Relationships:

Finally I want to relate rule finding to the basic techniques and to other methods. We saw that we are interested in the marginal distribution of one variable (Y) which is just a projection into this variable. The focus is to find a condition, meaning a subsetting to values $X_1=x_1, \ldots, X_n=x_n$, such that the distinctiveness between the subseted projection (the a posteriori distribution) and just the projection (the a priori distribution) is high and the entropy of the a posteriori distribution low. As we remember from section 2.2, low entropy means that the uncertainty about the conditionalized variable Y is very low which in turn reflects a high transition probability into one value $y \in dom(Y)$.

To summarize, ``mining rules'' means subsetting and projecting, subsetting the precondition and projecting into the conclusion. Probabilities and entropy measures are then used to evaluate the corresponding rule.

In comparison with reconstructability analysis, rule induction (similar to DEEP) looks more into specific relationships between values while reconstructability analysis concentrates on general structure between variables.

If we preset the conclusion variable Y then a connection to logistic regression and general linear models becomes apparent. All these methods focus in finding other variables which are good in discriminating one value $y \in dom(Y)$ from the other values. The only difference is (as already discussed in section 3.3) that we can use `ordered' aggregation functions like multiplication, adding and other continuous functions for logistic regression, etc., while in this case we are `stuck' with logic functions: $X_1=x_1 \wedge X_2=x_2 \wedge \ldots \wedge X_n=x_n$ .