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where rule R has n ATs. Swing surprisingness is inversely proportional to the mean confidence of the ATs that make up the antecedent of the rule. The measure assigns

rules a higher value if they have less predictive ATs, irrespective of the confidence of the rule.

Swing and swing surprisingness are closely related measures; as can be seen, Swing(R) = SS(R) × Conf (R). Hence, a rule of moderate confidence will have lower swing than a more confident rule composed of equivalently good predictors. This is not the case with swing surprisingness.

The particular intuition we wish to capture with these measures is that good rules are rules that improve on the individual predictive power of the ATs in their an- tecedent. If such rules are being eliminated, then we know that the BruteSuppression algorithm is not working to preserve the predictive power of the rule set, regardless of its effect on confidence and support.

We use these measures because BruteSuppression uses confidence as a measure of rule quality; as we demonstrate in Chapter 2, many commonly used interestingness measures are monotonic with respect to confidence, so there is no benefit in using any of them rather than confidence. We want to ensure, however, that we are not eliminating rules that may have other qualities useful for prediction.

We do not test the effects of suppression merely in terms of confidence or support, as this is a relatively narrow definition of interestingness that may not capture what makes a rule predictive. We examine the effect of suppression with confidence and support, and also in terms of swing and swing surprisingness; our aim is to identify whether BruteSuppression deletes rules that may be interesting or predictive in a way that might not be obvious in terms of count-based interestingness measures.

6.7.2

Methodology

We compare three reduced rule sets with the original rule set generated from the Adult dataset (for brevity, we focus on Adult; see [86] for qualitative analysis of a number

of other datasets). We reduce them to approximately the same size using either the minimum confidence parameter, the minimum antecedent support parameter, or the BruteSuppression algorithm. The effects of reduction are assessed in two ways. First, we compare the distribution of rules using a chi-squared test. We take it that a reduced rule set should have a similar distribution of rules to the original set, as this suggests that no particular classes of potentially predictive rules are being removed. Second, we examine the distribution of rules visually. This enables us to discover which rules are being eliminated when the rule set is reduced. We take it that a good reduction should leave the same shaped distribution but with fewer rules, rather than a completely different shaped distribution.

The Adult dataset has 30,162 records in the training set and 12,435 records in the test set. It has 14 attributes, of which six are continuous. The target class is > 50K; the base incidence rate of this class is 0.249 in the training data and 0.236 in the test data. We generate the original rule set using a minimum support of 2% and minimum confidence of 0.25. The minimum confidence is the base incidence rate of the target class (we assume that rules with lower confidence than this are uninteresting). The minimum support is selected to allow Apriori to generate the rule set in a reasonable time frame. We feel that this has not compromised the results, as the setting is what a user might select, giving us a more realistic idea of the effectiveness of our algorithm. We have tested the algorithm on a single unconstrained rule set with similar results to the constrained rule sets.

We select the parameter settings for the increased minimum confidence and in- creased minimum antecedent support rule sets to produce rule sets similar in size to the suppressed set. This way, a fair comparison can be made between the effects of the BruteSuppression algorithm and the effects of the same degree of reduction from

the parameter settings. We use a minimum confidence of 0.69 for the increased min- imum confidence rule set, and a minimum support of 8% for the increased minimum support rule set (in each case, the other parameter remains unchanged). All of the rule sets are assessed on previously unencountered test sets; the various measures we use are assessed on the rules’ performance on the test set, rather than the training set.

We initially investigate the effect of the reduction methods on the distribution of rules in a rule set using the chi-squared statistic. If two sets of values are drawn from the same distribution, the chi-squared statistic obtained by comparing them is likely to be small. Large chi-squared values are indicative of the rule sets having different distributions of the qualities in question. We rank the different methods by their chi-squared values (see Table 6.4) for rule confidence, coverage, swing, and swing surprisingness.

We also visually examine how suppression affects the distribution of rules in terms of coverage (see Chapter 2), confidence, swing, and swing surprisingness. In particu- lar, we are interested in whether certain classes of rules are eliminated by suppression. We can divide rules into four classes: strong (high coverage and high confidence), general (high coverage, low confidence), exception (low coverage, high confidence, see [121, 93]), and weak (low coverage, low confidence). We do not discuss the effect of suppression on weak rules, as these are unlikely to be of interest, but the other three classes should be reduced equally to yield a rule set that is likely to be predictive. We are also interested in rules with high swing/swing surprisingness; eliminating these rules is likely to compromise the predictiveness of the rule set.

Table 6.4: Chi-squared values for the suppressed rule set, rule set reduced using increased minimum confidence, and rule set reduced using increased minimum an- tecedent support. A lower chi-squared value indicates a more similar distribution of rules relative to the original rule set.

Measure Suppressed Min. Min. Antecedent Confidence Support Confidence 43.643 (1) 360.815 (3) 105.867 (2) Coverage 9.133 (1) 66.599 (2) 234.239 (3) Swing 5.098 (1) 309.183 (3) 63.489 (2) Swing Surprisingness 24.653 (2) 150.697 (3) 18.431 (1) Avg. Rank 1.25 2.75 2