The Multilevel Classification Problem and a Monotonicity Hint

We introduce and formalize the multilevel classi cation problem, in which each category can be subdivided into dierent levels. We analyze the framework in a Bayesian setting using Normal class conditional densities. Within this framework, a natural monotonicity hint converts the problem into a nonlinear programming task, with non-linear constraints. We present Monte Carlo and gradient based techniques for addressing this task, and show the results of simulations. Incorporation of monotonicity yields a systematic improvement in performance