Magnetic resonance spectroscopy (MRS) is a common tool for brain tumor detection. To help automate and improve upon today's clinical practice, we apply deep learning (DL) to distinguish between patients with and without tumors. In general, two problems arise in the application of DL for medical diagnosis. First, the amount of training data may be scarce, as it is limited by the number of patients who have acquired the medical condition in question. Second, the training data may be corrupted by various types of noise including labeling noise. Both of these problems are prominent in our data set. Furthermore, a varying number of spectra are available for the different patients. We address these issues by considering the task as a multiple instance learning (MIL) problem. Specifically, we aggregate multiple spectra from the same patient into a ``bag'' for classification. We also apply data augmentation techniques to increase the amount of available training data. To achieve the permutation invariance during the process of bags of spectra, we proposed two approaches: (1) to apply min-, max-, and average-pooling on the features of all samples in one bag and (2) to apply an attention mechanism. We tested these two approaches on two neural network structures, i.e., multi-layer perceptron (MLP) and an Inception variant. We demonstrate that classification performance is significantly improved when training on multiple instances rather than single spectra. We propose a simple data augmentation method, i.e., over-sampling instances from each patient to generate bags for MIL and show that this simple DA method could further improve the performance. Finally, we demonstrate that our proposed model outperforms manual classification by neuroradiologists according to most performance metrics.