## Our Approach

*wasBornIn(x, Munich) => isCitizenOf(x,Germany)*

*hasWonPrize(x, OrderOfCanada) => isCitizenOf(x, Canada)*

### Hybrid Confidence

**Support**. The support of a rule is defined to be the number of correct predictions the rule makes.

**Standard Confidence.**Confidence measures how confident we are about the predictions of a rule. Standard confidence assumes the closed world assumption by regarding predictions out of the KB as false, thus it is defined as the ratio of a rule’s predictions in the knowledge base

**PCA Confidence.**Due to the incompleteness of KBs, predictions that are not in the KB are not necessarily false, because they might just be missing from the KB. Thus, a more relaxed assumption is employed in Partial Closed-world Assumption (PCA) confidence by assuming that the KB is locally complete for (pred, sub) pairs existing in the KB.

**Hybrid Confidence.**While PCA confidence tries to deal with the incompleteness and has been demonstrated to be useful especially for (quasi) functional predicates, PCA is still a strong assumption and can fail in cases where the unknown is simply wrong for uncommon predicates. For example, in YAGO2 the predicate “hasWonPrize” is actually a rare attribute for person, film or music albums. Since KBs usually do not contain negative triples, PCA would simply ignore unknown predictions containing this rare attribute and severely overestimate the quality of those rules. In those cases, standard confidence is a closer estimate for rules with rare predicates as the head. Motivated by this observation, we propose a hybrid confidence metric:

### Relational Model

We utilize the relational model from ProbKB [https://dsr.cise.ufl.edu/projects/probkb-web-scale-probabilistic-knowledge-base/] for mining conditional rules in batches. Our mining algorithm can be written in one SQL sentence per rule type:

However, directly executing the SQL sentence would be infeasible due to the large KB sizes and multiple self joins on the KBs. Instead we implement the algorithm in Spark with a number of optimization techniques.

## Experiments

### Performance Comparison

### Link Prediction

#### Cross-validation

Figure 1 and Figure 2 compare the predictive ability of conditional rules and normal rules, respectively. We can see that conditional rules achieves higher precision that normal rules consistently.