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人工知能全国大会 発表資料
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WY
June 13, 2023
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人工知能全国大会 発表資料
WY
June 13, 2023
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Transcript
KYOTO UNIVERSITY KYOTO UNIVERSITY 1 ܈ͷ୯Ұεφο プ γϣοτ͔Βͷ ूஂ ダ
ΠφϛΫεͷ෮ݩ ɹएҪ ༤لɹ ɹࣛౡ ٱ࢚ ژେֶ
KYOTO UNIVERSITY 2 ݚڀഎܠ
KYOTO UNIVERSITY 3 ݚڀഎܠ ܈σʔλͷੳ༷ʑͳͰߦΘΕ͍ͯΔ ▪ ۙɺσʔλੳ͕ΜʹߦΘΕ͍ͯΔ͕ɺ σʔλܗࣜͷ1छʹ܈σʔλ͕͋Δ ▪
܈σʔλͷྫͱͯ͠܈ऺͷGPSσʔλ͕ଘࡏ͢Δ ▪ ܈σʔλͷੳʹɺ ɾۙ୳ࡧ ɾΫϥελϦϯά ɾ༧ଌ ͱ͍ͬͨλεΫ͕ߟ͑ΒΕΔ
KYOTO UNIVERSITY 4 ݚڀഎܠ ܈σʔλͷ༧ଌ༷ʑͳͰߦΘΕ͍ͯΔ ▪ ܈σʔλͷ༧ଌͱɺ͋Δ࣌ࠁͷ܈σʔλ͔Β ࣍ͷ࣌ࠁͷ֤ͷಈ͖Λਪఆ͢ΔੳͰ͋Δɻ
▪ ܈σʔλͷ༧ଌݱࡏ༷ʑͳͰߦΘΕ͍ͯΔɻ ɾGPSσʔλ͔Βͷߦಈ༧ଌ ɾࡉ๔ूஂͷҨࢠൃݱղੳ ɾϚϧνλʔήοτ
KYOTO UNIVERSITY 5 ຊݚڀͷઃఆ ܈ͷ༧ଌͰɺ܈ͷ࠲ඪ͔Β֤ͷಈ͖Λ෮ݩ͢Δ ▪ ܈σʔλͷ༧ଌͱ 、 ͋Δ࣌ࠁͷ܈Λೖྗͱͯ͠ ࣍ͷ࣌ࠁͷ֤ͷಈ͖Λग़ྗ͢Δ͜ͱ
ೖྗ ग़ྗ
KYOTO UNIVERSITY 6 ຊݚڀͷઃఆ ܈ͷ༧ଌͱɺूஂͷμΠφϛΫεͷ෮ݩͰ͋Δ ▪ ͭ·Γ܈σʔλͷ༧ଌͱɺ ܈શମͷ࣌ؒൃలʢμΠφϛΫεʣΛਪఆ͢Δ ೖྗ
ग़ྗ
KYOTO UNIVERSITY 7 ݚڀഎܠ ຊݚڀ୯࣌ࠁͰ࠲ඪͷΈͷ܈σʔλ͔ΒيΛਪఆ͢Δ ▪ GPSσʔλղੳҨࢠൃݱղੳͰɺ ෳ࣌ࠁͰಉҰͷ܈ΛͰ͖ͳ͍έʔε͕ଘࡏ ▪
طଘݚڀɺෳ࣌ࠁͰಉ࢜ͷରԠ͕औΕͳ͍߹ ɺ୯࣌ࠁͰ֤ͷಛྔ͕๛ͳ߹͕ର ▪ ຊݚڀͰɺ ୯࣌ࠁ͔֤ͭͷಛྔ࠲ඪͷΈͷ߹Λѻ͏
KYOTO UNIVERSITY 8 ຊݚڀͷߩݙ ಈ͖ͷͳ͍܈ͷ࠲ඪ͔Β֤ͷಈ͖Λ෮ݩ ▪ ຊݚڀͰɺʮ୯࣌ࠁ͔֤ͭͷಛྔ࠲ඪͷΈʯ ͷ܈σʔλ͔Β֤ͷيΛਪఆͨ͠ɻ ▪ ͢ͳΘͪɺ
ಈ͖ͷͳ͍܈ͷ࠲ඪ͔Β֤ͷಈ͖Λ෮ݩͨ͠ɻ ▪ ຊݚڀͰɺ࠷దԽͷతؔશମͷఆࣜԽख๏ ΛఏҊ͠ɺͦΕΛղ͘ΞϧΰϦζϜߟҊͨ͠ɻ
KYOTO UNIVERSITY 9 ఏҊख๏
KYOTO UNIVERSITY 10 ຊݚڀͷઃఆ ܈ͷ࠲ඪ͔Βɺ֤ͷϕΫτϧΛ෮ݩ ▪ ೖྗ: ܈தͷ ͷ࠲ඪ
ग़ྗ: ܈ͷ֤ͷϕΫτϧ ▪ ಈ͖ͷͳ͍܈ͷ࠲ඪ͔Β֤ͷಈ͖Λ෮ݩ͢Δ N x1 , …, xN ∈ RD f1 , …, fN ∈ RD ೖྗ ग़ྗ
KYOTO UNIVERSITY 11 ຊݚڀͷఏҊख๏ ఏҊख๏Ͱ2ͭͷԾఆΛͱʹ࠷దԽͱͯ͠ఆࣜԽ ▪ ఏҊख๏Ͱ2ͭͷԾఆΛஔ͘ Ծఆ 1:
֤1࣌ࠁޙʹۙભҠ֬ ͰҠಈ Ծఆ 2: ۙؒͰϕΫτϧ Β͔ ▪ 2ͭͷԾఆ͔Β࠷దԽʹؼணͤ͞Δ pij f fi i j k xi xj vij fk pij xk vjk pjk fj
KYOTO UNIVERSITY 12 ຊݚڀͷఏҊख๏ ఏҊख๏Ͱ2ͭͷԾఆΛͱʹ࠷దԽͱͯ͠ఆࣜԽ ▪ ఏҊख๏Ͱ2ͭͷԾఆΛஔ͘ Ծఆ 1:
֤1࣌ࠁޙʹۙભҠ֬ ͰҠಈ Ծఆ 2: ۙؒͰϕΫτϧ Β͔ ▪ 2ͭͷԾఆ͔Β࠷దԽʹؼணͤ͞Δ pij f fi i j k xi xj vij fk pij xk vjk pjk fj
KYOTO UNIVERSITY 13 ຊݚڀͷઃఆ(࠶ܝ) ܈ͷ࠲ඪ͔Βɺ֤ͷϕΫτϧΛ෮ݩ ▪ ೖྗ: ܈தͷ ͷ࠲ඪ
ग़ྗ: ܈ͷ֤ͷϕΫτϧ N x1 , …, xN ∈ RD f1 , …, fN ∈ RD ೖྗ ग़ྗ
KYOTO UNIVERSITY 14 ຊݚڀͷఏҊख๏ ࠷దԽͷతؔ(ଛࣦؔ) ▪ ࠷খԽ͢Δతؔ
Ծఆ 1: ֤1࣌ࠁޙʹपғͷۙʹҠಈ ▪ ͔Β ͷભҠ֬ ͕େ͖͍ͱ͖ɺ ͕ۙϕΫτϧ ʹྨࣅ͢ΔΑ͏ʹ࠷దԽ i j pij fi vij ଛࣦؔ ※ ͷۙ j i ※ ͔Β ͷҐஔϕΫτϧ vij i j fi i j xi xj vij pij fj
KYOTO UNIVERSITY 15 ຊݚڀͷఏҊख๏ ࠷దԽͷతؔ(ฏԽ߲ɾՃฏԽ߲) ▪ ࠷খԽ͢Δతؔ
▪ Ծఆ 2: ۙؒͰϕΫτϧΒ͔ ▪ ۙͷϕΫτϧ , , ͕ ྨࣅ͢ΔΑ͏ʹ࠷దԽ fi fj fk ՃฏԽ߲ ฏԽ߲ ※ ͷۙɺ ͷۙ j i k j fi i j k xi xj vij fk pij xk vjk pjk fj
KYOTO UNIVERSITY 16 ຊݚڀͷఏҊख๏ ભҠ֬࠷ద༌ૹΛղ͘͜ͱͰಘΒΕΔ ▪ ͔Β ͷભҠ֬ ͲͷΑ͏ʹఆΊΔ͔ʁ
▪ ఏҊख๏Ͱɺ࠷ద༌ૹͷղΛٻΊͯ ભҠ֬ ΛఆΊΔ i j pij pij fi i j xi xj vij pij fj
KYOTO UNIVERSITY 17 ຊݚڀͷఏҊख๏ ࠷ద༌ૹ܈ؒͷ࣭ྔ༌ૹίετΛ࠷খԽ͢Δ ▪ ࠷ద༌ૹͱɺ ֤͕࣭ྔΛ࣋ͭ܈͕2ͭଘࡏ͠ɺ܈ؒͰॏΈΛ
༌ૹ͢Δ࣌ʹඞཁͳίετΛ࠷খԽ͢ΔͰ͋Δɻ ▪ ྫ ೖྗ ग़ྗ
KYOTO UNIVERSITY 18 ຊݚڀͷఏҊख๏ ભҠ֬࠷ద༌ૹΛղ͘͜ͱͰಘΒΕΔ ▪ ͔Β ͷભҠ֬ ͲͷΑ͏ʹఆΊΔ͔ʁ
▪ ༩͑ΒΕͨ܈͕ఆৗʹ͋ΔͱԾఆ͢Δͱɺ ֤ͷ࣭ྔ͕1ɺ࠲ඪ͕ಉҰͷ܈ؒͰ ࣗʹ༌ૹͰ͖ͳ͍࠷ద༌ૹʹؼண i j pij N ∑ i=1 pij = 1 (∀j, 1 ≤ j ≤ N), N ∑ j=1 pij = 1 (∀i, 1 ≤ i ≤ N) fi i j xi xj vij pij fj
KYOTO UNIVERSITY 19 ຊݚڀͷఏҊख๏ ֬ߦྻ ͱϕΫτϧ Λަޓ࠷దԽͯ͠ Λਪఆ͢Δ P f
f ▪ ࠷খԽ͢Δతؔ ▪ ؔશମඇತ͕ؔͩ ͱ ʹ͍ͭͯತؔ ▪ ͱ Λަޓʹ࠷దԽͯ͠ϕΫτϧ ΛٻΊΔɻ ࠷ద༌ૹΛղ͖ɺ ೋ࣍ܭըΛղ͘ɻ P f P f f P f ՃฏԽ߲ ฏԽ߲ ※ ͷۙɺ ͷۙ j i k j ଛࣦؔ
KYOTO UNIVERSITY 20 ࣮ݧ
KYOTO UNIVERSITY 21 ຊݚڀͷ࣮ݧઃఆ ࣮ݧʹ༻͍ͨσʔλͱධՁࢦඪ ▪ ࣮ݧͰϕΫτϧ͔Βੜͨ͠ਓσʔλΛར༻ (ઢܕɾٵҾܕɾճసܕɾӔרܕͷ4σʔλ) ▪
ਪఆ݁ՌͷϕΫτϧ ͷํͷҰக߹͍Λ ίαΠϯྨࣅͷ૯Λ༻͍ͯఆྔతʹධՁ f ઢܕ ٵҾܕ ճసܕ Ӕרܕ
KYOTO UNIVERSITY 22 ຊݚڀͷ࣮ݧ݁Ռ ฏԽɾՃฏԽʹΑΓେ෯ͳਫ਼্ ▪ ίαΠϯྨࣅͷ૯Λ༻͍ͯఆྔతʹධՁ ઢܕ ٵҾܕ ճసܕ
Ӕרܕ ۙϕΫτϧͷ ฏۉ 0.014 0.242 0.088 0.165 ଛࣦؔͷΈ 0.019 0.264 0.084 0.143 ฏԽ 0.057 0.567 0.311 0.480 ฏԽ+ ՃฏԽ 0.133 0.920 0.397 0.695
KYOTO UNIVERSITY 23 ຊݚڀͷ࣮ݧ݁Ռ ฏԽɾՃฏԽʹΑΔਪఆఆੑతʹྑ͍ ▪ ఏҊख๏ͷਪఆ݁ՌɺϕΫτϧͷ͖͕ۙͰἧ͏ ۙϕΫτϧͷฏۉ ฏԽ
+ ՃฏԽ
KYOTO UNIVERSITY 24 ຊݚڀͷ࣮ݧ݁Ռ ฏԽɾՃฏԽʹΑΔਪఆఆੑతʹྑ͍ ▪ ϕΫτϧͷେ͖͞ͷਪఆਫ਼͕ྑ͍ఔɺ֎͔Βͷ ৭ͷάϥσʔγϣϯ͕៉ྷʹͳΔ
ۙϕΫτϧͷฏۉ ฏԽ + ՃฏԽ
KYOTO UNIVERSITY 25 ݁
KYOTO UNIVERSITY 26 ݁ ܈ͷ࠲ඪ͔Βɺ֤ͷϕΫτϧΛ෮ݩ ▪ ೖྗ: ܈தͷ ͷ࠲ඪ
ग़ྗ: ܈ͷ֤ͷϕΫτϧ N x1 , …, xN ∈ RD f1 , …, fN ∈ RD ೖྗ ग़ྗ
KYOTO UNIVERSITY 27 ݁ ܈ͷ୯Ұεφο プ γϣοτ͔Βͷूஂ ダ ΠφϛΫεͷ෮ݩ
▪ ຊݚڀͰɺʮ୯࣌ࠁ͔֤ͭͷಛྔ࠲ඪͷΈʯ ͷ܈σʔλ͔Β֤ͷيΛਪఆͨ͠ɻ͢ͳΘͪɺ ಈ͖ͷͳ͍܈ͷ࠲ඪ͔Β֤ͷಈ͖Λ෮ݩͨ͠ɻ ▪ ຊݚڀͰɺ࠷దԽͷతؔશମͷఆࣜԽख๏ ΛఏҊ͠ɺͦΕΛղ͘ΞϧΰϦζϜߟҊͨ͠ɻ ▪ ࣮ݧͷ݁ՌɺฏԽͱՃฏԽʹΑΓ ਪఆਫ਼͕େ෯ʹ্͢Δ͜ͱ͕ࣔ͞Εͨɻ
KYOTO UNIVERSITY 28
KYOTO UNIVERSITY 29 ධՁࢦඪ ▪ ධՁҎԼͷΑ͏ʹఆΊΔɻ
ਪఆ͞ΕͨيϕΫτϧ ͱਖ਼ղͷϕΫτϧ ͷcosྨࣅΛ ٻΊɼͦͷฏۉͷઈରΛධՁͱ͢Δɻ ▪ ୯࣌ࠁͷ܈εφοϓγϣοτ͔ΒͰɼ֤͕ਖ਼ղͷϕΫ τϧͷ͖͔ਅରͷ͖ͷͲͪΒʹҠಈ͢Δ͔ΛܾఆͰ͖ ͳ͍ɻ͕ͨͬͯ͠ɺ࠷ޙʹઈରΛऔΔɻ fi f′  i
KYOTO UNIVERSITY 30 ܈σʔλͷੜखॱ 1. ܈σʔλΛੜ͢ΔϕΫτϧ ΛఆΊΔɻ 2. ϕΫτϧʹ͓͚Δॳظ
ΛϥϯμϜʹఆΊΔɻ 3. ϕΫτϧʹैͬͯॳظΛ1࣌ࠁ( )Ҡಈͤ͞Δɻ ͷͱ͖ɺ1࣌ࠁޙͷ࠲ඪ ͱͳΔɻ 4. 1ͭͷॳظʹ͍ͭͯɺ3ͷૢ࡞Λ ࣌ࠁ܁Γฦ͢ɻ 5. 2͔Β4·Ͱͷૢ࡞Λॳظ ݸ܁Γฦ͢ɻ࠷ऴతʹɺ ܈σʔλͷ૯ ͱͳΔɻ V : ℝD → ℝD x0 ∈ ℝD Δt V(x0 ) = v0 x0 + v0 Δt T − 1 N0 N N = TN0
KYOTO UNIVERSITY 31 ܈σʔλͷੜʹ༻͍ͨϕΫτϧ ٵҾܕ ઢܕ
KYOTO UNIVERSITY 32 ܈σʔλͷੜʹ༻͍ͨϕΫτϧ Ӕרܕ ճసܕ
KYOTO UNIVERSITY 33 ઢܕσʔλͰධՁͷ૬ࡴ͕ى͜ΓධՁ͕͘ͳΔ ۙϕΫτϧͷฏۉ ฏԽ + ՃฏԽ
KYOTO UNIVERSITY 34 ٵҾܕσʔλͰͷ࣮ݧ݁Ռ ۙϕΫτϧͷฏۉ ฏԽ + ՃฏԽ
KYOTO UNIVERSITY 35 ճసܕσʔλͰͷ࣮ݧ݁Ռ ۙϕΫτϧͷฏۉ ฏԽ + ՃฏԽ
KYOTO UNIVERSITY 36 ࠷ద༌ૹ܈ؒͷ࣭ྔ༌ૹίετΛ࠷খԽ͢Δ ▪ ࠷ద༌ૹͱɺ ֤͕ॏΈΛ࣋ͭ܈͕2ͭଘࡏ͠ɺ܈ؒͰॏΈΛ
༌ૹ͢Δ࣌ʹඞཁͳίετΛ࠷খԽ͢ΔͰ͋Δɻ ▪ ྫ ೖྗ ग़ྗ
KYOTO UNIVERSITY 37 ࠷ద༌ૹઢܗܭըͱͯ͠ఆࣜԽՄೳ ▪ ࠷ద༌ૹΛఆࣜԽ͢ΔͱҎԼͷઢܗܭըͱͳΔɻ
▪ ͔Β ͷ༌ૹίετ ɺ༌ૹྔ ͱද͢ɻ ༌ૹલͷ ͷॏΈɺ ༌ૹޙͷ ͷॏΈͰ͋Δɻ i j cij pij ai i bj j
KYOTO UNIVERSITY 38 ೋॏ֬ߦྻ ࠷ద༌ૹΛղ͍ͯٻΊΔ P ▪ ࠷খԽ͢Δతؔ
▪ ࠷ద༌ૹΛղ͘͜ͱͰٻΊΒΕΔɻ ͜ͷͱ͖ɺ ͔Β ͷ༌ૹίετ Ͱ͋Γɺ ೋॏ֬ߦྻ ͷ੍Լʹ͋Δɻ P i j ∥fi − vij ∥2 P ( N ∑ i=1 pij = 1 (∀j), N ∑ j=1 pij = 1 (∀i) ) ՃฏԽ߲ ฏԽ߲ ※ ͷۙɺ ͷۙ j i k j ଛࣦؔ
KYOTO UNIVERSITY 39 ϕΫτϧ ೋ࣍ܭըΛޯ๏Ͱղ͍ͯٻΊΔ f ▪ ࠷খԽ͢Δతؔ
▪ ೋ࣍ܭըΛޯ๏Ͱղ͘ͱಘΒΕΔɻ (తؔ) = ͱͳΔํʹ ͷߋ৽Λ܁Γฦ͢ɻ f ∂ ∂fi 0 fi ՃฏԽ߲ ฏԽ߲ ※ ͷۙɺ ͷۙ j i k j ଛࣦؔ
KYOTO UNIVERSITY 40 ݱࡏͷ࣮ݧ݁Ռ ϕΫτϧਪఆͰฏԽ߲͕༗༻ ▪ ϕΫτϧΛMLPͰۙࣅ͠ɺҙͷ࠲ඪʹ֦ு͢Δ ۙϕΫτϧͷฏۉ ฏԽ +
ՃฏԽ