Marginal maximum entropy partitioning yields asymptotically consistent probability density functions

The marginal maximum entropy criterion has been used to guide recursive partitioning of a continuous sample space. Although the criterion has been successfully applied in pattern discovery applications, its theoretical justification has not been clearly addressed. In the paper, it is shown that the basic marginal maximum entropy partitioning algorithm yields asymptotically consistent density estimates. This result supports the use of the marginal maximum entropy criterion in pattern discovery and implies that an optimal classifier can be constructed