Classification trhough density estimation some new ideas.

AGNELLI J.P., CADEIRAS M., TABAK E.G., TURNER C.V. AND VANDEN-EIJNDEN E.

Angra dos Reis

Workshop; Mathematical Methods and Modeling of Biophysical Phenomena; 2009

Instituto de Matemática Pura y Aplicada, Brasil

Classification can be view as a statistical decision theoru problem. Given a set of observations X, each of them belonging to a class C_k, from a set of p different classes, and given a new observation x, one is asked about the probabilities p_k that this new sample belong to each class C_k. Then, one assign x to the class with maximum probability, the one wich with the new observations has the most  "traits in common". In this work we try to solve the classification problem through density estimation. The idea is to estimate the probability dostribution rho_k(x), that spicifies how likely it would be to find a sample with observed value x in the class C_k. Then using Bayes formula we can compute the posterior probabilities p_k that we are seeking. We present a methodology that estimate the probability distributions rho_k by ascent of the log-likehood of the observations. In this process not only the training data is used, we also consider the testing dataand we include it on the log-likehood of each class weighted by the probability that they belong to the corresponding class. Then in an expectation-maximization approach, we iterate the procedure improving the posteriors until convergence. Also we propose a methodology to select a subset of variables that best represents the "commom traits" of each class.