Abstract: Effects in multiple linear regression may be decorrelated to decompose and attribute risk to common and proper effects. In other words, an attribute risk may be decomposed to two or more causes, where each cause is characterized by multiple attributes. The risk decomposition may decompose risk into a first residual part associated with a first set of risk factors, a second residual part associated with a second set of risk factors, and a common part associated with a set of common hidden variables that minimize a correlation between the first set of factors and the second set of factors. The common hidden variables may be modeled using a hidden factor model. An effect of the correlation may be minimized on the first set of risk factors and the second set of risk factors, and how correlated the terms of the risk decomposition are may be quantified.

Abstract: Methods for discovering portions of a multi-dimensional database that are significant to an analyst can be computer-implemented. The methods can include specifying a data view having at least two dimensions and all records of the database. A plurality of operation iterations are then performed on the data view, wherein each iteration is a chain operation, a hop operation or an anti-hop operation. The operation iterations are ceased upon satisfaction of a termination criteria. The resulting data view can then be presented to an analyst. The methods can facilitate a users' knowledge discovery tasks and assist in finding relevant patterns, trends, and anomalies.