A nonparametric approach based on a Markov like property for classification

We suggest a new approach for classification based on nonparametricly estimated likelihoods. Due to the scarcity of data in high dimensions, full nonparametric estimation of the likelihood functions for each population is impractical. Instead, we propose to build a class of estimated nonparametric candidate likelihood models based on a Markov property and to provide multiple likelihood estimates that are useful for guiding a classification algorithm. Our density estimates require only estimates of one and two-dimensional marginal distributions, which can effectively get around the curse of dimensionality problem. A classification algorithm based on those estimated likelihoods is presented. A modification to it utilizing variable selection of differences in log of estimated marginal densities is also suggested to specifically handle high dimensional data.

► We have developed a new classification method.
► It is based upon a Markov approximation.
► It uses only one and two dimensional nonparametric density estimates.
► Some theory and several examples are provided.