Monotonic Networks

Monotonicity is a constraint which arises in many application domains. We present a machine learning model, the monotonic network, for which monotonicity can be enforced exactly, i.e., by virtue offunctional form. A straightforward method for implementing and training a monotonic network is described. Monotonic networks are proven to be universal approximators of continuous, differentiable monotonic functions. We apply monotonic networks to a real-world task in corporate bond rating prediction and compare them to other approaches. 1 Introduction Several recent papers in machine learning have emphasized the importance of priors and domain-specific knowledge. In their well-known presentation of the biasvariance tradeoff (Geman and Bienenstock, 1992)' Geman and Bienenstock conclude by arguing that the crucial issue in learning is the determination of the "right biases" which constrain the model in the appropriate way given the task at hand.