The design of new methods and models when only weakly-labeled data are available is of paramount importance in order to reduce the costs of manual annotation and the considerable human effort associated with it. In this work, we address Sound Event Detection in the case where a weakly annotated dataset is available for training. The weak annotations provide tags of audio events but do not provide temporal boundaries. The objective is twofold: 1) audio tagging, i.e. multi-label classification at recording level, 2) sound event detection, i.e. localization of the event boundaries within the recordings. This work focuses mainly on the second objective. We explore an approach inspired by Multiple Instance Learning, in which we train a convolutional recurrent neural network to give predictions at frame-level, using a custom loss function based on the weak labels and the statistics of the frame-based predictions. Since some sound classes cannot be distinguished with this approach, we improve the method by penalizing similarity between the predictions of the positive classes during training. On the test set used in the DCASE 2018 challenge, consisting of 288 recordings and 10 sound classes, the addition of a penalty resulted in a localization F-score of 34.75%, and brought 10% relative improvement compared to not using the penalty. Our best model achieved a 26.20% F-score on the DCASE-2018 official Eval subset close to the 10-system ensemble approach that ranked second in the challenge with a 29.9% F-score.