  In this paper, we study the problem of establishing the accountability and
fairness of transparent machine learning models through monotonicity. Although
there have been numerous studies on individual monotonicity, pairwise
monotonicity is often overlooked in the existing literature. This paper studies
transparent neural networks in the presence of three types of monotonicity:
individual monotonicity, weak pairwise monotonicity, and strong pairwise
monotonicity. As a means of achieving monotonicity while maintaining
transparency, we propose the monotonic groves of neural additive models. As a
result of empirical examples, we demonstrate that monotonicity is often
violated in practice and that monotonic groves of neural additive models are
transparent, accountable, and fair.
