In this paper, we generalize the noisy-or model. The generalizations are three-fold. First, we allow parents to be multivalued ordinal variables. Second, parents can have both positive and negative influences on their common child. Third, we describe how the suggested generalization can be extended to multivalued child variables. The major advantage of our generalizations is that they require only one parameter per parent. We suggest a model learning method and report results of experiments on the Reuters text classification data. The generalized noisy-or models achieve equal or better performance than the standard noisy-or. An important property of the noisy-or model and of its generalizations suggested in this paper is that it allows more efficient exact inference than logistic regression models do.
The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally some comments concerning a method called enhancement and robustness of median estimator are given and results of simulation experiment comparing behavior of median estimator with other robust estimators for GLM's known from the literature are reported.