Learning tasks such as those involving genomic data often poses a serious challenge: the number of input features can be orders of magnitude larger than the number of training examples, making it difficult to avoid overfitting when training deep learning models. Improving the ability of deep learning to handle such datasets could have an important impact in precision medicine, where high-dimensional data regarding a particular patient is used to make predictions of interest. We propose a novel neural network parameterization, that we call Diet Networks, which considerably reduces the number of free parameters in the model. The Diet Networks parametrization is based on the idea that we can first learn or provide an embedding for each input feature and then learn how to map a feature's representation to the parameters linking the value of the feature to each of the hidden units of the classifier network. We experiment on a population stratification task of interest to medical studies and show that the proposed approach can significantly reduce both the number of parameters and the error rate of the classifier. This work was accepted at ICLR 2017.