Estimation of Classification Rules From Partially Classified Data

We consider the situation where observed sample contains some observations whose class of origin is known (that is, they are classified with respect to g underlying classes interest), and remaining in unclassified their labels unknown). For class-conditional distributions taken be up a vector unknown parameters, aim estimate Bayes’ rule allocation for subsequent observations. Estimation on basis both data can undertaken straightforward manner by fitting g-component mixture model maximum likelihood (ML) via EM algorithm assumed an random from adopted distribution. This assumption applies if missing-data mechanism ignorable terminology pioneered Rubin (1976). An initial approach was use so-called classification ML whereby missing parameters estimated along distributions. However, as it lead inconsistent estimates, focus attention switched after appearance (Dempster et al. 1977). Particular given here asymptotic relative efficiency (ARE) partially sample. Lastly, we briefly recent results situations label pattern non-ignorable purposes estimation model.