In this paper, we present an extensive study of different neural network-based approaches and loss functions applied to the Multiple Instance Learning (MIL) problem and binary classification. In the MIL setting, training is performed on small sets of instances called bags, where each positive bag contains at least one positive instance and each negative bag contains only negative instances. We propose a new loss function based on the generalised mean and an effective training strategy particularly suited to this setting and to problems where the instances of one class contain a considerable amount of label noise. Furthermore, we present a probabilistic approach to dynamically estimate the label noise in this unbalanced binary classification setting and utilise it to automatically modulate the hyper-parameter of our proposed loss function. We experimentally evaluated our approach on a number of standard benchmarks for binary classification and showed that it outperforms standard neural network optimisation algorithms as well as most state-of-the-art MIL methods, both on numerical/categorical vector data with MLP architectures and images with Convolutional Neural Networks.