On the random generation of monotone data sets

Many of the state-of-the-art classification algorithms for data with linearly ordered attribute domains and a linearly ordered label set insist on the monotonicity of the induced classification rule. Training and evaluation of such algorithms requires the availability of sufficiently general monotone data sets. In this short contribution we introduce an algorithm that allows for the (almost) uniform random generation of monotone data sets based on the Markov Chain Monte Carlo method.