PANTALLA

DNN3describes the neural network that maps a combination of 1,000 mRNA and 1,000

CNA features to PAM subtypes with five possible values: LumA, LumB, HER2-enriched, basal-like, and normal-like. The best average accuracy (75.99%) over five folds was achieved with the network’s structure 2000-256-32-2, 100 epochs, and batch size 64. Due to the poor time performance of the decompositional baseline, DeepRED, on the first modelDNN1, we present the results for modelDNN3only for our algorithm and

the pedagogical C5.0 baseline.

Table 18 shows the accuracy of the neural network, whose activation values on the training set were used for rule extraction with our algorithm, along with the accuracy and fidelity of the rule sets, generated with our algorithm and pedagogical C5.0. Note that due to the high number of rules in fold 5, we were not able to calculate their accu- racy and fidelity in a reasonable time (annotated with *). The neural network’s accuracy is 73.66% as this is a harder task than classifying for the two classes of ER expression. With the acquired results, pedagogical C5.0 generates more accurate rules, but our al- gorithm has slightly higher fidelity. Table 19 shows that the pedagogical C5.0 algorithm extracts very comprehensible rules. In the average rule set, there were twelve rules, each consisting of less than four conditions. Our algorithm extracts more than four million rules per rule set with the average of 16.11 conditions per rule, which does not seem very comprehensible, but it could be improved with further pruning of the rule set. As we reported in Section 4.1, with large rule sets there is a big proportion of rules that are never applicable, so these could be removed from the rule set. Further studies are needed on how to approach further processing of extracted rules to extract compre-

hensible, but still accurate rules with a high level of fidelity. Table 20 gives the required time (in minutes) and used memory (in megabytes). Pedagogical C5.0 does not seem very affected by more input features and outputs. Our rule extraction algorithm uses, on average, almost 55 minutes to extract a rule set. However, there is a high variance in time used across folds. The minimum time needed was about 23 minutes, while the maximum was a bit over 2.5 hours.

Accuracy [%] Fidelity [%]

Fold NN ped C5.0 our alg. ped C5.0 our alg.

1 78.73 65.57 60.76 70.89 65.57 2 73.42 62.28 65.32 64.81 71.65 3 72.66 63.04 60.51 65.82 65.57 4 68.86 61.01 54.94 62.03 61.77 5 74.62 59.64 * 62.94 * Average 73.66 62.31 60.38 65.30 66,14

Table 18: Accuracy and fidelity for modelDNN3.

Rule set size Average rule length

Fold ped C5.0 our alg. ped C5.0 our alg.

1 12 1,134,997 3.33 18.10 2 10 3,472,408 3.30 16.08 3 14 850,138 3.43 12.01 4 16 1,084,973 3.56 16.67 5 10 13,549,053 3.30 17.69 Average 12 4,018,313.8 3.38 16.11

Table 19: Comprehensibility for modelDNN3.

Time [min] Memory [MB]

Fold ped C5.0 our alg. ped C5.0 our alg.

1 0.34 28.78 0.20 22.75 2 0.30 41.95 0.20 21.54 3 0.32 24.90 0.20 24.04 4 0.32 22.77 0.20 18.39 5 0.31 154.82 0.20 24.65 Average 0.32 54.64 0.20 22.27

Table 20: Time and memory consumption for modelDNN3.

Our algorithm extracts rules from deep neural networks, which have conditions on the features in the input layer and map to the output layer. The algorithm takes into ac- count the whole structure of a neural network as it splits the network into neuron levels and aggregates the results obtained from each neuron to represent the neural network

as a whole. With these simple and understandable IF-THEN rules that approximate the behaviour of the neural network, the algorithm makes the network more interpretable and explains the network’s decision, which was the main goal of this thesis.

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