Regression Databases: Probabilistic Querying Using Sparse Learning Sets

We introduce regression databases (REDB) to formalize and automate probabilistic querying using sparse learning sets. The REDB data model involves observation data, learning set data, views definitions, and a regression model instance. The observation data is a collection of relational tuples over a set of attributes; the learning data set involves a subset of observation tuples, augmented with learned attributes, which are modeled as random variables; the views are expressed as linear combinations of observation and learned attributes; and the regression model involves functions that map observation tuples to probability distributions of the random variables, which are learned dynamically from the learning data set. The REDB query language extends relational algebra project-select queries with conditions on probabilities of first-order logical expressions, which in turn involve linear combinations of learned attributes and views, and arithmetic comparison operators. Such capability relies on the underlying regression model for the learned attributes. We show that REDB queries are computable by developing conceptual evaluation algorithms and by proving their correctness and termination