経営課題にAIを!ビジネスインフォマティクス研究会 (第13回)
JSAI Special Interest Group on Business Informatics (SIG-BI #13)

࣮਺஋ GA Λ‫ਂͨ͠༻׆‬૚ֶशϞσϧʹ͓͚ΔύϥϝʔλͱΠϯϓοτσʔλͷॏཁ౓ͷਪ‫ܭ‬Estimation of importance of parameters and input data in deeplearning models using real-coded GAখാਸ߂ 1 ૔‫ڮ‬અ໵ 1
Takahiro Obata1
Setsuya Kurahashi11ஜ೾େֶେֶӃϏδωεՊֶ‫ڀݚ‬Պ
1
University of Tshukuba

Abstract: ۙ೥ɺը૾ղੳͷ෼໺Λ͸͡Ίͱͯ͠ਂ૚ֶशϞσϧ΁ͷ‫ظ‬଴͕ߴ·ΔҰํɺෳࡶͳϒϥοΫϘοΫεϞσϧͰ͋Δ͜ͱʹର͢Δ‫ݒ‬೦΋ࢦఠ͞Ε͖͓ͯͯΓɺϞσϧͷղऍੑɾઆ໌ੑʹؔ
͢Δ‫͕ڀݚ‬੝ΜʹߦΘΕ͍ͯΔɻຊ‫Ͱڀݚ‬͸ɺਂ૚ֶशϞσϧͷύϥϝʔλਪ‫਺࣮ʹܭ‬஋ GA Λద༻͠ɺ࣮਺஋ GA ͷҨ఻ࢠͷ෼ࢄΛ‫ͨ͠༻׆‬ม਺બ୒ख๏Λ‫ਂ͔ͯ͠׆‬૚ֶशϞσϧ಺ʹ͓͚ΔΠϯϓοτσʔλͷॏཁ౓ΛఆྔతʹධՁͰ͖Δ࢓૊ΈΛߏங͠ɺϞσϧͷղऍੑ޲্Λ໨ࢦ͢ɻ1͸͡Ίʹۙ೥ɼ༷ʑͳ෼໺Ͱ‫ػ‬ցֶशͷख๏͕‫͞༻׆‬Ε͖͓ͯͯΓɼதͰ΋ը૾ղੳ΍Ի੠ೝࣝͱ͍ͬͨ෼໺Λத৺ʹਂ૚ֶशϞσϧͷ‫͍͕ͯͬ޿͕༻׆‬ΔɽҰํͰɼ͜ΕΒͷϞσϧ͕ෳࡶͳϒϥοΫϘοΫεϞσϧͰ͋Δ͜ͱʹର͢Δ‫ݒ‬೦΋ࢦఠ͞Ε͖͓ͯͯΓɼϞσϧͷղऍੑɾઆ໌ੑʹؔ͢Δ‫͕ڀݚ‬੝ΜʹߦΘΕ͍ͯΔ [1]ɽຊ‫Ͱڀݚ‬͸ɼਂ૚ֶशϞσϧͷύϥϝʔλਪ‫࣮ʹܭ‬਺஋Ҩ఻తΞϧΰϦζϜʢ࣮਺஋ GA,RCGAʣΛద༻͠ɼRCGA ͷҨ఻ࢠͷ෼ࢄΛ‫ͨ͠༻׆‬ม਺બ୒ख๏Λ‫ਂ͔ͯ͠׆‬૚ֶशϞσϧ಺ʹ͓͚ΔΠϯϓοτσʔλͷॏཁ౓ΛఆྔతʹධՁͰ͖Δ࢓૊ΈΛߏங͠ɼϞσϧͷղऍੑ޲্Λ໨ࢦ͢ɽຊߘͷߏ੒͸࣍ͷ௨ΓͰ͋ΔɽSection 2 Ͱɼؔ࿈‫ݚ‬‫ਂͯ͠ͱڀ‬૚ֶशϞσϧʹ͓͚Δ֤Πϯϓοτσʔλͷߩ‫ݙ‬ΛଌΔख๏ͷҰͭͰ͋Δ LRP ͓Αͼ RCGA ͷҨ఻ࢠͷ෼ࢄΛ‫ͨ͠༻׆‬ม਺બ୒‫ج‬४ I ஋ུ͍ͭͯ֓
͢ΔɽSection 3 Ͱ͸ਂ૚ֶशϞσϧͷղऍੑΛߴΊΔ৽ͨͳख๏ΛఏҊ͢ΔɽSection 4 ͸ఏҊख๏Λ‫͢༻׆‬Δ͜ͱͰ‫ظ‬଴͞ΕΔ੒Ռʹ͍ͭͯͰ͋Δɽ2ؔ࿈‫ڀݚ‬

2.1

Layer-Wise Relevance Propagationਂ૚ֶशϞσϧͷղऍੑɾઆ໌ੑΛ޲্ͤ͞Δ‫ڀݚ‬Ͱ͸ɼग़ྗ͔ΒೖྗΛ‫ʹٯ‬୧Δ͜ͱͰϞσϧͷग़ྗʹେ͖ͳӨ‫ڹ‬Λ༩͑ΔΠϯϓοτσʔλΛಛఆ͢Δख๏͕ଟ͘ఏҊ͞Ε͍ͯΔɽ୅දతͳख๏ͷҰͭʹ LRP
ʢLayer-Wise Relevance Propagationʣ͕͋Δ [2]ɽLRP ͸ɼ֤૚͝ͱʹग़ྗʹର͢Δ֤ೖྗͷߩ‫ݙ‬ʢRelevanceʣͷ૯࿨Λ‫ͦͯ͠ࢉܭ‬ΕΛલͷ૚ʹ఻ൖͤ͞ΔॲཧΛೖྗ૚·Ͱ‫܁‬Γฦ͢͜ͱͰग़ྗʹେ͖ͳӨ‫ڹ‬Λ༩͑ΔΠϯϓοτσʔλΛಛఆ͠Α͏ͱ͢Δख๏Ͱ͋ΔɽLRP ͷৄࡉʹೖΔલʹਂ૚ֶशϞσϧΛఆࣜԽ͔Β࢝ΊΔɽਂ૚ֶशϞσϧ಺ͷ͋Δϊʔυ j ͔Βͷग़ྗΛ xj ͱ͠ɼ‫׆‬ੑԽؔ਺Λ g Ͱද͢ͱ͢Δͱɼxj ͸࣍ͷΑ͏ʹදͤΔɽ!
xj = g(wij xi + b)(1)i͜͜Ͱ wij ͸ϊʔυ i ͔Βϊʔυ j ʹ޲͚ͨग़ྗʹର͢Δਂ૚ֶशϞσϧ಺Ͱͷ΢ΣΠτΛද͢ɽೖྗσʔληοτ x ͕ਂ૚ֶशϞσϧ f Λ‫ͯܦ‬ग़ྗ͞ΕΔ݁ՌΛ f (x) ͱ͢Δͱɼͦͷग़ྗʹର͢Δ֤ೖྗσʔλ p ͷߩ‫ݙ‬͸࣍ࣜͷΑ͏ʹදͤΔɽ
!
f (x) ≈
Rp(1)(2)p࣍ʹ LRP ΛఆࣜԽ͢Δɽਂ૚ֶशϞσϧ಺ͷ૚ l ʹ͋Δϊʔυ i ͷߩ‫ݙ‬͸! zij(l)(l+1)(l,l+1)"Ri =Rjwith zij = xli wij(3)′i ′ zi jj

ͱදͤΔɽ͞Βʹ͜ΕΛվྑͨ͠ख๏΋‫͔ͭز‬ఏҊ͞Ε͓ͯΓɼz ͷූ߸͝ͱʹ‫͢ࢉܭ‬Δख๏͕਺ࣜ (4) Ͱ経営課題にAIを!ビジネスインフォマティクス研究会 (第13回)
JSAI Special Interest Group on Business Informatics (SIG-BI #13)

͋Δɽ
(l)

Ri =!#j−zij+zij(1 + β) "+ −β"−i ′ zi ′ j
i ′ zi ′ j$4(l+1)Rj(4)RCGA ͷҨ఻ࢠͷ෼ࢄΛ‫ͨ͠༻׆‬ม਺બ୒‫ج‬४2.2Ҩ఻తΞϧΰϦζϜ͸ਐԽ‫ࢉܭ‬ͷҰछͰɼ‫ʹڥ؀‬దԠͨ͠ੜ෺͕ੜ͖࢒ΓɼదԠͰ͖ͳ͔ͬͨੜ෺͕ࢮ໓͢Δࣗવ౫ଡͷߟ͑ํ͕औΓೖΕΒΕ͓ͯΓ [3]ɼ(1)໨తؔ਺ͷඍ෼ՄೳੑΛԾఆ͢Δඞཁ͕ͳ͍ɼ(2) େҬత୳ࡧ͕Մೳɼͱ͍ͬͨಛ௃Λ࣋ͭɽGA Ͱ͸Ҩ఻ࢠ‫͔͘ݹͯ͠ͱܕ‬Β 0 ͱ 1 ʹΑΔϏοτίʔσΟϯά͕࢖ΘΕ͖͕ͯͨɼ࣮਺஋Λѻ͏࠷దԽ໰୊Ͱ͸ղ୳ࡧʹແବ͕ੜ͡ΔՄೳੑ͕ࢦఠ͞Ε͖ͯͨɽ͜͏ͨ͠ࢦఠʹରԠͨ͠ͷ͕ɼҨ఻ࢠ‫ͯ͠ͱܕ‬࣮਺஋ϕΫτϧΛѻ͏ RCGA Ͱ͋Δ [4]ɽRCGA ͰύϥϝʔλਪఆΛߦ͏ࡍʹɼRCGA ͷҨ఻ࢠͷ෼ࢄΛม਺બ୒ʹ‫͢༻׆‬Δํ๏Λ‫ݕ‬౼ͨ͠‫ʹڀݚ‬[5] ͕͋Δɽ[5] Ͱ͸ɼ(5) ࣜͰද͞ΕΔ I ஋ΛఏҊ͠ɼI஋͕ઢ‫ܗ‬ॏճ‫ؼ‬Ϟσϧʹ͓͚Δ T ஋ͷ 2 ৐ʹൺྫ͢Δ͜ͱΛ֬ೝͨ͠ɽ

Ii =νi2Vgi(5)Ii ͸෼ੳϞσϧ಺ͷ͋Δύϥϝʔλ ai ʹର͢Δ I ஋Ͱ
͋Δ. νi ͸ύϥϝʔλ ai ͷਪఆ஋ɼVgi ͸ಉҰੈ୅಺ͷ‫ݸ‬ମͷύϥϝʔλ ai ʹରԠ͢ΔҨ఻ࢠͷ෼ࢄΛද͢ɽ3෼ੳํ๏ຊߘͰ͸‫ڀݚ‬ͷ୺ॹͱͯ͠ɼճ‫ؼ‬༧ଌΛߦ͏ਂ૚ֶशϞσϧΛѻ͏ɽ·ͣɼRCGA ʹΑΓਂ૚ֶशϞσϧͷ֤૚Λͭͳ͙ωοτϫʔΫͷ΢ΣΠτΛਪఆ͢Δɽ࣍ʹɼҰఆੈ୅਺ RCGA ΛਐΊΔ͝ͱʹલड़ͷ LRP ͱ I ஋Λ૊Έ߹Θͤͨ (6) ࣜ·ͨ͸ (7) ࣜͷ஋Λ‫͢ࢉܭ‬Δɽ
! Iij zij (l+1)(l)"Ri =Rj(6)′i ′ zi jj(l)
Ri =!
jIij

#

$+−zijzij(l+1)(1 + β) " + − β " − Rj
(7)i ′ zi ′ j
i ′ z i′ j

RCGA ͕ऴྃͨ࣌͠఺ͰվΊͯ͜ͷ 2 छྨͷ஋Λ‫ࢉܭ‬͠ɼग़ྗʹର͢ΔΠϯϓοτσʔλͷߩ‫ݙ‬ΛධՁ͢Δɽͳ͓ɼຊߘͰ͸ RCGA ͷੈ୅ަ୅Ϟσϧͱͯ͠ Just
Generation Gap (JGG) ΛɼަࠥϞσϧͱͯ͠ AREXΛ༻͍ͨ [6][7][8]ɽJGG ͱ AREX ͷ૊Έ߹Θͤ͸ղͷ୳ࡧೳྗʹ༏Εͨ୅දతͳ૊Έ߹ΘͤͰ͋Δɽ‫ظ‬଴͞ΕΔ੒ՌຊߘͰఏҊͨ͠ख๏ʹΑͬͯɼਂ૚ֶशϞσϧ಺ͷωοτϫʔΫΛ௨ͯ͡఻ΘΔ஋ͷେ͖͚ͩ͞Ͱͳ͘ɼͦͷ༗ҙੑΛՃຯͯ͠ग़ྗʹର͢Δ֤Πϯϓοτσʔλͷߩ‫ݙ‬ΛධՁͰ͖ΔΑ͏ʹͳΔͱߟ͑Β͑ΔɽఏҊख๏ʹΑΓɼ‫ػ‬ցֶशʹ͓͚Δղऍੑ޲্ͱͱ΋ʹઆ໌ͷ৴པੑΛߴΊΔޮՌ΋‫ظ‬଴Ͱ͖Δɽࠓ‫ޙ‬͸ LRP ͱ I ஋Λ૊Έ߹ΘͤΔํ๏Ͱผͷ΍ΓํΛ‫ݕ‬౼͢Δͱͱ΋ʹɼLRP Ҏ֎ͷਂ૚ֶशϞσϧղऍख๏ͱͷ૊Έ߹Θͤ΋‫ݕ‬౼͍͖͍ͯͨ͠ͱߟ͍͑ͯΔɽࢀߟจ‫ݙ‬[1] ‫ݪ‬૱ ɿ‫ػ‬ցֶशʹ͓͚Δղऍੑɼ ਓ޻஌ೳֶձ
ࢽ 33(3), pp. 366–369,ʢ2018ʣ
[2] Alexander Binder et al: Layer-Wise Relevance
Propagation for Deep Neural Network Architectures, Information Science and Applications(ICISA) pp. 913-922 (2016)[3] David E. Goldberg ɿGenetic Algorithms inSearch, Optimization and Machine Learningɼ
Addison Wesley Longman Publishing Co. Inc.,(1989)[4] Alden H. Wright ɿGenetic Algorithms for RealParamter Optimization, Foundations of GeneticAlgorithms, pp. 205-218 (1991)[5] Takahiro Obata and Setsuya Kurahashi: A Studyof Variable Selection within A Framework ofReal-coded Genetic Algorithm, 2018 IEEE International Conference on Systems, Man, and Cybernetics (IEEE SMC 2018)[6] ळຊ༸ฏ, Ӌࠤాཧ‫ܙ‬, ࠤ‫ؒٱ‬३, খ໺ޭ, খྛॏ৴ɿଟ਌Λ༻͍࣮ͨ਺஋ GA ͷͨΊͷੈ୅ަ୅Ϟσϧʙ Just Generation Gap (JGG) ͷఏҊͱධՁʙɼSICE ୈ 19 ճࣗ཯෼ࢄγεςϜγϯϙδ΢Ϝࢿྉɼpp. 341-346 (2007)[7] ळຊ༸ฏ, Ӌࠤాཧ‫ܙ‬, ࠤ‫ؒٱ‬३, খ໺ޭ, খྛॏ৴ɿదԠత࣮਺஋ަࠥ AREX ͷఏҊͱධՁɼਓ޻஌ೳֶձࢽ 24(6), pp. 446–458,ʢ2009ʣ
[8] Youhei Akimoto, Jun Sakuma, Isao Ono, andShigenobu Kobayashi ɿAdaptation of expansion
rate for real-coded crossovers, Proc. of the 11th
Annual Conf. on Genetic and Evolutionary Computation (GECCO’09), pp. 739-746 (2009)