Databases contain information about which relationships do and do not hold
among entities. To make this information accessible for statistical analysis
requires computing sufficient statistics that combine information from
different database tables. Such statistics may involve any number of {\em
positive and negative} relationships. With a naive enumeration approach,
computing sufficient statistics for negative relationships is feasible only for
small databases. We solve this problem with a new dynamic programming algorithm
that performs a virtual join, where the requisite counts are computed without
materializing join tables. Contingency table algebra is a new extension of
relational algebra, that facilitates the efficient implementation of this
M\"obius virtual join operation. The M\"obius Join scales to large datasets
(over 1M tuples) with complex schemas. Empirical evaluation with seven
benchmark datasets showed that information about the presence and absence of
links can be exploited in feature selection, association rule mining, and
Bayesian network learning.Comment: 11pages, 8 figures, 8 tables, CIKM'14,November 3--7, 2014, Shanghai,
Chin
