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決定木のpredict_proba()の話
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Aipa
January 19, 2019
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決定木のpredict_proba()の話
決定木のpredict_proba()の話
Aipa
January 19, 2019
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Transcript
ܾఆͷ ࣾ-5ΞΠύʔୂ
͢͜ͱ
͢͜ͱ w ܾఆͷॲཧϑϩʔ w ָ࣮͍͠
൪ ͓͢͢ΊͷөըΛΈ͍ͨେ౷ྖ
൪ w "ʣେ౷ྖɺΑ͘ฉ͍͍ͯͩ͘͞ w "ʣʮϫχʯʹજΔ͚ͩͰύλʔϯ͕͋Γ·ͤΜ w "ʣʮαϝʯͦ͜ࢤͰ͢ A͞Μ
൪ w #ʣʮαϝʯઃఆΨϯແࢹͯ͠ϦΞϦςΟ͕ͳ͍ w #ʣαϝʹଟ٭ͷັྗͳ͍ w #ʣωλ͕ΕͨΒ͙͢ϩϘԽʹΔʂʂ w "ʣʮϩϘΫϩίʯΛΕΔΜ͡Όͳ͍ B͞Μ
൪ w "ʣʮϫχʯʹʮ+"84ʯͷΑ͏ͳ໊࡞ͳ͍ͩΖ͏ʂʂ w #ʣʮϚϯΠʔλʔʯྑ࡞Αʂલඈ͍͍͚ͯ͠Ͳ
൪ w "ʣେ౷ྖʂͭΒྫྷࠅͳʮϨϓςΟϦΞϯʯͰ͢ɻܾ͝அΛ w #ʣΕʂʮαϝχετʯʂʂେ౷ྖɻ͓ئ͍͠·͢ɻ
൪ w େ౷ྖʣʮελʔΥʔζʯΈΔΘ
൪ʢݩωλͱ͍͏ؙ͔ύΫϦʣ w ӕࣈນγϦʔζ w େ౷ྖʹ͓͢͢Ί͢ΔөըͲͪΒ͔Λ૪͏ಈը w ݱࡏআ͞Ε͍ͯΔʢ೦ ɾТɾʆ ʣ
൪ w ·͊ͰؾʹͳΓ·͢ΑͶʢαϝ͕໘ന͍ͷ͔ϫχ͕໘ന͍ͷ͔ʣ
൪ w ܦݧΛݩʹܰྔͳσʔληοτΛ༻ҙ͢Δ ߦ͙Β͍
൪ w ܾఆΛ࡞͢Δ
൪
൪ w Ͳͷ͘Βֶ͍श͕͏·͍ͬͯ͘ΔΜ͚ͩͬʁ
൪ w ;Ή;Ήʙʙʙʢനʣ
ٙ ͜Ε
ࢲɺؾʹͳΓ·͢ w ͲΜͳͯ͠ܭࢉ͞Ε͍ͯΔͷʁ w ༧ w ʮྨ͞ΕͨΫϥεZJྨ͞Εͨσʔλ૯֬ʯ
ٙ w ௐͯΈͨ
ܾఆͷॲཧϑϩʔ
ܾఆͷॲཧϑϩʔ ᶃroot nodeΛ༻ҙ͢Δ
ܾఆͷॲཧϑϩʔ ᶄೖྗ͞Εͨσʔλͷ ΫϥεϥϕϧΛଟܾͰܾΊΔ ͭ·Βͳ͍
ᶅׂ͢Δલʹ giniΛٻΊΔ => [9, 9] => 0.5 ͭ·Βͳ͍ ܾఆͷॲཧϑϩʔ
ᶆׂީิʢಛྔʣΛ࡞͠ɺ ݅Λ࡞͢Δ ͭ·Βͳ͍ or ʮ1ͳΒαϝ 0ͳΒϫχʯͳͱ͖ ݅ਅΜத => 0.5ͱͳΔ ܾఆͷॲཧϑϩʔ
ᶇ࡞ͨ݅͠Ͱׂͯ͠ΈΔ ͭ·Βͳ͍ or ϫχ13 αϝ5 ܾఆͷॲཧϑϩʔ
ᶈׂޙͷσʔλͦΕͧΕͰ giniΛܭࢉ ͭ·Βͳ͍ or ϫχ13 => 0.497 αϝ5 => 0.48
ܾఆͷॲཧϑϩʔ
ᶉׂ݅ͷળ͠ѱ͠Λ அ͢ΔͨΊʹɺ ׂલޙͷෆ७ͷมԽΛ ٻΊ·͢ ͭ·Βͳ͍ or ϫχ13 => 0.497 ׂ͞Εׂͨ߹
=> 13/18 => 0.72 αϝ5 => 0.48 ׂ͞Εׂͨ߹ => 5/18 => 0.27 ܾఆͷॲཧϑϩʔ
ᶉׂ݅ͷળ͠ѱ͠Λ அ͢ΔͨΊʹɺ ׂલޙͷෆ७ͷมԽΛ ٻΊ·͢ ͭ·Βͳ͍ or ׂલͷgini - ((ϫχׂޙͷgini *
ϫχׂ͞Εׂͨ߹) + (αϝׂޙͷgini * αϝׂ͞Εׂͨ߹)) => 0.5 - ((0.497 * 0.72) + (0.48 * 0.27)) => 0.00769 ܾఆͷॲཧϑϩʔ
ᶊධՁޙͷ(จࣈ)Λอ͓࣋ͯ͘͠ => ᶆʙᶉΛ܁Γฦ͠ൺֱͯ͠ Ұ൪େ͖͍Λ => ׂʹϕετͳಛྔ͕ܾ·Δ ͭ·Βͳ͍ or ׂલͷgini -
((ϫχׂޙͷgini * ϫχׂ͞Εׂͨ߹) + (αϝׂޙͷgini * αϝׂ͞Εׂͨ߹)) => 0.5 - ((0.497 * 0.72) + (0.48 * 0.27)) => 0.00769 ܾఆͷॲཧϑϩʔ
ͭ·Βͳ͍ ᶋϫχͱαϝΛྨͨ͠σʔλΛ༻͍ͯ ࠨଆͱӈଆʹࢬΛ࡞Δ => ᶃʙᶊͱಉ͜͡ͱΛ͢Δ ܾఆͷॲཧϑϩʔ
ͭ·Βͳ͍ ᶌධՁޙͷ͕มԽ͠ͳ͚Εऴྃ => ࠓճಛྔ͔̍ͭ͠ͳ͍ͷͰ ਂ͞2ͰऴΘΔ ܾఆͷॲཧϑϩʔ
ͭ·Βͳ͍ ݁Ռ ※max_depthͱ͔ min_sample_leafͱ͔Ͱ ͬͱࡉ͔͍ܾ݅ΊΕΔ͚ͲׂѪ ϫχ ͭ·Βͳ͍ 7 ͓͠Ζ͍ 6
αϝ ͭ·Βͳ͍ 2 ͓͠Ζ͍ 3 ܾఆͷॲཧϑϩʔ
ͭ·Βͳ͍ ϫχ ͭ·Βͳ͍ 7 ͓͠Ζ͍ 6 αϝ ͭ·Βͳ͍ 2 ͓͠Ζ͍
3 ܾఆͷॲཧϑϩʔ
QSFEJDU@QSPCBͷ࣮
QSFEJDU@QSPCBͷ࣮ ϫχ ͭ·Βͳ͍ 7 ͓͠Ζ͍ 6 αϝ ͭ·Βͳ͍ 2 ͓͠Ζ͍
3 ιʔεΛಡΜͰΈΔͱ ܇࿅࣌ʹྨ͞Ε͍ͯΔ σʔλΛͬͯࢉग़ͯ͠ ͍Δ͜ͱ͕Θ͔ͬͨ
QSFEJDU@QSPCBͷ࣮ ϫχ ͭ·Βͳ͍ 7 ͓͠Ζ͍ 6 αϝ ͭ·Βͳ͍ 2 ͓͠Ζ͍
3 ᶃςετσʔλΛೖྗ͢Δ ςετσʔλ
QSFEJDU@QSPCBͷ࣮ ϫχ ͭ·Βͳ͍ 7 ͓͠Ζ͍ 6 αϝ ͭ·Βͳ͍ 2 ͓͠Ζ͍
3 ᶄྨ͢Δ ςετσʔλ ϫχͬΆ͍
QSFEJDU@QSPCBͷ࣮ ϫχ ͭ·Βͳ͍ 7 ͓͠Ζ͍ 6 ᶅྨ͞ΕͨNodeʹ͋Δ ܇࿅࣌ͷྨσʔλΛͬͯ ֬ΛٻΊΔ ςετσʔλ
-> [[ͭ·Βͳ͍,͓͠Ζ͍]] -> [[7, 6]] σʔλຖʹ߹ܭ͢Δ [[7 ,6]].sum(axis=1) -> [13] ׂΔ [[7, 6]] / [13] -> [[0.538, 0.461]]
QSFEJDU@QSPCBͷ࣮ w TDJLJUMFBSOͷ࣮ ೖྗͨ͠σʔλ͕ͲͷNodeʹ͋ͯ·Δ͔୳ࡧͯ͠ɺ֘ ͨ͠Node͕ྨͨ͠܇࿅࣌ͷσʔλΛฦ͢(Cython) ֘ͨ͠Ϋϥε͝ͱͷσʔλΛσʔλ૯ͰׂΔ ex) [[ͭ·Βͳ͍,͓͠Ζ͍]] -> [[7,
6]] σʔλຖʹ߹ܭ͢Δ [[7 ,6]].sum(axis=1) -> [13] ׂΔ [[7, 6]] / [13] -> [[0.538, 0.461]]
ࡶײ
ࡶײ w ܾఆͷͳͷͰɺଞͷΞϧΰϦζϜͷ࣮Έ͍ͨ w αϝόϯβΠ w ϫχόϯβΠ
͓·͚
͓·͚ ʮαϝਓΛऻ͏ʯϨοςϧΛషͬͨ ໊࡞தͷ໊࡞ લඈ͍͍͚ͯ͠Ͳ ྑ࡞
͓·͚ ʮαϝਓΛऻ͏ʯϨοςϧΛషͬͨ ໊࡞தͷ໊࡞ લඈ͍͍͚ͯ͠Ͳ ྑ࡞