  We consider the problem of maintaining sparsity in private distributed
storage of confidential machine learning data. In many applications, e.g., face
recognition, the data used in machine learning algorithms is represented by
sparse matrices which can be stored and processed efficiently. However,
mechanisms maintaining perfect information-theoretic privacy require encoding
the sparse matrices into randomized dense matrices. It has been shown that,
under some restrictions on the storage nodes, sparsity can be maintained at the
expense of relaxing the perfect information-theoretic privacy requirement,
i.e., allowing some information leakage. In this work, we lift the restrictions
imposed on the storage nodes and show that there exists a trade-off between
sparsity and the achievable privacy guarantees. We focus on the setting of
non-colluding nodes and construct a coding scheme that encodes the sparse input
matrices into matrices with the desired sparsity level while limiting the
information leakage.
