  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, even
when using the known regularization techniques. We focus here on tasks in which
the input is a description of the genetic variation specific to a patient, the
single nucleotide polymorphisms (SNPs), yielding millions of ternary inputs.
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. Even though the
amount of data for such tasks is increasing, this mismatch between the number
of examples and the number of inputs remains a concern. Naive implementations
of classifier neural networks involve a huge number of free parameters in their
first layer: each input feature is associated with as many parameters as there
are hidden units. We propose a novel neural network parametrization which
considerably reduces the number of free parameters. It is based on the idea
that we can first learn or provide a distributed representation for each input
feature (e.g. for each position in the genome where variations are observed),
and then learn (with another neural network called the parameter prediction
network) how to map a feature's distributed representation to the vector of
parameters specific to that feature in the classifier neural network (the
weights which link the value of the feature to each of the hidden units). We
show experimentally on a population stratification task of interest to medical
studies that the proposed approach can significantly reduce both the number of
parameters and the error rate of the classifier.
