  Real-world machine learning applications may require functions that are
fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of
the learned function can be critical to user trust. We propose meeting these
goals for low-dimensional machine learning problems by learning flexible,
monotonic functions using calibrated interpolated look-up tables. We extend the
structural risk minimization framework of lattice regression to train monotonic
look-up tables by solving a convex problem with appropriate linear inequality
constraints. In addition, we propose jointly learning interpretable
calibrations of each feature to normalize continuous features and handle
categorical or missing data, at the cost of making the objective non-convex. We
address large-scale learning through parallelization, mini-batching, and
propose random sampling of additive regularizer terms. Case studies with
real-world problems with five to sixteen features and thousands to millions of
training samples demonstrate the proposed monotonic functions can achieve
state-of-the-art accuracy on practical problems while providing greater
transparency to users.
