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正規分布でpythonに絡む
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yobe
February 17, 2018
Technology
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正規分布でpythonに絡む
正規分布でpythonに絡む
yobe
February 17, 2018
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Transcript
ਖ਼ن͔ΒQZUIPO ʹབྷΉ ΜͳΓ1ZUIPO ٢ాɹوً
ࣗݾհ 1)1FS͙̑Β͍ 1ZUIPOJTUB͙Β͍ ΤϯδχΞ
։ൃڥ IPNFCSFX NBDύοέʔδཧιϑτʁ QZFOW 1ZUIPO"OBDPOEBDVTUPN CJU +VQJUFSMBCɺOPUFCPPLʑ
ਖ਼نͬͯ w ͜Μͳײ͡
ਖ਼نͱ ɺମॏɺଌఆޡࠩ,ςετͷͳͲ௨ৗɺதԝۙͷ ฏۉͷۙ͘ͷਓ͕Ұ൪ଟ͘ɺ0100ʹۙͮ͘΄Ͳਓ ͕গͳ͘ͳΓɺಘͷࠨӈରশͷܕʹͳΔ͜ͱ͕ ଟ͍ͱݴΘΕ·͢ɻ͜ͷΑ͏ͳͷܕΛਖ਼نʢΨε ʣͱݴ͍·͢ɻ
ਖ਼نͬͯ
ਖ਼نͷಛ ɾ໘ੵΛશͯੵ͢Δͱ1ʹͳΔɻ(֬ͷੑ࣭) ͋Δ۠ؒͷ໘ੵͷੵɺͦͷ۠ؒ ͷσʔλ͕ൃੜ͢Δ֬ͱͯ͠ѻ͑Δɻ • ඪ४ภࠩΛσ(γάϚʣͱͨ͠ͱ͖ɺ±σʢϛϡʔʣͷൣғʹ68%ͷσʔλ͕͓͞· Δɻ±2σͷൣғʹ95%ͷσʔλ͕͓͞·Δɻ • ൃੜ͢Δ͕͍֬Λ؍ଌ͢ΔͱҟৗͳͰ͋Δͱఆ͍ͨ࣌͠ʹ͑Δɻ
ඪ४ภࠩͱʢͪΐͬͱิʣ ͷΒ͖ͭΛݟΔ͜ͱ͕Ͱ͖Δɻ ઌʹࢄΛٻΊΔɻ ฏۉͱͦΕͧΕͷͱͷࠩͷೋʹର͢Δฏۉ ͕ࢄΒ͍ͬͯΔͱେ͖͘ͳΔɻ
ਖ਼نͷಛ
ਖ਼نͷ͍ॴ #͓ళͷདྷళऀΛຖʹ͚Δͱ
ਖ਼نͷ͍ॴ ਖ਼نͰݟΔͱ ചΓ্͛ͷ͋Δͳ͍ͻ
͍ͭͰʹࠞ߹Ψε ౷ܭͷΛ͢Δͱ৭Μͳख๏͕͋Γ·͢ɻ
͍ͭͰʹࠞ߹Ψε ͷΫϥελϦϯάͱݴΘΕΔɻσʔλͷಛ͔Βྨ͢Δख๏ ͰΘΕɺͳʔΜͱͳ͘σʔλͷಛΛྨͯ͘͠Ε·͢ɻ
ΑΓΑࣝ͘ผͰ͖Δ K-meansʢࠨਤʣͱͷൺֱʹͳΓ·͕͢
ྫ͑ ͜Μͳਖ਼ن
Α͘ݟΔͱ ೋͭͷਖ਼ن ͷֻ͚߹Θͤʹ ݟ͑·͢ɻ
Α͘ݟΔͱ ͷͯ·Γ͕ྑ͍ΜͰ͢ʂ
w&.ΞϧΰϦζϜΛ༻ ֬ϞσϧͷύϥϝʔλΛ࠷ਪఆ͢Δख๏ͷҰͭ Ͱ͋Γɺ؍ଌෆՄೳͳજࡏมʹ֬Ϟσϧ͕ґଘ ͢Δ߹ʹ༻͍ΒΕΔɻɹ -ͪͳΈʹ࠷ਪఆ ύϥϝʔλ͕͋Δ a,ba,b ͩͬͨ࣌ʹͦͷσʔλ͕ग़ྗ͞ΕΔ֬ p(x,y|a,b)p(x,y|a,b) Λ
ͱݺͿ -ͪͳΈʹͱ ʢͬͱʣΒ͍͠ͷ߹ ͕࠷ߴʹͳΔΑ͏ʹa,ba,bΛબͿ(࠷ਪఆ)ɿ
w&.ΞϧΰϦζϜ E εςοϓͱ M εςοϓͷऩଋ͢Δ·Ͱ܁Γฦ͠ॲཧΛ͓͜ͳ͏ΞϧΰϦζϜ E εςοϓʢظࢉग़ʣɹ ଟมྔਖ਼نͷμσͱࠞ߹Λݻఆ͠ɺΛ࠷େʹ͢ΔॴଐΫϥεΛٻΊ͍ͯΔ͜ͱʹ૬ ͢Δ --
Ϋϥελ͝ͱʹɺ֤σʔλ͕ͦ͜ʹଐ͢Δ֬Λࢉग़ -- ࢉग़͞Εͨ֬ͷ߹ܭΛٻΊΔ -- ΫϥελͰͷ֬ɺ͖݅֬Ͱ͋Δʹҙ M εςοϓʢظ࠷େԽͷͨΊͷใߋ৽ʣɹ – ॴଐΫϥεΛݻఆ͠ɺΛ࠷େʹ͢Δଟมྔਖ਼نͷμσͱࠞ߹ΛٻΊΔɻ • Ϋϥελ͝ͱʹࢉग़֬ͷฏۉΛٻΊɺͦΕΛΫϥελॴଐ֬ʢ͖݅֬ͷ݅෦ͷ ֬ʣͱ͢Δ • ࣍ͷॏ৺Λɺσʔλ࠲ඪΛ֬ͰॏΈ͚ͯ͠ࢉग़͢Δ • ৽͍͠ॏ৺Λ͍֬ͰॏΈ͚
͓͠·͍ ͝੩ௌ͋Γ͕ͱ͏͍͟͝·ͨ͠ɻ