Interpretation with baseline shapley value for feature groups on tree models

doi:10.1007/s11704-024-40117-2

Front. Comput. Sci.

2025, Vol. 19

Issue (5) : 195316 https://doi.org/10.1007/s11704-024-40117-2

Artificial Intelligence

Interpretation with baseline shapley value for feature groups on tree models

Fan XU, Zhi-Jian ZHOU, Jie NI, Wei GAO(

)

National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210023, China School of Artificial Intelligence, Nanjing University, Nanjing 210023, China

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Abstract

Tree models have made an impressive progress during the past years, while an important problem is to understand how these models predict, in particular for critical applications such as finance and medicine. For this issue, most previous works measured the importance of individual features. In this work, we consider the interpretation of feature groups, which is more effective to capture intrinsic structures and correlations of multiple features. We propose the Baseline Group Shapley value (short for BGShapvalue) to calculate the importance of a feature group for tree models. We further develop a polynomial algorithm, BGShapTree, to deal with the sum of exponential terms in the BGShapvalue. The basic idea is to decompose the BGShapvalue into leaves’ weights and exploit the relationships between features and leaves. Based on this idea, we could greedily search salient feature groups with large BGShapvalues. Extensive experiments have validated the effectiveness of our approach, in comparison with state-of-the-art methods on the interpretation of tree models.

Keywords interpretability shapley value random forests decision tree

Corresponding Author(s): Wei GAO

Just Accepted Date: 08 May 2024 Issue Date: 12 June 2024

Cite this article:

Fan XU,Zhi-Jian ZHOU,Jie NI, et al. Interpretation with baseline shapley value for feature groups on tree models[J]. Front. Comput. Sci., 2025, 19(5): 195316.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-024-40117-2
https://academic.hep.com.cn/fcs/EN/Y2025/V19/I5/195316

Fig.1 An illustration of four cases for

A j, B j

and

T j

when

A j ∪ B j = L j

. (a)

T j ? A j ∩ B j

; (b)

T j ? A j a n d T j ? B j

; (c)

T j ? A j a n d T j ? B j

; (d)

T j ? A j a n d T j ? B j

Tab.1 Benchmark datasets

Fig.2 Illustration of differences on salient feature groups between our approach and TreeSHAP (individual features)

Datasets	Our approach	TreeSHAP	ACVTree	TreeInterpret	LocalMDI	GlobalMDI	SplitCount	GroupSHAP
Diabetes	.8382 $±$ .0331	.7924 $±$ .0318 $?$	.8155 $±$ .0293 $?$	.8171 $±$ .0309 $?$	.7933 $±$ .0287 $?$	.8021 $±$ .0309 $?$	.7629 $±$ .0298 $?$	N/A
Australia	.8709 $±$ .0113	.8591 $±$ .0189 $?$	N/A	.8517 $±$ .0174 $?$	.7965 $±$ .0298 $?$	.8180 $±$ .0317 $?$	.5077 $±$ .0505 $?$	.8602 $±$ .0248 $?$
Vehicle	.6480 $±$ .0324	.6276 $±$ .0303 $?$	N/A	.5961 $±$ .0376 $?$	.5361 $±$ .0291 $?$	.4334 $±$ .0407 $?$	.2956 $±$ .0395 $?$	N/A
Collins	.9126 $±$ .0178	.8992 $±$ .0151 $?$	.8848 $±$ .0208 $?$	.8672 $±$ .0222 $?$	.8258 $±$ .0291 $?$	.7731 $±$ .0352 $?$	.7822 $±$ .0302 $?$	N/A
Phishing	.7573 $±$ .0219	.7449 $±$ .0249 $?$	.7474 $±$ .0243	.7428 $±$ .0243 $?$	.7165 $±$ .0267 $?$	.7333 $±$ .0312 $?$	.4647 $±$ .0486 $?$	N/A
Segment	.7864 $±$ .0282	.7380 $±$ .0317 $?$	N/A	.6651 $±$ .0357 $?$	.6487 $±$ .0034 $?$	.6406 $±$ .0348 $?$	.3941 $±$ .0420 $?$	N/A
Ginaprior	.9198 $±$ .0029	.9184 $±$ .0014	N/A	.8056 $±$ .0264 $?$	.8266 $±$ .0215 $?$	.7621 $±$ .0253 $?$	.6397 $±$ .0347 $?$	N/A
Texture	.6884 $±$ .0390	.6275 $±$ .0396 $?$	5952 $±$ .0397 $?$	.5815 $±$ .0410 $?$	.5654 $±$ .0419 $?$	.5114 $±$ .0445 $?$	.4476 $±$ .0417 $?$	N/A
Mushro	.9783 $±$ .0126	.9766 $±$ .0141	N/A	.9782 $±$ .0146	.9640 $±$ .0156 $?$	.9195 $±$ .0223 $?$	.8340 $±$ .0322 $?$	N/A
Indian	.7806 $±$ .0348	.6646 $±$ .0365 $?$	N/A	.7067 $±$ .0351 $?$	.6823 $±$ .0390 $?$	.5387 $±$ .0441 $?$	.4908 $±$ .0435 $?$	N/A
Har	.9796 $±$ .0020	.9718 $±$ .0075 $?$	N/A	.9614 $±$ .0123 $?$	.9580 $±$ .0097 $?$	.6208 $±$ .0463 $?$	.8058 $±$ .0330 $?$	N/A
Pendigits	.6310 $±$ .0432	.5655 $±$ .0426 $?$	.5233 $±$ .0411 $?$	.4769 $±$ .0454 $?$	.4689 $±$ .0435 $?$	.2770 $±$ .0392 $?$	.1755 $±$ .0347 $?$	N/A
Drybean	.5112 $±$ .0444	.5030 $±$ .0377	.4487 $±$ .0407 $?$	.4767 $±$ .0410 $?$	.4665 $±$ .0439 $?$	.4253 $±$ .0438 $?$	.1488 $±$ .0.301 $?$	N/A
Eggeye	.6579 $±$ .0337	.5547 $±$ .0393 $?$	N/A	.5816 $±$ .0408 $?$	.5123 $±$ .0348 $?$	.5092 $±$ .0474 $?$	.4971 $±$ .0232 $?$	.6405 $±$ .0170 $?$
Magic04	.5447 $±$ .0413	.5207 $±$ .0374 $?$	.5172 $±$ .0396 $?$	.4944 $±$ .0415 $?$	.4737 $±$ .0339 $?$	.4314 $±$ .0396 $?$	.4540 $±$ .0362 $?$	.5224 $±$ .0406 $?$
Bank	.8356 $±$ .0271	.8163 $±$ .0271 $?$	N/A	.8127 $±$ .0261 $?$	.8304 $±$ .0273	.8089 $±$ .0282 $?$	.8170 $±$ .0312 $?$	N/A
Shuttle	.8524 $±$ .0267	.7830 $±$ .0381 $?$	.8038 $±$ .0387 $?$	.7738 $±$ .0340 $?$	.7397 $±$ .0351 $?$	.7347 $±$ .0341 $?$	.5970 $±$ .0389 $?$	.8322 $±$ .0221 $?$
Sensor	.9184 $±$ .0239	.8886 $±$ .0256 $?$	N/A	.8391 $±$ .0284 $?$	.8154 $±$ .0340 $?$	.7089 $±$ .0408 $?$	.6597 $±$ .0367 $?$	N/A
Mnist	.9499 $±$ .0010	.9504 $±$ .0002	N/A	.8957 $±$ .0178 $?$	.8490 $±$ .0214 $?$	.8743 $±$ .0146 $?$	.8703 $±$ .0187 $?$	N/A
Fmnist	.8518 $±$ .0015	.7529 $±$ .0146 $?$	N/A	.7239 $±$ .0129 $?$	.7143 $±$ .0012 $?$	.2732 $±$ .0217 $?$	.2261 $±$ .0229 $?$	N/A
Average	.7955 $±$ .1372	.7578 $±$ .1503	?	.7324 $±$ .1518	.7092 $±$ .1551	.6298 $±$ .1891	.5435 $±$ .2203	?
Win/tie/loss		16/4/0	20/0/0	19/1/0	19/1/0	20/0/0	20/0/0	20/0/0

Tab.2 Comparisons of the testing accuracies (mean

±

std) for random forests classifiers.

?

indicates that our approach is significantly better than the corresponding methods for the selections of salient feature groups (pairwise

t

-test at

95 %

significance level). N/A means that the corresponding method does not return results within 72 hours

Fig.3 Comparisons on the selections of salient feature groups with different cardinalities, where we scale the cardinality of salient feature groups to

[0, 1]

. The higher the curve, the better the performance. (a) Diabetes; (b) texture; (c) pendigits; (d) eggeye; (e) magic04; (f) shuttle

Fig.4 Comparisons of the running time on 10 benchmark datasets (in seconds). Notice that the y-axis is in log-scale and full black columns imply that no result was obtained after running out 72 hours

Fig.5 Comparisons of interpretation visualization between our approach and other compared methods

Fig.6 Comparisons on different baseline combinations, where we scale the cardinality of salient feature groups to

[0, 1]

. The higher the curve, the better the performance. (a) Texture; (b) pendigits; (c) drybean

Fig.7 Comparisons on different parameter

κ

, where we scale the cardinality of salient feature groups to

[0, 1]

. The higher the curve, the better the performance. (a) Texture; (b) pendigits; (c) drybean

Datasets	Our approach	TreeSHAP	ACVTree	TreeInterpret	LocalMDI	GlobalMDI	SplitCount	GroupSHAP
Diabetes	.9316 $±$ .0145	.8334 $±$ .0296 $?$	.8850 $±$ .0253 $?$	.8593 $±$ .0310 $?$	.8961 $±$ .0199 $?$	.7803 $±$ .0312 $?$	.6239 $±$ .0411 $?$	.9173 $±$ .0017 $?$
Australia	.8564 $±$ .0215	.8371 $±$ .0312 $?$	.7119 $±$ .0348 $?$	.8318 $±$ .0194 $?$	.8588 $±$ .0160	.6798 $±$ .0338 $?$	.5054 $±$ .0438 $?$	.8293 $±$ .0155 $?$
Vehicle	.6910 $±$ .0315	.6359 $±$ .0344 $?$	.6001 $±$ .0328 $?$	.6478 $±$ .0318 $?$	.5651 $±$ .0341 $?$	.4452 $±$ .0392 $?$	.2739 $±$ .0388 $?$	N/A
Collins	.9805 $±$ .0022	.9798 $±$ .0016	.9519 $±$ .0129 $?$	.9755 $±$ .0046 $?$	.9686 $±$ .0014 $?$	.9655 $±$ .0182 $?$	.9518 $±$ .0028 $?$	N/A
Phishing	.7623 $±$ .0320	.7616 $±$ .0275	.7283 $±$ .0346 $?$	.7343 $±$ .0299 $?$	.7013 $±$ .0294 $?$	.7124 $±$ .0337 $?$	.4327 $±$ .0501 $?$	N/A
Segment	.9353 $±$ .0102	.9043 $±$ .0152 $?$	.8771 $±$ .0204 $?$	.8774 $±$ .0151 $?$	.9012 $±$ .0151 $?$	.7707 $±$ .0216 $?$	.3951 $±$ .0444 $?$	N/A
Ginaprior	.8519 $±$ .0129	.8663 $±$ .0063 $∘$	N/A	.7750 $±$ .0270 $?$	.7668 $±$ .0272 $?$	.8704 $±$ .0045 $∘$	.8737 $±$ .0043 $∘$	N/A
Texture	.8592 $±$ .0138	.7990 $±$ .0273 $?$	.8223 $±$ .0228 $?$	.8265 $±$ .0202 $?$	.8406 $±$ .0178 $?$	.5336 $±$ .0375 $?$	.5641 $±$ .0444 $?$	N/A
Mushro	.9998 $±$ .0010	.9543 $±$ .0233 $?$	.9568 $±$ .0223 $?$	.9956 $±$ .0045 $?$	.9926 $±$ .0065 $?$	.9065 $±$ .0197 $?$	.8981 $±$ .0279 $?$	N/A
Indian	.7974 $±$ .0131	.7541 $±$ .0321 $?$	N/A	.6723 $±$ .0376 $?$	.6738 $±$ .0422 $?$	.4709 $±$ .0415 $?$	.5132 $±$ .0377 $?$	N/A
Har	.9208 $±$ .0086	.9221 $±$ .0113	N/A	.8938 $±$ .0157 $?$	.9077 $±$ .0149 $?$	.9105 $±$ .0018 $?$	.9026 $±$ .0025 $?$	N/A
Pendigits	.4807 $±$ .0394	.4284 $±$ .0439 $?$	.4481 $±$ .0383 $?$	.3824 $±$ .0366 $?$	.3891 $±$ .0331 $?$	.3331 $±$ .0407 $?$	.3077 $±$ .0413 $?$	.4360 $±$ .0419
Drybean	.7089 $±$ .0338	.6561 $±$ .0471 $?$	.5924 $±$ .0327 $?$	.6647 $±$ .0331 $?$	.5789 $±$ .0404 $?$	.4923 $±$ .0404 $?$	.1914 $±$ .0394 $?$	.6871 $±$ .0266 $?$
Eggeye	.6456 $±$ .0360	.6225 $±$ .0395 $?$	.5439 $±$ .0352 $?$	.6019 $±$ .0362 $?$	.5467 $±$ .0379 $?$	.5608 $±$ .0416 $?$	.4536 $±$ .0428 $?$	.6459 $±$ .0106
Magic04	.6639 $±$ .0461	.6232 $±$ .0437 $?$	.5303 $±$ .0405 $?$	.5398 $±$ .0441 $?$	.5309 $±$ .0471 $?$	.5051 $±$ .0445 $?$	.5203 $±$ .0410 $?$	.6220 $±$ .0429 $?$
Bank	.6878 $±$ .0394	.5894 $±$ .0418 $?$	.5656 $±$ .0439 $?$	.4823 $±$ .0503 $?$	.4931 $±$ .0466 $?$	.5186 $±$ .0496 $?$	.6141 $±$ .0403 $?$	.6790 $±$ .0286 $?$
Shuttle	.8721 $±$ .0305	.9271 $±$ .0207 $∘$	.6764 $±$ .0361 $?$	.8607 $±$ .0304 $?$	.7987 $±$ .0259 $?$	.5671 $±$ .0446 $?$	.6728 $±$ .0261 $?$	.9018 $±$ .0262 $∘$
Sensor	.9426 $±$ .0169	.7174 $±$ .0311 $?$	N/A	.8635 $±$ .0201 $?$	.9011 $±$ .0147 $?$	.6136 $±$ .0387 $?$	.6443 $±$ .0316 $?$	N/A
Mnist	.8976 $±$ .0057	.8985 $±$ .0036	N/A	.7251 $±$ .0236 $?$	.7324 $±$ .0139 $?$	.8618 $±$ .0016 $?$	.7046 $±$ .0265 $?$	N/A
Fmnist	.8108 $±$ .0026	.7247 $±$ .0050 $?$	N/A	.6755 $±$ .0136 $?$	.6947 $±$ .0110 $?$	.4330 $±$ .0082 $?$	.2512 $±$ .0046 $?$	N/A
Average	.8148 $±$ .1306	.7716 $±$ .1428	?	.7443 $±$ .1582	.7370 $±$ .1701	.6465 $±$ .1840	.5647 $±$ .2201	?
Win/tie/loss		14/4/2	20/0/0	20/0/0	19/1/0	19/0/1	19/0/1	17/2/1

Tab.3 Comparisons of the testing accuracies (mean

±

std) for individual decision trees.

?

∘

indicates that our approach is significantly better/worse than the corresponding methods for the selections of salient feature groups (pairwise

t

-test at

95 %

significance level). N/A means that the corresponding method does not return results within 72 hours

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