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Learning Rules from Incomplete Examples via Observation Models

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##### Learning Rules from Incomplete Examples via Observation Models

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**Learning Rules from Incomplete Examples via Observation**Models Janardhan Rao Doppa, Mohammad NasresFahani, Mohammad S. Sorower, Jed Irvine Thomas G. Dietterich, Xiaoli Fern and Prasad Tadepalli • If the data is generated by the novelty mention model • conservative scoring leads to an underestimateand aggressive scoring leads to an overestimate of true confidence of the rule • aggressive scoring provides a very good estimate of true confidence when novelty mention model is very strong • true ranking order of rules is preserved with ONLY aggressive scoring Introduction Implicit mention models • How can we learn general rules from natural data sources such as the web, natural language texts, or medical histories ? • Natural language texts are • radically incomplete - only a very small part of the “whole truth” is actually mentioned in the documents. Even smaller parts are successfully extracted • systematically biased -information is biased towards newsworthiness, which correlates with infrequency or surprise, the so called “man bites dog” phenomenon • Graphical representation • Random mention model (MAR) • Probability that B is mentioned only depends on A • Conservative scoring: confidence of the rule is defined as • ``Khadr, a Canadian citizen, was killed in Pakistan“ • Above text neither supports nor contradicts the rule citizen(X,Y) => borinIn(X,Y) as we are not told that bornIn(Khadr,Canada) • Novelty mention model • Special case of Missing Not At Random (MNAR) model • B will be mentioned with higher probability when the rule is violated, i.e., P(M|V) >> P(M|¬V) • Aggressive scoring: confidence of the rule is defined as • ``Khadr, a Canadian citizen, was killed in Pakistan“ • Above text supports the rule citizen(Y) => bornIn(Y) because, adding bornIn(Canada) supports the rule without contradicting the available evidence A => B is a rule M : random variable that represents the fact that B is mentioned B’ : observed value of B V : random variable that represents violation of the rule Fig 1: Bayes nets for data generation using (a) Random mention model, (b) Novelty mention model Experimental results • Synthetic experiments: learn and test on examples generated with different levels of missingness. Evaluated by the accuracy of predicting missing facts on test set. • Random mention model data • Novelty mention model data • Experiments with real data: • NFL data – extractions from BBN system on a training corpus of 110 documents • Birthplace-Citizenship data -- extractions from BBN on a training corpus of 248 text documents • Since the data matches the assumption of aggressive scoring, it learns the correct rule “citizen(Y) => bornIn(Y)” • Both conservative scoring and MLNs fail to learn the right rule • conservative and aggressive • scoring perform equally well • SEMperforms better at small • missing percentages (see 0’s), but conservative scoringoutperformsSEM at large missing percentages (see O‘s) Our solution • Model the generative process of mentioned facts and extracted facts • Use this mention model for rule learning • Explicit mention model: invert the mention model to infer a distribution over the true facts and score the likelihood of rules. Highly intractable due to the need to marginalize over all possible mentioned and true sets of facts • Implicit mention model: adapt the scoring function used to score the hypothesized rules based on a presumed mention model • Multiple Predicate Bootstrapping (MPB) • Iterate the following two steps until convergence • Learn rules: learn rules from incomplete examples using implicit mention model. Prune the rules based on support and confidence thresholds. • Impute missing facts: apply the learned rules to infer the missing facts • aggressive scoringsignificantly outperformsconservativescoring • aggressive scoring significantly outperformsSEM until missingness is tolerable (0.2, 0.4, 0.6) • since this is similar to MAR case, both conservative and aggressive scoringperform equally well, and outperform SEM and MLNs Analysis of implicit mention models • If the data is generated by the random mention model • conservative scoringleads to an unbiased estimate and aggressive scoring leads to an overestimate of true confidence of the rule • true ranking order of rules is preserved with both conservative and aggressive scoring