Detecting Interesting Decision Rules in Tree Ensembles

A computer program product comprising a computer readable storage medium having a computer readable program stored therein, wherein the computer readable program, when executed on a computing device, causes the computing device to:

• traverse each tree in a tree ensemble in order to assign each individual data record from a set of data records in an evaluation data set to an identified leaf node in a set of leaf nodes in each tree;
• determine predicted values defined by the tree ensemble based on predictions provided by each leaf node to which each individual data record is assigned;
• determine interesting sub-indices for decision rules from a set of decision rules corresponding to the leaf nodes in the tree ensemble, wherein the computer readable program to determine the interesting sub-indices for decision rules corresponding to the leaf nodes in the tree ensemble for continuous targets further causes the computing device to:
• determine a standardized measure value D(t);
• determine a first sub-index of interestingness I1t between a decision rule and the ensemble prediction based on the conformance requirement as I1t=1−D(t);
• identify decision rules that predict either high or low values of the target variable to be the most interesting;
• determine an effect size measure corresponding to a t-test;
• transform the effect size measure into an interestingness sub-index with values between 0 and 1;
• define a second sub-index of interestingness I2t of the decision rule accuracy as:
• I
• 2
• t
• =
• {
• 0
• ,
• p
• vlaue
• 
• (
• t
• )
• ≥
• sig
• f
• 
• (
• E
• s
• 
• (
• t
• )
• )
• ,
• p
• vlaue
• 
• (
• t
• )
• <
• sig
• wherein sig is a specified significance level, pvalue(t) is a p-value from the t-test, Ex(t) is the effect size measure, and f(x) is a monotone cubic interpolation function:
• determine an R squared metric for the ensemble model on data records determined by the leaf node t:
• determine R squared as I minus the relative error, where the relative error is given by the sum of squared errors for the ensemble model divided by the total sum of squares;
• and
• define a third sub-index of interestingness I3t for accuracy of the ensemble model prediction to be I3t=R2(t);
• for each decision rule corresponding to the leaf nodes in the tree ensemble, combine the sub-indices into interestingness index It;
• rank the decision rules corresponding to the leaf nodes in the tree ensemble according to the associated value of the interestingness index It;
• and
• report a subset of the decision rules corresponding to the leaf nodes in the tree ensemble in order to provide a notification of the interesting decision rules in the tree ensemble.

An apparatus comprising:

• a processor;
• and
• a memory coupled to the processor, wherein the memory comprises instructions which, when executed by the processor, cause the processor to:
• traverse each tree in a tree ensemble in order to assign each individual data record from a set of data records in an evaluation data set to an identified leaf node in a set of leaf nodes in each tree;
• determine predicted values defined by the tree ensemble based on predictions provided by each leaf node to which each individual data record is assigned;
• determine interesting sub-indices for decision rules from a set of decision rules corresponding to the leaf nodes in the tree ensemble, wherein the instructions to determine the interesting sub-indices for decision rules corresponding to the leaf nodes in the tree ensemble for continuous targets further cause the processor to:
• determine a standardized measure value D(t);
• determine a first sub-index of interestingness I1t between a decision rule and the ensemble prediction based on the conformance requirement as I1t=1−D(t);
• identify decision rules that predict either high or low values of the target variable to be the most interesting;
• determine an effect size measure corresponding to a t-test:
• transform the effect size measure into an interestingness sub-index with values between 0 and 1;
• define a second sub-index of interestingness I2t of the decision rule accuracy as:
• I
• 2
• t
• =
• {
• 0
• ,
• p
• vlaue
• 
• (
• t
• )
• ≥
• sig
• f
• 
• (
• E
• s
• 
• (
• t
• )
• )
• ,
• p
• vlaue
• 
• (
• t
• )
• <
• sig
• wherein sig is a specified significance level, pvalue(t) is a p-value from the t-test, ES(t) is the effect size measure, and f(x) is a monotone cubic interpolation function;
• determine an R squared metric for the ensemble model on data records determined by the leaf node t;
• determine R squared as I minus the relative error, where the relative error is given by the sum of squared errors for the ensemble model divided by the total sum of squares;
• and
• define a third sub-index of interestingness I3t for accuracy of the ensemble model prediction to be I3t=R2(t);
• for each decision rule corresponding to the leaf nodes in the tree ensemble, combine the sub-indices into interestingness index It;
• rank the decision rules corresponding to the leaf nodes in the tree ensemble according to the associated value of the interestingness index It;
• and
• report a subset of the decision rules corresponding to the leaf nodes in the tree ensemble in order to provide a notification of the interesting decision rules in the tree ensemble.