document: A Bayesian network framework for reject inference Most learning methods assume that the training set is drawn randomly from the population to which the learned model is to be applied . However in many applications this assumption is invalid . For example , lending institutions create models of who is likely to repay a loan from training sets consisting of people in their records to whom loans were given in the past ; however , the institution approved loan applications previously based on who was thought unlikely to default . Learning from only approved loans yields an incorrect model because the training set is a biased sample of the general population of applicants . The issue of including rejected samples in the learning process , or alternatively using rejected samples to adjust a model learned from accepted samples only , is called reject inference . The main contribution of this paper is a systematic analysis of different cases that arise in reject inference , with explanations of which cases arise in various real-world situations . We use Bayesian networks to formalize each case as a set of conditional independence relationships and identify eight cases , including the familiar missing completely at random ( MCAR ) , missing at random ( MAR ) , and missing not at random ( MNAR ) cases . For each case we present an overview of available learning algorithms . These algorithms have been published in separate fields of research , including epidemiology , econometrics , clinical trial evaluation , sociology , and credit scoring ; our second major contribution is to describe these algorithms in a common framework .
doc_bio_tags: O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O