「高次認知」と知覚の理論：認知バイアス、条件文、因果推論

「高次認知」と知覚の理論：
認知バイアス、条件文、因果推論

東京電機大学 理工学部, ドワンゴ 人工知能研究所
高橋 達二

玉川大学 脳科学研究所
社会神経科学共同研究拠点研究会
「世界や社会と相互作用して生きるヒトや動物の視覚 －生理学、心理物理学、計算論」
2018年9月13日（木）・14日（金）

1. ʮߴ࣍ೝ஌ʯͱ஌֮ͷཧ࿦ɿ ೝ஌όΠΞεɺ৚݅จɺҼՌਪ࿦ ౦ژిػେֶ ཧ޻ֶ෦, υϫϯΰ ਓ޻஌ೳݚڀॴ ߴڮ ୡೋ ۄ઒େֶ ೴Պֶݚڀॴ ࣾձਆܦՊֶڞಉݚڀڌ఺ݚڀձ ʮੈք΍ࣾձͱ૬ޓ࡞༻ͯ͠ੜ͖Δώτ΍ಈ෺ͷ ࢹ֮ ʵੜཧֶɺ৺ཧ෺ཧֶɺܭࢉ࿦ʯ 2018೥9݄13೔ʢ໦ʣɾ14೔ʢۚʣ
2. ڞಉݚڀऀ • େ༻ݿஐ ؔ੢ֶӃେֶ ૯߹੓ࡦ ֶ෦ ઐ೚ߨࢣ (tenured) • ۄ଄ߊ޺ D2 ࣾձਓത࢜ • ԣ઒७و D2 • Ṥޱᕣن M1 • ๅాɹ༔ B4 • ٢୔ӳو B4 • ࠤ౻࠼ࢠ B3 • David E Over • Jean Baratgin • ෰෦խ࢙ • ෰෦Үࢠ • தଜߛࢠ • ࢁ༞࢚ • Guy Politzer
3. ঞ࿥ • ਪ࿦΍ҙࢥܾఆɺϓϥϯχϯάΛؚΉ͍ΘΏΔʮߴ࣍ೝ஌ʯͷݚڀ͸ɺਓؒಛ༗ͱݟΒΕΔػೳ ͕ଟ͘ɺ·ͨه߸΍࿦ཧʹґଘ͍ͯ͠Δͱߟ͑ΒΕͨͨΊɺ௕͍ؒɺ஌֮ͳͲͷଞ෼໺ͷݚڀͱ ͸ಠཱͯ͠ਐΊΒΕͯདྷͨɻ͔͠͠ͳ͕Βલੈل຤͔ΒɺదԠ߹ཧੑ΍ੜଶֶత߹ཧੑͱ͍ͬͨ ඪޠͷ΋ͱɺߴ࣍ೝ஌΋·ͨɺ؀ڥͷߏ଄ʢ֬཰෼෍ʣΛ൓ө͠ɺదԠΛ໨తͱͨ͠ػೳͱͯ͠ Ґஔ෇͚௚͞Ε͖ͯͨɻ͜ͷΞϓϩʔν͸ଟ͘ͷ෼໺Ͱ੒ޭΛऩΊͨଞɺ֬཰ϞσϦϯάͷݴ༿ ͕ػցֶशͳͲ޻ֶͱڞ௨͍ͯ͠Δ͜ͱ͔Βɺਓ޻஌ೳͷ։ൃʹ΋ӨڹΛ༩͖͍͑ͯͯΔɻେ· ͔ʹݴ͑͹ɺೝ஌ͷଊ͑ํͱͯ͠ɺԋ៷͔Βؼೲ΁ɺ࿦ཧ͔Β֬཰΁ɺͱ͍͏γϑτ͕͋Γɺਓ ؒͷೝ஌͕ɺ؀ڥͷෆ࣮֬ੑͱϦιʔεͷ༗ݶੑΛ৫ΓࠐΜ্ͩͰదԠతͳ΋ͷͰ͋Δ͜ͱ͕໌ Β͔ʹͳͬͨɻଞํͰۙ೥Ͱ͸ɺݴ༿΍ه߸ͷॏཁੑ΍ɺ࿦ཧతͳߏ଄Λߟྀͨ͠ਪ࿦ɺͱ͍ͬ ͨ؍఺͕ܰࢹ͞Εͯདྷͨ͜ͱʹ൓ল͕ू·Γͭͭ͋Δɻ • ຊߨԋͰ͸ɺෆ࣮֬ੑΛߟ্ྀͨ͠Ͱه߸΍ߏ଄Λѻ͏͜ͱͷͰ͖Δɺ de Finetti ͷओ؍֬཰࿦ ཧֶΛϦόΠόϧͤ͞ɺ৚݅จʹ৽͍͠ϞσϧΛ༩͑Δೝ஌৺ཧֶͷݚڀΛ঺հ͢ΔɻʮpͳΒ ͹qʯͱ͍͏৚݅จ͸ɺϧʔϧ΍ҼՌؔ܎ͷදݱͱ఻ୡɺࣾձతͳ΍ΓͱΓʢ໿ଋ΍ڴഭʣͳ Ͳɺίϛϡχέʔγϣϯʹத৺తͳ໾ׂΛՌͨ͢ଞɺϩϘςΟΫε΍ࣗવݴޠॲཧʹͱͬͯ΋ॏ ཁͰ͋Δɻ͜ΕʹΑΓɺਓ͕ؒ࿦ཧֶʹैΘͣෆ߹ཧͰ͋Δ͜ͱͷূڌͷҰͭͱ͞Ε͖ͯͨʮܽ ؕ৚݅จʯύλʔϯ͕આ໌͞Εɺਅཧ஋දλεΫͰසൃ͍ͯͨ͠Ṗͷύλʔϯ΋·ͨઆ໌͞ΕΔɻ ·ͨɺ2ࣄ৅ͷڞى৘ใͷ؍࡯͔ΒͦͷؒͷҼՌؔ܎Λ൑அ͢ΔҼՌؼೲʹ͓͍ͯɺσʔλΛ࠷ ΋Α͘આ໌͢ΔߨԋऀΒͷϞσϧΛɺ֬཰࿦ཧֶ͔Βಋ͚Δɻ͜ΕʹΑΓɺԋ៷͔Βؼೲ·Ͱɺ ༷ʑͳλεΫΛ౷Ұతʹѻ͏Մೳੑ͕։͚Δ͜ͱΛ͍ࣔͨ͠ɻ
4. ߏ੒ • ࣗݾ঺հͱจ຺ • ਪ࿦৺ཧֶͷ஌ݟ • ৚݅จͱਪ࿦ • ҼՌਪ࿦
5. ࣗݾ঺հɿߴڮୡೋ • ܭࢉ࿦తೝ஌Պֶ • ਪ࿦ɺ൑அɺҙࢥܾఆɺ৚݅จɺจ຺ɺ൱ఆ • AIɺಛʹڧԽֶशʢιϑτίϯϐϡʔςΟϯά෼໺ʣ • ʮݶఆ߹ཧੑΛඋ͑ͨਂ૚ڧԽֶशཧ࿦ͷల։ʯएखݚڀ(A) • ࣾձతֶश (imitation from experts ʹରͯ͠ emulation from pioneers Λఏএ, JNNS 2018), ࠾㕒ߦಈɾϓϩεϖΫτཧ࿦త ڧԽֶशΞϧΰϦζϜΛԠ༻ • ʮਓؒೝ஌ͷదԠతಛੑΛ࣮૷ͨ͠Ձ஋ؔ਺ͷఏҊͱେن໛ίϯ ϐϡʔςΟϯά΁ͷԠ༻ʯएखݚڀ(B)
6. Self-Introduction 2016 Japanese academic year (April 2016 to March 2017) in Europe For 11 months I live in Paris and then the last month in London. Jean Baratgin at CHArt (EPHE, Paris 8) Cognitive psychology of probability judgment and reasoning Mike Oaksford at UL Birkbeck Cognitive psychology of reasoning and argumentation Tatsuji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹ Visiting Scholar at University of London, Birkbeck Observational causal induction as independence test under rarity assumption 2017-01-18 Wed 7 / 73
7. ਪ࿦৺ཧֶͷ࠷ۙ • 20ੈلʹ͓͍ͯɺਪ࿦ΛؚΊͨߴ࣍ೝ஌ʹ͸ɺ஌֮ͱͷཧ࿦ తɾ࣮ݧతஅઈ͕Ծఆ͞Ε͍ͯͨ • 20ੈل຤ʢಛʹ John R. Anderson ͷ߹ཧ෼ੳ rational analysis (1990) Ҏ߱ʣ͔Βݱࡏ·Ͱɺߴ࣍ೝ஌΋ɺ؀ڥͷߏ ଄Λ൓ө͠ɺޮ཰తʹ୳ࡧ͠ɺయܕతͳঢ়گͰ͏·͍γϣʔ τΧοτΛ༻͍ͯҙࢥܾఆ͍ͯ͠Δ͜ͱ͕ͲΜͲΜ໌Β͔ʹ • ߴڮ͸2008೥Ҏ߱ɺ৚݅จɺ֬཰࿦ཧɺԋ៷ਪ࿦ɺҼՌਪ ࿦ͷݚڀ
8. ۙ೥ͷਪ࿦৺ཧֶͷ஌ݟ • ਓؒ͸ɺਪ࿦λεΫͷҙຯ಺༰ʢΧόʔετʔϦʔʣΛ๨ ΕΖͱࢦࣔͯ͠΋๨Εͳ͍ɹˠɹඇԋ៷త • ࿦ཧλεΫΛղ͚ͱࢦࣔͯ͠΋ؼೲɾҙࢥܾఆΛߦ͏ • σʔλΛݟͤͯهड़౷ܭ͠Ζͱݴͬͯ΋ɺprior ΛΨϯΨ ϯޮ্͔ͤͨͰਪଌ౷ܭΛ͢Δ • ܗࣜతͳਖ਼ղͰͳ͘ɺయܕతͳ؀ڥ΁ͷదԠΛ໨ࢦ͍ͯ͠ Δͱ͍͏ղऍ͕ɺৗʹΑΓଥ౰
9. ਪ࿦ͷϞσϦϯάݴޠ • ਓؒͷਪ࿦͸ɺඇԋ៷తͰͳ͘ؼೲɾҙࢥܾఆతɺهड़Ͱͳ ͘ਪଌɺܗࣜతͰͳ͘దԠత • →ɹݹయ࿦ཧֶతϞσϦϯά͸ෆద౰ • →ɹ֬཰࿦తϞσϦϯάͰे෼͔ʁ • ґવͱͯ͠ɺࣗવݴޠ΍ٞ࿦ͷߏ଄ʢ࿦ཧʣʹ͸ڧ͘൓Ԡɻ ֬཰෼෍͚ͩͰ͸ͳ͍ • →ɹ֬཰࿦ཧֶతϞσϦϯά (2010೥Ҏ߱)
10. ৚݅จͷϞσϦϯάͷॏཁੑ ଟ͘ͷϧʔϧ͸৚݅จʮpͳΒ͹qʯͰදݱ ϩϘοτͱͷର࿩ΠϯλʔϑΣΠεͰ ϩϘοτ͕ਓؒʹ߹ΘͤΔʹ΋ɺٯʹ΋ɺॏཁ ৚݅จ͸ʮӕͰ΋ໝ૝Ͱ΋ͳ͍͕ɺࣄ࣮͔Β཭ Εͨ࿩ʯɺԾ૝ɾԾઆతࢥߟΛՄೳʹ ৚݅දݱΛ࣋ͨͳ͍ਓؒͷݴޠ͸ଘࡏ͠ͳ͍ ਪ࿦ͱෆՄ෼
11. ਪ࿦ͱ৚݅จ ਪ࿦ͷࡾܗࣜ (C. S. Peirce) ԋ៷ɹ ৚݅จΛલఏͱͯ͠࢖༻ɿࡾஈ࿦๏ ؼೲɹ ৚݅จΛܗ੒ɿσʔλʢڞى৘ใͳͲʣ͔Βͷ๏ଇΛܗ੒ ΞϒμΫγϣϯ ৚݅จΛḪΓɺ݁Ռ͔ΒݪҼʢԾઆʣΛ୳Δɾ࡞Δ deduction induction abduction premise 1 p p q premise 2 p→q q p→q conclusion q p→q p
12. ৚݅จʹؔ͢Δࣄ࣮ • 1966೥ͷใࠂ (Peter Wason) • ࣮ݧࢀՃऀʹɺτϥϯϓͷΧʔυΛɺϧʔ ϧʮࠇͳΒ͹ۮ਺ʯʹै͍ͬͯΔ͔൱͔ͷ ೋ୒Ͱ෼ྨͤ͞Δ • ʮࠇʯͱ͍͏લ݅Λ൱ఆ͢Δ੺͍Χʔ υ͸ɺೋ୒ΛٻΊͯ΋ࡾͭΊͷΧςΰ ϦʮͲͪΒͰ΋ͳ͍ʯͱ౴͑Δؤ݈ͳ ܏޲ • ਓؒͷ৚݅จ͸ʮܽؕ৚݅จʯͱݺ͹ΕΔ ෼ྨʢਅཧ஋ʣ Χʔυͷྫ ֬ূ͢Δɾ ै͍ͬͯΔɾ ਅ ൓ূ͢Δɾ ै͍ͬͯͳ͍ɾ ِ ͲͪΒͰ΋ͳ͍ɾ ʢʁʣ
13. ৚݅จͷϞσϧ ೋ஋࿦ཧ಺Ͱ͸දݱͰ͖ͳ͍ ࿦ཧֶͷʮؚҙʯͱ͸ҟͳΔ ෆ࣮֬ੑΛ৫ΓࠐΜͰ͓Γɺ֬཰஋ʢ·ͨ͸࠷ ௿ݶࡾ஋࿦ཧʣ͕ඞཁ P(pͳΒ͹q) = P(q|p) “The Equation” ͱݺ͹ΕΔ “new paradigm psychology of reasoning” ΁ ਪ࿦͕ɺҙࢥܾఆɺ൑அɺ஌֮ɺӡಈ΁ͱܨ͕Δ
14. ৚݅จͷҙຯ࿦తੑ࣭ɿ ਅཧ஋දλεΫɹઃఆ • ࣮ݧࢀՃऀʹʮp͔ͭqʯ΍ʮpͳΒ͹qʯͱ͍ͬͨจɾ৚ ݅จΛఏࣔ • p (લ݅) ͱ q (ޙ݅) ʹ͍༷ͭͯʑͳέʔεΛఏࣔɺͦͷ έʔεͰจ͕ਅ, ِ, ͲͪΒͱ΋͍͑ͳ͍(ෆఆ)ͷͲΕͰ͋ Δ͔Λճ౴ • ਅཧ஋දλεΫ࣮ݧ (Qualtrics) ϦϯΫ
15. ৚݅จͷҙຯ࿦తੑ࣭ɿ ਅཧ஋දλεΫɹ݁Ռ • De Finetti ͷओ؍֬཰࿦ཧֶ (1936) ͷମܥͷΈ͕࣮ࡍͷճ౴Λྑ͘આ໌ • Baratgin, J., Politzer, G., Over, D.E., Takahashi, T., 2018. The Psychology of Uncertainty and Three-Valued Truth Tables. Front. Psychol. 9, 1479. doi:10.3389/fpsyg.2018.01479 • ৚݅จͷҙຯ͸ɺ৚݅෇͖Ṍ͚ͱύϥϨϧ • ʮ໌೔੖ΕͨΒ೔ຊνʔϜ͕উͭʯʹ୭͔͕Ṍ͚ɺଞͷਓ͕ड͚ͯ ཱͭ • ໌೔ʹͳͬͯӍͳΒṌ͚͸ྲྀΕΔ (void)
16. ૒৚݅จ • զʑͷ2018೥ͷ݁Ռͷ΋͏Ұͭͷཁ఺ɿ • ʮpͳΒ͹qɺ͔ͭɺqͳΒ͹pʯͱ͍͏૒৚݅จͷҙຯɿ • ͜Ε͸զʑͷҼՌؔ܎ʹؔ͢Δ௚ײΛද͍ͯ͠ΔͷͰ͸ͳ ͍͔ʁ • ʹTakahashi et al. (2010) ͷҼՌؼೲͷ pARIs Ϟσϧ P(q||p) = P(p & q|p or q) = P(p, q) P(p ∪ q)
17. ҼՌਪ࿦ʢҼՌؼೲʣ • ೋͭͷࣄ৅͕͋Δ • ʮ݁Ռʯ (E: effect) • ʮݪҼީิʯ (C: cause) • ਓؒ͸ೋͭͷࣄ৅ C, E ͷڞى৘ใ͔ΒɺͲͷΑ͏ʹͦͷؒͷҼՌ ؔ܎Λؼೲతʹਪ࿦͢Δ͔ʁ • ҼՌؔ܎ͦͷ΋ͷΛ؍ଌ͢Δ͜ͱ͸Ͱ͖ͳ͍͕ • աڈͷ਍அɾະདྷͷ༧ଌɾཧ༝ͷઆ໌ʹར༻ՄೳͰඇৗʹ༗༻
18. ɹਓ޻஌ೳֶձ
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19. ҼՌਪ࿦ͷجຊϞσϧ • Delta P Ϟσϧ ʢJenkins & Ward, 1965ʣ • ࣮ݧ܈ͱίϯτϩʔϧ܈ͷ͕ࠩҼՌڧ౓ • Պֶ࣮ݧͷઃఆͦͷ΋ͷ ΔP = P(E|C) − P(E|¬C)
20. ❖ proportion of assumed-to-be rare instances [2]: ྆ऀͷ࿈ݴ(AND) ❖ ༧ଌ৚݅จʮC ͳΒ͹
    Eʯ
    ❖ ਍அ৚݅จʮE ͳΒ͹
    Cʯ ҼՌਪ࿦ͷ૒৚݅෇֬཰ ʢ૒৚݅จͷ֬཰ʣ !20 ɹɹɹ " [2] Takahashi, T., Kohno, Y., and Oyo, K.: in Proc. of ICCS2010, pp. 361–362 (2010) effect (E) No effect(¬E) पลස౓ cause (C) N(C, E) N(C, ¬E) N(C) no cause (¬C) N(¬C, E) N(¬C, ¬E) N(¬C) पลස౓ N(E) N(¬E) N(Ω) C E Causal Induction pARIs (proportion of assumed-to-be rare instan (Takahashi, Oyo, & Kohno, 2010; Takahashi et al., in prep.) Shares the rarity assumption with DFH. pARIs: the probability of "if C then E, and if E then C" (biconditional probability of C and E) pARIs = P(C ∧ E|C ∨ E) = P(C, E) P(C ∨ E) = N(C, E) N(C ∨ E) We will get back to this index later in terms of conditionals and i relationship to other indices.
21. ɹਓ޻஌ೳֶձ
    ୈճ ୯७ͳҼՌؼೲͷઃఆ ❖ ҼՌؼೲͱ͸ɿɹʮڇೕˠෲ௧ʁʯ !21 ࣄྫ
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22. ϝλΞφϦγε • Hattori & Oaksford (2007) ͷϝλ෼ੳ • ൴Βͷ DFH Ϟσϧ͕શ41Ϟσϧத࠷ߴͷϑΟοτ • pARIs ͸ͦΕΑΓ΋୯७͔ͭޡ͕ࠩখ͘͞ϑΟοτ΋ྑ͍ • AS95 ͷΈ͸ଞͱҟͳΓɺͦ͜ͰͷΈ pARIs ΑΓ DFH ͕ྑ͍͕ɺಛघͳ࣮ݧ • 40ਓͷֶੜࢀՃऀશһ͕ฒ֎Εͯଟ͍શ80ͷܹࢗʹҰ͔͚࣌ؒͯճ౴ʢϝ λ෼ੳͷશ8࣮ݧͷશܹࢗͷ߹ܭ143ͷ͏ͪա൒਺ʣ AS95 BCC03.1 BCC03.3 HO07.1 HO07.2 LS00 W03.2 W03.6 R 2 RMSE R 2 RMSE’ pARIs 0.89 0.96 0.94 0.93 0.99 0.80 0.78 0.88 0.90 9.69 0.93 8.97 DFH 0.91 0.95 0.91 0.93 0.96 0.80 0.69 0.80 0.91 13.0 0.91 17.49 ∆P 0.78 0.84 0.70 0.50 0.00 0.77 0.00 - 0.71 35.18 0.53 25.51 no. of stimul 80 13 6 12 9 11 8 4 143 143 63 63
23. ɹਓ޻஌ೳֶձ
    ୈճ ϝλ෼ੳ      pA RIs D FH ΔP AS95 BCC03.1 BCC03.3 HO07.1 HO07.2 LS00 W03.2 W03.6 AS95 BCC03.1 BCC03.3 HO07.1 HO07.2 LS00 W03.2 W03.6 pARIs 0.89 0.96 0.94 0.93 0.99 0.80 0.78 0.88 DFH 0.91 0.95 0.91 0.93 0.96 0.80 0.69 0.80 ΔP 0.78 0.84 0.70 0.50 0.00 0.77 0.00 NA N 80 13 6 12 9 11 8 4 r^2 RMSE r^2* RMSE* pARIs 0.90 9.44 0.93 8.30 DFH 0.91 12.16 0.91 14.85 ΔP 0.72 17.73 ❖ աڈͷ࣮ݧͷϝλ෼ੳ
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    ͷ
    [ม׵ޙɺॏΈ෇͚ฏۉ
24. ࣮ݧͷઃఆ • ੜσʔλ͕ͳ͍ͱLMEͳͲͰे෼ͳղੳ͕Ͱ͖ͳ͍ͷ Ͱ࣮ݧ • ΦϯϥΠϯ࣮ݧʢΫϥ΢υιʔγϯάʣ • ࣮ݧͷઆ໌Λදࣔͨ͠ͷͪʹΧόʔετʔϦʔͷઆ ໌Λఏࣔ • Ұఆճ਺ͷܹࢗΛϥϯμϜఏࣔͨ͠ޙɺ࣮ݧࢀՃऀ ͸ධՁೖྗϖʔδ΁ભҠ͠εϥΠμʔʹΑΔਪఆ஋ Λೖྗ • ܁Γฦ͠ • AWS ্ͷ࣮ݧϓϩάϥϜ ܹࢗ a b c d 1 1 0 6 3 2 1 3 3 3 3 1 6 0 3 4 3 1 1 5 5 1 2 2 5 6 0 0 7 3 7 0 7 0 3
25. ࣮ݧ݁Ռ ຌྫ • pARIs ▪ DFH ˛ ΔP ◆ mean 1 2 3 4 5 6 7 ܹࢗ ܾఆ܎਺ pARIs DFH DP ܹࢗ1-7 0.953136306369 ܭࢉෆೳ* ܭࢉෆೳ* ܹࢗ1-5 0.946234780516 0.906088860769 0.504823039081 ܹࢗ1-5: ∆BIC = BIC(DFH)-BIC(pARIs)=4.8 ܹࢗ1-7: ∆BIC = BIC(DFH)-BIC(pARIs)=40.6
26. pARIs ͸ԿΛ΍͍ͬͯΔͷ͔ʁ • ֬཰࿦ཧͰ͸ɺ૒৚݅จͷҙຯͱͯ͠͸نൣత • ͔͠͠ɺҼՌਪ࿦ͱͯ͠ͲͷΑ͏ͳཧ࿦తҙຯ͕͋Δͷ͔ʁ • ਓؒͷ௚ײ͕ҼՌ૒৚݅จతͩͱͯ͠ɺͦΕ͸ͳ͔ͥʁ • ʮ৯தಟͷਓ͸ੜϨόʔΛ৯΂͍ͯͨɺ͔ͭɺੜϨόʔ Λ৯΂͍ͯͨਓ͸৯தಟʹͳͬͨʯ
27. ɹਓ޻஌ೳֶձ
    ୈճ ؍࡯తҼՌؼೲʹඞཁͳཁૉ ❖ ҼՌؔ܎ͷ͋Γͦ͏ͳࣄ৅ରͷϐοΫΞοϓ
    ❖ ૬͕ؔߴ͍΋ͷΛϐοΫΞοϓ
    ❖ ૬͕ؔ௿͍΋ͷΛ;Δ͍མͱ͢
    ❖ ૬ؔ܎਺͕ߴ͍࣌ɺҼՌؔ܎ʢC⇒Eʣ͕͋Δͱ͸ݶΒͳ͍
    ❖ ҼՌؔ܎ʢC⇒Eʣ͕͋Δ࣌ɺ૬ؔ܎਺͸ߴ͍৔߹͕ଟ͍
    ❖ C
    ͱ
    E
    ͕ಠཱͰ͋Δ͔ʁʢಠཱੑݕఆʣ !27
28. ɹਓ޻஌ೳֶձ
    ୈճ ۃ كগੑԾఆ ❖ كগੑԾఆ
    ❖ ਓؒ͸
    P(C), P(E)
    ͕খ͍͞ͱԾఆ͢Δ
    ❖ ͋Δର৅͕ੜى͢Δ֬཰ʢখʣ
    ❖ ͋Δର৅͕ෆੜىͷ֬཰ʢେʣ
    • զʑ͕ͦͷҼՌؔ܎ʹڵຯΛ࣋ͭΑ͏ͳࣄ৅ʹ͸ͦ΋ͦ΋كগ ੑ͕͋Δʢੜى֬཰͕௿͍ʣͱ͍͏ࣄલ஌ࣝ • ʢগͳ͘ͱ΋೔ৗతʹ͸ɺ͋Γ;Εͨ͜ͱʢex. ࠭യͰͷ੖ ΕʣͷݪҼ΍݁Ռ͸͋·Γ໰Θͳ͍ʣ !28
29. ɹਓ޻஌ೳֶձ
    ୈճ كগੑԾఆͷ্Ͱͷಠཱੑݕఆ ❖ CͱE͕ಠཱͰ͋ΔͱԾఆ͢Δͱɺ(P(C), P(E) > 0) ❖ ۃكগੑԾఆ
    N(¬C,¬E) → ∞ ❖ ୈҰࣜɺୈೋ͕ࣜ
    0
    ʹऩଋ͢Δۙͮ͘
    ❖ ୈࡾࣜ͸ۃݶૢ࡞ޙ΋ෆมʢܭࢉՄೳʣ
    ❖ ୈࡾ͕ࣜ
    0
    ʹ͚ۙΕ͹ɺಠཱʹ͍ۙͱݴ͑Δ
    ❖ ୈࡾ͕ࣜ
    0
    ͔Βԕ͚Ε͹ɺඇಠཱੑΛ࣋ͭͱݴ͑Δ !29 We assume that people try to judge if C and E are independent, i.e. see whether the following equation holds or not: P(C, E) = P(C)P(E) = P(C|E)P(E|C). (8) In terms of frequencies, N(C, E) N(Ω) = N(C) N(Ω) · N(E) N(Ω) = N(C, E) N(E) · N(C, E) N(C) . (9) Under the extreme rarity assumption (XRA), N(¬C, ¬E) → ∞, the first and second converge to 0, while the third remains the same. So, as much as the third, P(C|E)P(E|C) is close to 0, C and E are independent. Otherwise, i.e. if P(C|E)P(E|C) is large (close to 1), C and E are somehow dependent. Tatsuji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹ Visiting Scholar at University of London, Birkbeck and Observational causal induction as independence test under rarity assumption 2017-01-18 Wed 48 / 73 Statistical Independence indep under XRA We assume that people try to judge if C and E are independent, i.e see whether the following equation holds or not: P(C, E) = P(C)P(E) = P(C|E)P(E|C). (8 n terms of frequencies, N(C, E) N(Ω) = N(C) N(Ω) · N(E) N(Ω) = N(C, E) N(E) · N(C, E) N(C) . (9 Under the extreme rarity assumption (XRA), N(¬C, ¬E) → ∞, the first and second converge to 0, while the third remains the same. So, as much as the third, P(C|E)P(E|C) is close to 0, C and E ar ndependent. Otherwise, i.e. if P(C|E)P(E|C) is large (close to 1) C and E are somehow dependent. uji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹ Visiting Scholar at University of London, Observational causal induction as independence test under rarity assumptio 2017-01-18 Wed 36
30. ɹਓ޻஌ೳֶձ
    ୈճ كগੑԾఆͷ্Ͱͷಠཱੑݕఆ ❖ ܾఆ܎਺ͷۃݶܗ
    ❖ P(E|C)P(C|E)
    ͸
    ❖ DFH ͷ৐Ͱ͋Γɺ
    ❖ pARIs = P(E|CorE) ͸୯Ұͷ৚݅෇͖֬཰ͷܗࣜͷதͰ ͷۙࣅͱଊ͑ΒΕΔ
    ❖ ৚݅෇͖֬཰Λߟ͑Δೝ஌తෛ୲͔Βɺ
    Q"3*T
    ͕ଥ౰ !30 limN(¬C,¬E)→∞ φ2 = P(E|C)P(C|E). P(E|C)P(C|E) corresponds to the populati
31. τϨʔυΦϑͷՄࢹԽ • γϛϡϨʔγϣϯͰɺ฼ूஂͷ૬ؔ܎਺ͷਪఆ • τϨʔυΦϑʹ༻͍Δࢦඪ
 ʮ஗͞ʯɿ֤Ϟσϧͷ஋͕ͦͷཧ࿦஋ʹऩଋ͢Δ
 ɹɹɹɹɹ(ޡࠩ0.01ʹऩ·Δ)·Ͱʹཁ͢Δࣄ৅ͷ਺
 ʮෆਖ਼֬ੑʯɿ֤Ϟσϧͷ෼ࢄͷࣄ৅਺200·Ͱͷฏۉ஋ • ֤Ϟσϧʹରͯ͠0 ʹ0.0͔Β1.0ʹ͔͚ͯ࠲ඪΛग़ྗ͠ɺ ಉҰͷϞσϧΛͦͷॱʹԊ͏Α͏ʹ໼ҹͰ࿈݁
32. ɹਓ޻஌ೳֶձ
    ୈճ Sim !32 pARIs infers the population correlation with averagely the highest precision from small data. Time development of average value ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ĭĨİĄ÷õ÷ ĭĨİĄ÷õø ĭĨİĄ÷õù ĭĨİĄ÷õú ĭĨİĄ÷õû ĭĨİĄ÷õü ĭĨİĄ÷õý ĭĨİĄ÷õþ ĭĨİĄ÷õÿ ĭĨİĄ÷õĀ ĭĨİĄøõ÷ φ 0 20 40 60 80 100 0 20 40 60 80 100 φ φ ฏۉ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ĭĨİĄ÷õ÷ ĭĨİĄ÷õø ĭĨİĄ÷õù ĭĨİĄ÷õú ĭĨİĄ÷õû ĭĨİĄ÷õü ĭĨİĄ÷õý ĭĨİĄ÷õþ ĭĨİĄ÷õÿ ĭĨİĄ÷õĀ ĭĨİĄøõ÷ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ĭĨİĄ÷õ÷ ĭĨİĄ÷õø ĭĨİĄ÷õù ĭĨİĄ÷õú ĭĨİĄ÷õû ĭĨİĄ÷õü ĭĨİĄ÷õý ĭĨİĄ÷õþ ĭĨİĄ÷õÿ ĭĨİĄ÷õĀ ĭĨİĄøõ÷ DFH (N) DFH (NW) φ (N) ∆P (N) pARIs (N) pARIs (NW) ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ĭĨİĄ÷õ÷ ĭĨİĄ÷õø ĭĨİĄ÷õù ĭĨİĄ÷õú ĭĨİĄ÷õû ĭĨİĄ÷õü ĭĨİĄ÷õý ĭĨİĄ÷õþ ĭĨİĄ÷õÿ ĭĨİĄ÷õĀ ĭĨİĄøõ÷ φ 0 0 10 20 30 40 50 1 ! .5 ! 0 1 ! .5 ! 0 1 ! .5 ! 0 mean value samples 0 10 20 30 40 50 - ˠ DFH is slow in convergence ˠ ∆P is fast and precise (but see th next slide) ˠ pARIs is fast, and is high only when φ0 is high(er): scooping more promising candidate causes uji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹvisiting scholar at EPHE and University of A simple (bi)conditional form for necessity and sufficienty: The pARIs rule 2016-05May-03 Tue 29 pARIs infers the population correlation with sm small samples are given. Time development of variance ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ φ φ φ DFH (N) DFH (NW) φ (N) ∆P (N) pARIs (N) pARIs (NW) ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ĭĨİĄ÷õ÷ ĭĨİĄ÷õø ĭĨİĄ÷õù ĭĨİĄ÷õú ĭĨİĄ÷õû ĭĨİĄ÷õü ĭĨİĄ÷õý ĭĨİĄ÷õþ ĭĨİĄ÷õÿ ĭĨİĄ÷õĀ ĭĨİĄøõ÷ φ 0 0 10 20 30 40 50 1 ! .5 ! 0 1 ! .5 ! 0 1 ! .5 ! 0 variance samples 0 10 20 30 40 50 Tatsuji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹvisiting A simple (bi)conditional form for necessit pARIs can always infer the Time development of unco DFH (N) ∆P (N) pARIs (N) ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ 0 10 20 30 40 50 1 ! .5 ! 0 1 ! .5 ! 0 1 ! .5 ! 0 rate of NA values samples 0 Tatsuji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹ A sim pARIs can always infer the population correlatio Time development of uncomputable samples φ φ φ DFH (N) DFH (NW) φ (N) ∆P (N) pARIs (N) pARIs (NW) ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ù÷ û÷ ý÷ ÿ÷ ø÷÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ĭĨİĄ÷õ÷ ĭĨİĄ÷õø ĭĨİĄ÷õù ĭĨİĄ÷õú ĭĨİĄ÷õû ĭĨİĄ÷õü ĭĨİĄ÷õý ĭĨİĄ÷õþ ĭĨİĄ÷õÿ ĭĨİĄ÷õĀ ĭĨİĄøõ÷ φ 0 ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ ÷ ø÷ ù÷ ú÷ û÷ ü÷ ÷õ÷ ÷õù ÷õû ÷õý ÷õÿ øõ÷ ĽĨijļĬ 0 10 20 30 40 50 1 ! .5 ! 0 1 ! .5 ! 0 1 ! .5 ! 0 rate of NA values samples 0 10 20 30 40 50 Tatsuji Takahashi (Tokyo Denki U.) ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ɹ ɹvisiting A simple (bi)conditional form for necessit
33. ଎͞ͱਖ਼֬͞ͷτϨʔυΦϑ • Ϟσϧͷൺֱํ๏͸Ұ ٛతͰͳ͍ɿɹ΋ͬͱ ΋ pARIs ͕ෆརͳج ४Ͱ·ͱΊͨͷ͕ӈਤ • DP (∆P) ͸͔ͳΓ଎͍ ͕ਖ਼֬Ͱͳ͍ • DH (DFH) ͸͔ͳΓ஗ ͍͕·͋·͋ਖ਼֬ • phi (φ) ͸஗ΊͰ·͋ ·͋ෆਖ਼֬ • pARIs ͸଎ͯ͘ਖ਼֬ ਖ਼֬ɹˡˠɹෆਖ਼֬ ଎͍ɹˡˠɹ஗͍
34. ਪ࿦৺ཧֶͷ஌ݟ • ਓؒ͸ɺਪ࿦λεΫͷҙຯ಺༰ʢΧόʔετʔϦʔʣΛ๨ ΕΖͱࢦࣔͯ͠΋๨Εͳ͍ɹˠɹඇԋ៷త • ࿦ཧλεΫΛղ͚ͱࢦࣔͯ͠΋ؼೲɾҙࢥܾఆΛߦ͏ • σʔλΛݟͤͯهड़౷ܭ͠Ζͱݴͬͯ΋ɺprior ΛΨϯΨ ϯޮ্͔ͤͨͰਪଌ౷ܭΛ͢Δ • ܗࣜతͳਖ਼ղͰͳ͘ɺయܕతͳ؀ڥ΁ͷదԠΛ໨ࢦ͍ͯ͠ Δͱ͍͏ղऍ͕ৗʹΑΓଥ౰
35. ҼՌਪ࿦Ͱͷ஌ݟ • զʑ͕ͦͷҼՌؔ܎ʹڵຯΛ࣋ͭΑ͏ͳࣄ৅ʹ͸ͦ΋ͦ΋كগੑ͕͋Δ ʢੜى֬཰͕௿͍ʣͱ͍͏ࣄલ஌ࣝ • ʢ͋Γ;Εͨ͜ͱʢex. ࠭യͰͷ੖ΕʣͷݪҼ΍݁Ռ͸͋·Γ໰Θͳ ͍ʣ • ਓؒ͸ɺਪ࿦λεΫͷҙຯ಺༰ʢΧόʔετʔϦʔʣΛ๨ΕΖͱࢦࣔͯ͠ ΋๨Εͳ͍ɹˠɹඇԋ៷తɹʢҙຯ಺༰ʹΑΓਪ࿦ͷ࿮૊ΈΛεΠονϯ άʣ • σʔλΛݟͤͯ࿦ཧλεΫɾهड़౷ܭΛղ͚ͱࢦࣔͯ͠΋prior ΛΨϯΨ ϯޮ্͔ͤͨͰؼೲɾҙࢥܾఆɾਪଌ౷ܭʢكগੑΛԾఆʣΛߦ͏ • ܗࣜతͳਖ਼ղ (∆P) Ͱͳ͘ɺయܕతͳ؀ڥ΁ͷదԠ (pARIs)
36. ·ͱΊ • ߴ࣍ೝ஌ʹࠜຊతͳ৚݅จͷཧ࿦Λݕূʢ֬཰࿦ཧϞσϧ ͷཱ֬ʣ • ؍࡯తͳҼՌਪ࿦ͷɺओ؍֬཰ͷ৚݅จཧ࿦Λ༻͍ͨϞ σϦϯάʹ੒ޭ • ΋ͬͱ΋ԑԕ͔ͬͨਪ࿦΋ɺ஌֮ͷݴޠʹͲΜͲΜ͍ۙͮ ͯདྷͨ • όΠΞεʁ
37. ೝ஌όΠΞε • ҼՌਪ࿦Ͱ஌ΒΕͨࡉ͔͍όΠΞεͷଞ… • ਓؒʹ͸ҼՌؔ܎Λͻͬ͘Γฦ͢όΠΞε͕͋Δ • ҼՌؔ܎ͷ޲͖ΛແޮԽ • ͜Ε͸ɺҼՌ୳ࡧʢҼՌؔ܎ͷωοτϫʔΫͷߏ଄ਪఆʣʹ͸߹ཧత • ← pARIs ʹ͸޲͖͕ͳ͍ • ౷ܭతσʔλ͔Βͷޮ཰తͳϕΠζωοτͷߏ଄ਪఆ • χ2 ΍ G2 ͷ୅ΘΓʹ pARIs ஋Ͱ PC ΞϧΰϦζϜͷແ޲ลઃఆ
38. ·ͱΊ • ߴ࣍ೝ஌ʹࠜຊతͳ৚݅จͷཧ࿦Λݕূʢ֬཰࿦ཧϞσϧ ͷཱ֬ʣ • ؍࡯తͳҼՌਪ࿦ͷɺओ؍֬཰ͷ৚݅จཧ࿦Λ༻͍ͨϞ σϦϯάʹ੒ޭ • ΋ͬͱ΋ԑԕ͔ͬͨਪ࿦΋ɺ஌֮ͷݴޠʹͲΜͲΜ͍ۙͮ ͯདྷͨ • ҼՌʹؔ͢ΔόΠΞεΛઆ໌
39. ༨ஊɿߴ࣍ೝ஌ͷϕΠδΞϯ • 2000೥୅ʹϕΠζత৺ཧֶΛཱ֬ • Josh Tenenbaum, Nick Chater, Mike Oaksford, Tom Griffiths, …
40. ༨ஊɿߴ࣍ೝ஌ͷϕΠδΞϯ • 2000೥୅ʹϕΠζత৺ཧֶΛཱ֬ • Nick Chater’s The Mind is Flat (2018) •
41. References • Hattori, M., Oaksford, M., 2007. Adaptive Non-Interventional Heuristics for Covariation Detection in Causal Induction: Model Comparison and Rational Analysis. Cogn. Sci. 31, 765–814. doi: 10.1080/03640210701530755 • Wason, P. C. (1966). “Reasoning,” in New Horizons in Psychology, ed B. Foss (Harmondsworth: Penguin Books), 135– 151. • Over, D. E., and Baratgin, J. (2017). “The ”defective“ truth table: its past, present, and future,” in The Thinking Mind: A Festschrift for Ken Manktelow, eds N. Galbraith, E. Lucas, and D. E. Over (London: Psychology Press), 15–28.

42. References • Baratgin, J., Politzer, G., Over, D.E., Takahashi, T., 2018. The Psychology of Uncertainty and Three-Valued Truth Tables. Front. Psychol. 9, 1479. doi:10.3389/fpsyg.2018.01479 • Hattori, M., Over, D.E., Hattori, I., Takahashi, T., Baratgin, J., 2016. Dual frames in causal reasoning and other types of thinking. The Thinking Mind: A Festschrift for Ken Manktelow, 98–114. doi: 10.4324/9781315676074 • Hattori, M., Over, D.E., Hattori, I., Takahashi, T., Baratgin, J., 2016. Dual frames in causal reasoning and other types of thinking. Think. Mind A Festschrift Ken Manktelow 98–114. doi:10.4324/9781315676074 • Hattori, I., Hattori, M., Over, D.E., Takahashi, T., Baratgin, J., 2017. Dual frames for causal induction: the normative and the heuristic. Think. Reason. 23, 292–317. doi:10.1080/13546783.2017.1316314 • Nakamura, H., Shao, J., Baratgin, J., Over, D.E., Takahashi, T., Yama, H., 2018. Understanding conditionals in the east: A replication study of Politzer et al. (2010) With Easterners. Front. Psychol. 9, 505. doi:10.3389/ fpsyg.2018.00505 • Takahashi, T., Kohno, Y., & Oyo, K. (2010). Causal induction heuristics as proportion of assumed-to-be rare Instances (pARIs). In Proceedings of the 7th International Conference on Cognitive Science (ICCS2010) (pp. 361–362) • ߴڮୡೋ, େ༻ݿஐ, ۄ଄ߊ߂, & ԣ઒७و. (2017). كগੑԾఆͷԼͰͷඇಠཱੑͷ൑அͱͯ͠ͷਓؒͷ؍࡯త ҼՌਪ࿦. JSAI 2017 (2017೥౓ਓ޻஌ೳֶձશࠃେձ(ୈ31ճ)) ༧ߘू. http://doi.org/10.14931/bsd.1509 • Takahashi, T., Oyo, K., Tamatsukuri, A. Correlation Detection with and without the Theory of Conditionals: A model update of Hattori & Oaksford (2007). A book chapter proposed, on BioRxiv, doi:10.1101/247742.
43. Papers in preparation • Higuchi, K., Oyo, K., Yokokawa, J., Takahashi, T., (in prep.). Adaptive rationality of the pARIs rule in observational causal induction (tentative). • Sato, A., Takahashi, T., (in prep.). Compounds of conditionals in probability judgments (tentative). • Observational Causal Induction as Independence Test Under Rarity Assumption • Takarada, Y., Oyo, K., Yokokawa, J., Takahashi, T., (in prep.) Causal induction with defective data and defective biconditionals (tentative). • Yoshizawa, H., Takahashi, T., (in prep.). Logical property of Japanese conditionals (tentative).
44. ɹਓ޻஌ೳֶձ
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    ❖ ΩʔΛճ͢
    (C)
    ͱΤϯδϯ͕͔͔Δ (E) ❖ ʮΩʔΛճͣ͞ɼ͔ͭΤϯδϯ͕͔͔Βͳ͔ͬͨʯ
    ❖ Χ΢ϯτࣗମ͸ϑϨʔϛϯάʹΑͬͯՄೳ
    ❖ զʑ͸ීஈϑϨʔϛϯάΛݫີʹܾΊ͍ͯΔ͔
    ❖ ʮ֬཰Ϟσϧʯͷܾఆʹ͸ඞཁෆՄܽ
    ❖ ݫີͳϑϨʔϛϯάΛܾΊΔ͜ͱͦ͜ɺੈք΍ண໨ࣄ৅ ΁ͷհೖͰ͸ͳ͍͔ !44 *Mike Oaksford, personal communication, 2017 ೥ 2 ݄ 13 ೔