Conclusive local interpretation rules for random forests

Abstract

In critical situations involving discrimination, gender inequality, economic damage, and even the possibility of casualties, machine learning models must be able to provide clear interpretations of their decisions. Otherwise, their obscure decision-making processes can lead to socioethical issues as they interfere with people’s lives. Random forest algorithms excel in the aforementioned sectors, where their ability to explain themselves is an obvious requirement. In this paper, we present LionForests, which relies on a preliminary work of ours. LionForests is a random forest-specific interpretation technique that provides rules as explanations. It applies to binary classification tasks up to multi-class classification and regression tasks, while a stable theoretical background supports it. A time and scalability analysis suggests that LionForests is much faster than our preliminary work and is also applicable to large datasets. Experimentation, including a comparison with state-of-the-art techniques, demonstrate the efficacy of our contribution. LionForests outperformed the other techniques in terms of precision, variance, and response time, but fell short in terms of rule length and coverage. Finally, we highlight conclusiveness, a unique property of LionForests that provides interpretation validity and distinguishes it from previous techniques.

Appendices

Deeper sensitivity analysis

In this appendix, we present a deeper sensitivity analysis, as originally presented in Sect. 5.2.

1.1 Binary classification

Diving deeper to the sensitivity analysis, Fig. 11 presents the FR% for the parameters of the RF while Fig. 12 refers to the parameters of LF. The parameter analysis reveals that when the RF’s max features parameter is set to 75%, the reduction in features in all datasets is higher. With regard to depth and estimators, LF achieves over 35% FR when the depth is greater than or equal to 5 and the estimators are 100 or more.

Fig. 11

Binary classification: analysis of FR relation to RF’s parameters. ‘sqrt’ and ‘log2’, as well as estimators 500 and 1000, have similar results, and they are grouped

Fig. 12

Binary classification: analysis of FR relation to LF’s parameters

In Fig. 12, we can see how the parameters of LF affect the FR% in these datasets. We observe that the two different AR (1) are performing identically in the FR%. In CR (2), the FR% seemed to diverge for the different algorithms. Specifically, k-medoids and SC manage to reduce the features by 20% or more in all datasets, while OPTICS could not manage to perform any reduction. RS (3) did not achieve any FR in Adult and Banknote, while it achieved low FR% in Heart (Statlog). Among the three approaches, AR seems necessary to achieve high FR%, while the combination of AR (1) with CL (2) seems to increase slightly in all three datasets the FR%.

Fig. 13

Binary classification: analysis of PR relation to RF’s parameters. Depth 7 and 10, as well as estimators 500 and 1000 are grouped

Fig. 14

Binary classification: analysis of PR relation to LF’s parameters

About the PR analysis, Fig. 13 reveals that when the RF’s max features parameter is set to ‘None’, the reduction in paths in all datasets is higher. Regarding depth and estimators, LF achieves over 40% PR when the depth is greater or equal to 5 and the estimators are 100 or over.

In Fig. 14, we can see how the parameters of LF affect the PR% in these datasets. In contrast to FR, for PR, CR (2) and RS (3) are both maximising the PR%. Recall that we cannot reduce more than a quorum in a binary setup, thus these techniques achieving 49% PR are performing optimally. AR (1), on the other hand, cannot seem to be able to optimally reduce paths. Finally, we observe that when combining all three techniques (123), for every parameter setting, the PR% is higher than 40%.

Fig. 15

Multi-class classification: analysis FR relation to RF’s parameters. ‘sqrt’ and ‘log2’, as well as estimators 500 and 1000, have similar results, and they are grouped

Fig. 16

Multi-class classification: analysis of FR relation to LF’s parameters

1.2 Multi-class classification

The tuning of RF’s parameters and their impact to the FR% are visible in Fig. 15. The analysis reveals that when the RF’s max features parameter is set to 75%, the FR in all datasets is higher. LF achieves over 17% FR when the depth is greater than or equal to 5 and estimators are 100 or over, while it achieves more than 25% and 34% for the individual datasets, Abalone and I. Segmentation, respectively.

Figure 16 presents how FR% is affected based on the different parameters of LF. As observed in the binary classification sensitivity analysis, here as well it is eminent that AR (1) is performing equally in the FR%. CR (2) in the Abalone dataset achieved a higher FR than AR, and when combined (123) with the other techniques, AR and RS, the FR% is not increasing. The analysis of Glass dataset revealed that rather than the FR achieved by the AR (1), no other method or combination managed to increase the FR%. Finally, on I. Segmentation seemed the combination of AR and CR (12), with specifically SC, to provide the highest FR%. Another interesting point is that the RS (3) managed to reduce the features of the rules in all three datasets, in contrast to the RS’s performance on the binary’s classification sensitivity analysis.

Through Fig. 17, observing the PR while tuning the RF’s parameters in these datasets, we can say that the max features parameters do not affect the PR%. We can not conclude the same for depth and estimators, where we need 5 or higher and 100 or more, respectively, to achieve higher PR%. The highest PR% it is achieved when depth equals 10 and estimators equals 1000.

Fig. 17

Multi-class classification: analysis of PR relation to RF’s parameters. Depth 7 and 10, as well as estimators 500 and 1000 are grouped

Fig. 18

Multi-class classification: analysis of PR relation to LF’s parameters

In Fig. 18, we can see how the parameters of LF affect the PR% in these datasets. RS (3) is maxing out the PR%. AR (1) cannot seem to achieve the desirable PR results, while CL (2) is performing well, but not as good as RS (3). Thus, RS or any combination with RS leads to a PR% of 38% or more.

1.3 Regression

Fig. 19

Regression: analysis FR relation to RF’s parameters. ‘sqrt’ and ‘log2’, as well as estimators 500 and 1000, have similar results, and they are grouped

In Fig. 19, the relation of RF’s parameters to the FR% is visible. We can say that the most influencing parameter is estimators. When estimators are equal or more than 500 and depth is either 1 or 5, then the reduction is between $35\%$ to $51\%$. Moreover, for Boston and Wine we observe that when max features is set to either ‘sqrt’ or ‘log2’, the FR% is higher. On the other hand, higher max features values like ‘0.75’ or ‘None’ seem to favour the FR% for Abalone.

Fig. 20

Regression: analysis of FR relation to LF’s parameters

Fig. 21

Regression: analysis of PR relation to LF’s parameters

Inspecting how the LF’s parameters are affecting the FR%, in Fig. 20, we can see that AR+RS method provides better results for Abalone, while DSi for Boston and Wine. However, DSo cannot reach desirable levels of FR% in any case.

Fig. 22

Regression: analysis of PR relation to RF’s parameters. ‘sqrt’ and ‘log2’, as well as estimators 500 and 1000, have similar results, and they are grouped

The same pattern we identified for the FR% relation to RF’s parameters, it is apparent for the relation of PR% with the RF’s parameters as well (Fig. 22). Setting estimators between 500 or 1000 and depth to either 1 or 5, the PR is between $50\%$ to $85\%$. However, max features do not affect the PR%.

In Fig. 21, we can see how the parameters of LF affect the PR% in these datasets. We observe the highest PR%, over 50%, with the DSi reduction method of LF. DSo is also better than AR+RS in terms of PR% (Fig. 22).

Fig. 23

Regression: analysis of FR relation to $local\_error$

Examining the relation of $local\_error$ with the FR% (Fig. 23), we can say that for the Wine dataset we can achieve high FR%, over 50%, with a low $local\_error$ of around 0.36. For the Abalone dataset, we need a $local\_error$ with a value between [1.1, 1.4] in order to achieve approximately 35% of FR. Finally, for Boston in order to achieve FR% higher than 40% we need a $local\_error$ around 2.2.

Fig. 24

Regression: analysis of PR relation to $local\_error$

Finally, about the relation of PR% with the $local\_error$, we observe, in Fig. 24, that we acquire higher PR% when we allow higher $local\_error$, in every dataset. In order to let the reader understand better the relation of both the FR% and PR% with the $local\_error$, we present the target variable statistics of each dataset in Table 12. This will help to associate the $local\_error$ with the actual values of the target variable of each dataset (Fig. 25).

Deeper analysis of time and scalability analysis

In this appendix, we present a deeper analysis regarding the runtime performance and scalability, as originally presented in Sect. 5.3.

Table 12 Statistics of target variable of regression task’s datasets

Fig. 25

Comparison of preliminary LF and LF on features’ ranges generation without reduction (y-axis in seconds)

Fig. 26

Comparison of preliminary LF and LF on features’ ranges generation without reduction (y-axis in second-zoomed)

In Fig. 26 we are zooming the y-axis in order to make visible that LF runs approximately between 0.2 and 0.6 s per explanation, in contrast to the preliminary version which generates explanations from 0.2 to almost 80 s (Fig. 27).

Fig. 27

Comparison of preliminary LF and LF on features’ ranges generation with reduction (y-axis in second)

Fig. 28

Comparison of preliminary LF and LF on features’ ranges generation with reduction (y-axis in second-zoomed)

In Fig. 28 we are zooming the y-axis in order to make visible that the version of LF runs approximately between 0.2 to 11 seconds per explanation, in contrast to the preliminary version which generates explanations from 2 to 128 s, and even over 280 in few extreme cases.

Fig. 29

Binary classification: analysis of runtime performance of LF for different number of features and different parameters for RF

As it is visible from Fig. 29, the worst performance in thee binary setup occurred when we used a dataset with 1000 features, 1000 estimators, and a depth of 10, reaching over 1 minute per explanation. An explanation takes 4 s in a typical configuration with 1000 features, 500 estimators, and a depth of 5. While 100 features, 1000 estimators, and depth 2 produce an explanation in half a second.

Fig. 30

Multi-class classification: analysis of runtime performance of LF for different number of features and different parameters for RF

In the multi-class experiments (Fig. 30), the lowest performance was with 1000 features, 1000 estimators, and a depth of 10, with either 10 or 100 classes, reaching over 1 minute, actually 64 s. In a common configuration with 1000 features, 500 estimators, and a depth of 5, an explanation takes 4.5 s. An explanation takes 0.8 s to generate using 100 features, 1000 estimators, and depth 2.

Fig. 31

Regression: analysis of runtime performance of LF for different number of features and different parameters for RF

In the regression experiments (Fig. 31), the worst performance was with 10 features, 1000 estimators, and a depth of 10, reaching almost 1 s. In a common configuration with 1000 features, 500 estimators, and a depth of 5, an explanation takes 0.64 s. An explanation takes 0.48 s to generate using 100 features, 1000 estimators, and depth 2.