or Boosting tend to overfit on real data. The celebrated Stability Selection overcomes these weaknesses by aggregating models, based on subsamples of the training data, followed by choosing a stable predictor set which is usually much sparser than the predictor sets from the raw models. The standard Stability Selection is based on a global criterion, namely the per-family error rate, while additionally requiring expert knowledge to suitably configure the hyperparameters. Since model selection depends on the loss function, i.e., predictor sets selected w.r.t. some particular loss function differ from those selected w.r.t. some other loss function, we propose a Stability Selection variant which respects the chosen loss function via an additional validation step based on out-of-sample validation data, optionally enhanced with an exhaustive search strategy. Our Stability Selection variants are widely applicable and user-friendly. Moreover, our Stability Selection variants can avoid the issue of severe underfitting which affects the original Stability Selection for noisy high-dimensional data, so our priority is not to avoid false positives at all costs but to result in a sparse stable model with which one can make predictions. Experiments where we consider both regression and binary classification and where we use Boosting as model selection algorithm reveal a significant precision improvement compared to raw Boosting models while not suffering from any of the mentioned issues of the original Stability Selection.