  In this paper we consider data storage from a probabilistic point of view and
obtain bounds for efficient storage in the presence of feature selection and
undersampling, both of which are important from the data science perspective.
First, we consider encoding of correlated sources for nonstationary data and
obtain a Slepian-Wolf type result for the probability of error. We then
reinterpret our result by allowing one source to be the set of features to be
discarded and other source to be remaining data to be encoded. Next, we
consider neighbourhood domination in random graphs where we impose the
condition that a fraction of neighbourhood must be present for each vertex and
obtain optimal bounds on the minimum size of such a set. We show how such sets
are useful for data undersampling in the presence of imbalanced datasets and
briefly illustrate our result using~\(k-\)nearest neighbours type
classification rules as an example.
