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[動画あり] 線形回帰を題材に汎用的な理解を身につける:座学編
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数理の弾丸
April 09, 2024
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[動画あり] 線形回帰を題材に汎用的な理解を身につける:座学編
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https://youtu.be/54pe6MDaGI0
数理の弾丸
April 09, 2024
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Transcript
ຊεϥΠυΛ༻ͨ͠ղઆಈը ֓ཁཝͷϦϯΫ͔Β
εϐʔΧʔ ٢ా ژେใܥ%"*ίϯαϧݴޠֶɾࣗવݴޠॲཧ εϛε چఇେଔ3ˍ%ݚڀһԽֶܥ
ࠓճͷΰʔϧ ઢܗճؼϞσϧͷϝΧχζϜͱͦͷॴɾॴΛΔ ઢܗճؼϞσϧͷ1ZUIPO࣮ΠϝʔδΛ࣋ͭ ্هΛ௨ͯ͠ɺ৽ͨͳϞσϧΛʮ׆༻Ͱ͖Δঢ়ଶ·Ͱཧղ͢Δʯ ͱ͍͏͜ͱͷഽײ֮Λ௫Ή
৽ͨͳϞσϧΛʮ׆༻Ͱ͖Δঢ়ଶ·Ͱཧղ͢Δʯͱ͍͏͜ͱͷഽײ֮Λ௫Ήͷؾ࣋ͪ ઢܗϞσϧ ܾఆ χϡʔϥϧωοτ Lฏۉ๏ ϚϧίϑϞσϧ FUD ৽ͨͳٕज़Λशಘ͢Δඞཁੑৗʹ͋Δ
ࠓճͷΰʔϧ ઢܗճؼϞσϧͷϝΧχζϜͱͦͷॴɾॴΛΔ ઢܗճؼϞσϧͷ1ZUIPO࣮ΠϝʔδΛ࣋ͭ ্هΛ௨ͯ͠ɺ৽ͨͳϞσϧΛʮ׆༻Ͱ͖Δঢ়ଶ·Ͱཧղ͢Δʯ ͱ͍͏͜ͱͷഽײ֮Λ௫Ή
͜ͷಈըͰ৮Εͳ͍͜ͱ ֶशΞϧΰϦζϜͷৄࡉ ࠷খೋ๏ʹΑΔύϥϝʔλ࠷దԽ ઢܗճؼͷੜख๏ ਖ਼ଇԽɺϩδεςΟοΫճؼFUD
ճؼͱʁ
ճؼͱʁ ճؼ େখʹҙຯͷ͋ΔΛ༧ଌ͢Δઃఆ
ճؼͱʁ ճؼ େখʹҙຯͷ͋ΔΛ༧ଌ͢Δઃఆ Ωϟϯϖʔϯछผ ސ٬ಛੑ ༧ଌ ޮՌࢦඪ ΩϟϯϖʔϯͷޮՌ༧ଌ ྫ
ճؼͱʁ ճؼ େখʹҙຯͷ͋ΔΛ༧ଌ͢Δઃఆ Ωϟϯϖʔϯछผ ސ٬ಛੑ ༧ଌ ޮՌࢦඪ ΩϟϯϖʔϯޮՌͷࣄલγϛϡϨʔγϣϯ ൢଅޮՌͷߴ͍ސ٬ಛੑͷൃݟ
ΩϟϯϖʔϯͷޮՌ༧ଌ ྫ
ճؼͱʁ ճؼ େখʹҙຯͷ͋ΔΛ༧ଌ͢Δઃఆ Ωϟϯϖʔϯछผ ސ٬ಛੑ ༧ଌ ޮՌࢦඪ ΩϟϯϖʔϯޮՌͷࣄલγϛϡϨʔγϣϯ ൢଅޮՌͷߴ͍ސ٬ಛੑͷൃݟ
ΩϟϯϖʔϯͷޮՌ༧ଌ ྫ આ໌มʢ༧ଌͷใݯͱ͢Δʣ తมʢ༧ଌͷରͱ͢Δʣ
ઢܗճؼϞσϧͱʁ
ઢܗճؼϞσϧͱʁ ઢܗճؼ తมΛઆ໌มͷҰ࣍ࣜͰ༧ଌ͢ΔϞσϧ y = w1 x1 + w2
x2 + b
ઢܗճؼϞσϧͱʁ ઢܗճؼ తมΛઆ໌มͷҰ࣍ࣜͰ༧ଌ͢ΔϞσϧ y = w1 x1 + w2
x2 + b આ໌ม తม ༧ଌͷରͱ͢Δ ༧ଌͷใݯͱ͢Δ
ઢܗճؼϞσϧͱʁ ઢܗճؼ తมΛઆ໌มͷҰ࣍ࣜͰ༧ଌ͢ΔϞσϧ y = w1 x1 + w2
x2 + b આ໌ม తม ύϥϝʔλ ಛʹ ʮઆ໌มͷ֤ΛͲΕ͘Β͍༧ଌʹӨڹͤ͞Δ͔ʯΛද͢ w ༧ଌͷରͱ͢Δ ༧ଌͷใݯͱ͢Δ
ΠϝʔδʮઢͷͯΊʯ ސ٬ಛੑʢFH݄ͨΓߪങֹʣ ޮՌࢦඪ
ΠϝʔδʮઢͷͯΊʯ ސ٬ಛੑʢFH݄ͨΓߪങֹʣ ޮՌࢦඪ
ΠϝʔδʮઢͷͯΊʯ ސ٬ಛੑʢFH݄ͨΓߪങֹʣ ޮՌࢦඪ
ΠϝʔδʮઢͷͯΊʯ ސ٬ಛੑʢFH݄ͨΓߪങֹʣ ޮՌࢦඪ ઢͷܗΛܾΊΔͷ͖ͱย w ͕͖ΛܾΊɺ ͕ยΛܾΊΔ w ͯ·Γͷྑ͞
Ͱܾ·Δ w ֶश Λσʔλʹ߹Θͤͯௐ͢Δ͜ͱ w b w, b w, b
ࠓճͷΰʔϧ ઢܗճؼϞσϧͷϝΧχζϜͱͦͷॴɾॴΛΔ ઢܗճؼϞσϧͷ1ZUIPO࣮ΠϝʔδΛ࣋ͭ ্هΛ௨ͯ͠ɺ৽ͨͳϞσϧΛʮ׆༻Ͱ͖Δঢ়ଶ·Ͱཧղ͢Δʯ ͱ͍͏͜ͱͷഽײ֮Λ௫Ή
ઢܗճؼϞσϧͷॴͱॴ
y = w1 x1 + w2 x2 + b ઢܗճؼϞσϧͷॴͱॴ
ॴ Ϟσϧͷ͕ࣜγϯϓϧͰɺֶशޙͷঢ়ଶΛղऍ͍͢͠ ➡︎ ୯ʹ༧ଌثͱͯ͠͏͚ͩͰͳ͘ɺཁҼੳʹ׆༻͍͢͠ 2.5 0.8
y = w1 x1 + w2 x2 + b ઢܗճؼϞσϧͷॴͱॴ
ॴ Ϟσϧͷ͕ࣜγϯϓϧͰɺֶशޙͷঢ়ଶΛղऍ͍͢͠ ➡︎ ୯ʹ༧ଌثͱͯ͠͏͚ͩͰͳ͘ɺཁҼੳʹ׆༻͍͢͠ 2.5 0.8
ॴ ઢܗճؼϞσϧͷॴͱॴ આ໌มͱతมͷؒʹઢܗͷ͕ؔͳ͍߹ɺ ͏·͘ϞσϦϯά͢Δͷ͍͠
ઢܗճؼϞσϧͷॴͱॴ ॴ આ໌มͱతมͷؒʹઢܗͷ͕ؔͳ͍߹ɺ ͏·͘ϞσϦϯά͢Δͷ͍͠ ॴ Ϟσϧͷ͕ࣜγϯϓϧͰɺֶशޙͷঢ়ଶΛղऍ͍͢͠ ➡︎ ୯ʹ༧ଌثͱͯ͠͏͚ͩͰͳ͘ɺཁҼੳʹ׆༻͍͢͠
ࠓճͷΰʔϧ ઢܗճؼϞσϧͷϝΧχζϜͱͦͷॴɾॴΛΔ ઢܗճؼϞσϧͷ1ZUIPO࣮ΠϝʔδΛ࣋ͭ ্هΛ௨ͯ͠ɺ৽ͨͳϞσϧΛʮ׆༻Ͱ͖Δঢ়ଶ·Ͱཧղ͢Δʯ ͱ͍͏͜ͱͷഽײ֮Λ௫Ή