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B3_Seminar_04
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kakubari
February 16, 2017
Technology
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60
B3_Seminar_04
長岡技術科学大学 自然言語処理研究室
角張竜晴
kakubari
February 16, 2017
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Transcript
Ԭٕज़Պֶେֶ ిؾిࢠใֶ՝ఔ ֶ෦ɹ֯ுཽ ࣗવݴޠݚڀࣨ ɹ#̏θϛ ʙୈճʙ ϏοΫσʔλղੳೖᶄ
目次 ˔౷ܭͷجૅ ˔֬ີؔɾྦྷੵؔ
統計の基礎 ˔ఆৗͱ ɹ࣌ܥྻղੳͰඞཁͱͳͬͯ͘Δ֓೦ ˔࣌ܥྻͱ ɹ࣌ؒͷྲྀΕͱڞʹ؍ଌྔͷมԽ͕ه͞Εͨσʔλ ɹྫ͑ɾɾɾ ɹɾҝସגͷՁ֨ ɹɾಉ͡ॴͷؾԹؾѹ
統計の基礎 ͋Δ࣌ࠁ̓ʹ؍ଌ͞ΕͨΛ͇ ̓ Ͱද͢ɻ ࣌ܥྻ͕ఆৗͰ͋ΔͨΊͷ݅ɾɾɾ ɾฏۉ͕࣌ؒʹΑΒͣҰఆɹ ɾࢄ͕࣌ؒʹΑΒͣҰఆ ɾࣗݾڞࢄ͕࣌ؒࠩͷؔ ͜͜ͰɺЖ
Мఆɺ̺࣌ؒࠩΛද͢ɻ E[x(t)] = µ E[x(t)− µ]2 = σ 2 E[(x(t)−µ)(x(t − k)−µ)]= C(k)
統計の基礎 ˔౷ܭղੳΛߦ͏্Ͱఆৗੑɺඇৗʹॏཁ ղੳΛ͢Δσʔλͷൣғ͕มΘͬͯಉ͡౷ܭ݁Ռ ͕ಘΒΕΔΛ͍ࣔࠦͯ͠Δɻ ͭ·Γɺ౷ܭ݁ՌʹൣғબʹΑΔۮવੑ͕བྷΉ͜ͱ Λഉআͯ͘͠ΕΔɻ
統計の基礎 ˔౷ܭղੳͱ ɹશମ͔Βൈ͖ग़ͨ͠Ұ෦ΛݟͯɺશମΛΔ ྫ͑ɾɾɾʮຊதͷখֶੜͷମॏΛௐࠪ͢Δʯ ɹௐࠪରɿຊશࠃͷখֶੜશһ ௐࠪͷରͱͳΔूஂΛूஂͱ͍͏ɻ ཧͱͯ͠ɺूஂΛͯ͢ௐࠪ͢ΕΑ͍ɻ
શௐࠪ
統計の基礎 ͕ͩɺूஂ͕େ͖͘ɺௐ͕ࠪࠔͰ͋Δɻ Ὃ ूஂ͔Β̽ݸΛൈ͖ग़ͯ͠؍ଌ͠ɺ ͔ͦ͜ΒશମͷಛΛਪఆ͢Δɻ
؍ଌͷूஂඪຊͱݺͿɻ ಛʹɺཁૉ͕̽ͷ߹େ͖̽͞ͷඪຊͱݺͿɻ
統計の基礎 ʙ౷ܭղੳΛߦ͏্Ͱॏཁͳ๏ଇʙ ˔େͷ๏ଇ ʮ͋Δूஂ͔Βແ࡞ҝநग़͞ΕͨඪຊฏۉඪຊͷαΠζΛ େ͖͘͢Δͱਅͷฏۉʢूஂͷฏۉʣʹۙͮ͘ʯ ˔த৺ۃݶఆཧ ʮฏۉЖɺࢄМΛ࣋ͭҙͷʹै͏ूஂ͔Βɺ େ͖̽͞ͷඪຊΛநग़ͨ࣌͠ɺඪຊฏۉ̚<͇>ͷɺ͕̽े େ͖͚ΕฏۉЖɺࢄМ̽ͷਖ਼نʹۙͮ͘ʯ
˔֬ີؔ ɹ֬มʢཧྔʣ̭͕ඍখͳ۠ؒ ʹͦͷΛͱΔ֬ʢ֬ີʣΛ༩͑Δؔ ɹ֬ม̭͕ɹɹɹɹɹͱͳΔ֬Λ ͱ͢Δͱɺ ֬ਖ਼Ͱ͋Γɺͦͷ͕̍Ͱ͋Δ͜ͱ͔Βɺ f
(x) x < X < x +δx P(a < X < b) = f (x)dx a b ∫ a < X < b P(a < X < b) f (x)dx −∞ +∞ ∫ =1 f (x) ≥ 0
確率密度関数・累積分布関数 ˔ώετάϥϜ ɹ۠ؒͷදΛԣ࣠ʹɺͦͷ۠ؒͷΛॎ࣠ʹͱͬͯࢹ֮Խ ͨ͠ͷ ֬มͷಛ͕Θ͔Δ ɹɾͲͷ͘Β͍͕ΓΛ͔࣋ͭ ɹɾҰ൪ଟ͍Կ͔
ͳͲʜ ώετάϥϜͷ֓ܗΛ͑ΔͨΊʹن֨ԽΛߦ͏ɻ ɹɾΛσʔλͰׂΓɺ֤۠ؒͰͷ֬Λܭࢉ͢Δ ɹɾ֤۠ؒͷ֬Λ۠ؒͷ෯ͰׂΓɺ֬ີΛܭࢉ͢Δ ɹɾԣ࣠ʹ֤۠ؒͷදɺॎ࣠ʹ֬ີΛϓϩοτ͢Δ
確率密度関数・累積分布関数 ˔ྦྷੵؔ ɹ֬มͷ͕͇ΑΓେ͖͘ͳΔ֬Λ༩͑Δؔ ֬ີؔΛ༻͍ͯɺ ͱఆٛ͞ΕΔؔ'Λ֬ม̭ͷྦྷੵؔͱ͍ ͏ɻ F(x)
= P(X > x) = f ( ! x )d ! x x ∞ ∫
確率密度関数・累積分布関数 ˔ར ۠ؒΛ۠Δඞཁ͕ͳ͍ͨΊɺσʔλ͕ൺֱతগͳ͘ ͯ͋Δఔ͖Ε͍ʹඳ͚Δɻ σʔλͱྦྷੵؔ̍ର̍ʹରԠ͢Δɻ ˔άϥϑͷॻ͖ํ ɹ֬ີؔʢੵʣΛܦ༝͢Δํ๏ɺݫີͳ݁Ռ
Λಘ͍ͨ߹ʹ΄ͱΜͲΘΕͳ͍ɻ࣮ࡍɺσʔλͷ ιʔτͰٻΊΔɻ ᾇ̣ݸͷσʔλΛେ͖͍ॱʹฒΔ ᾈঢॱʹσʔλʹରͯ͠ɺ͔̍Β/·ͰॱҐ3Λ͚ͭΔ ᾉσʔλͷΛԣ࣠ʹɺ3/Λॎ࣠ʹϓϩοτ͢Δ
参考文献 ˔ߴ҆ඒࠤࢠฤஶɺాଜޫଠɾࡾӜߤஶɺ ɹʮֶੜɾٕज़ऀͷͨΊͷϏοΫσʔλղੳೖʯ ʢୈ̍ষʙୈ̏ষʣɺ ɹגࣜձࣾຊධࣾɺ݄