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teratail_study
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tkow
December 19, 2016
Technology
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teratail_study
first step of understanding machine_learning
tkow
December 19, 2016
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Transcript
ػցֶशʹຊ֨తೖ͢Δ࣌ ʹ࠷ॳʹԡ͓͖͍͑ͯͨ͜͞ͱ !ULPX
ࣗݾհ ૣҴాେֶઌਐཧֶݚڀՊम࢜ ͖ͬͯͨ͜ͱ ࣗવݴޠॲཧɾ҉߸ཧͳͲ ϨόϨδʔζʹདྷ݄̐ೖࣾ༧ఆ
ϑϧεΫϥονͰΞϧΰϦζϜΛ࣮͍ͯ͠·͢
ػցֶशͰ Կ͕Ͱ͖Δ͔ΛΔ
ҟৗݕ ղ૾ ࠷దઓུ ࣝผ ମೝࣝ ༧ଌ ΫϥελϦϯά ͳͲͳͲʜ
ͦͦԿΛػցʹ͍ͤͯΔͷ͔ ୡͯ͠ཉ͍͠తΛϓϩάϥϛϯά͢Δɻ ίϯϐϡʔλతΛઃఆ͢Δ͜ͱ͕ۤखͳͷͰ ਓ͕ؒࣜͱͯ͠ઃܭͯ͋͛͠Δɻ ਓ͕ؒڭ͑ͳֶͯ͘ͿڧԽֶश༗Γ·͕͢ ༩͑Δਓ͕ؒղ͚ͳͯ͘ྑ͍ɻ ݟ͚͍ͭͨؔੑʹ͍ͭͯίϯϐϡʔλ͕উखʹ ղ͍ͯ͘ΕΔɻ ղ͚ͳ͍͜ͱ͋Δ͚Ͳ
ԿΛษڧ͢Εྑ͍ͷ͔ ϕΠζͷఆཧ ઢܗճؼϞσϧ ֬ ڞࣄલ ࢦ ΧςΰϦΧϧ
χϡʔϥϧωοτ ͜ΕΒΛ͔ͬ͠Γԡ͑͞Δ͚ͩͰݟ௨͕͠ྑ͘ͳΓ·͢ɻ ػցֶशͰ࠷ॳʹԡ͓͖͑ͯࣝ͘͞
ϕΠζͷఆཧ جຊతͳΈ p ( x | ✓ ) ԾఆВͷݩͰY͕ى͜Δ֬
ϕΠζͷఆཧ p(✓| x ) = p( x |✓)p(✓) R
p( x |✓)p(✓)d✓ ԾఆВ ͋ΔԾఆͷ ݩͰಘΒΕͨ σʔλY ಘΒΕͨσʔλ9͔ΒഎޙͷԾఆВΛ ਪఆ͢Δ جຊతͳΈ
ϕΠζͷఆཧ جຊతͳΈ ಘΒΕͨσʔλू߹ͷ͔Β࠷దͳΛਪఆ͢Δ ࠷ ਪఆ ࣄલΛԾఆͯ͠ಘΒΕͨσʔλू߹͔Βࣄલͷ࠷ దͳύϥϝʔλΛਪఆ͢Δ ."1ਪఆ
ಘΒΕͨσʔλू߹͔ΒύϥϝʔλΛपลԽ ϕΠζਪఆ p(✓| x ) = p( x |✓)p(✓) R p( x |✓)p(✓)d✓
ͳͥେࣄ͔ͲΜͳؔͰύϥϝʔλΛ૿ͤۙࣅՄ ೳɻҰԠղੳղ͕ग़ͤΔࣄ͕ଟ͍ ݱ࣮࣌ؒͰղ͚Δͱ ݴ͍ͬͯͳ͍ ɻ ඇઢܗͷϞσϧΛද͢ͷʹઢܗϞσϧ͕ΘΕΔ χϡʔϥ ϧωοτͰɺγάϞΠυؔͳͲͷύϥϝʔλΛઢܗϞ σϧʹಥͬࠐΜͰ͍Δ ɻ
ઢܗϞσϧ y = w0 + w1 1( x ) + · · · + wn n( x )
ϦϯΫؔ ઢܗϞσϧ f (x) = w0 + w1 1(x)
+ . . . + wn n(x) f (x) ϦϯΫؔͱɺઢܗճؼϞσϧΛΈ߹ΘͤΔͱɺϕΠζ ͷఆཧʹͯΊͯɺ࠷ਪఆ."1ਪఆ͕Ͱ͖Δɻ ྫ ɹϦϯΫؔʹMPHJUؔΛͯΊͯ࠷ਪఆΛղ͘ͱϩ δεςΟοΫճؼʹͳΔͳͲ
ͷಛΛԡ͑͞Δͱ͍ΖΜͳσʔλʹର͢Δ༧ଌਪ ఆʹʹཱͪ·͢ ֬ ϕϧψʔΠίΠϯͷදཪͷग़Δ֬ ϕʔλίΠϯͷදཪͷग़Δ͕֬ͲΕ͘Β͍ʹ ͳΔ͔ͷ֬ ΨϯϚਖ਼ͷͷग़͢͞ΛௐઅͰ͖Δ ଟ߲αΠίϩͷͷͲΕ͕ͰΔ͔ͷ σΟϦΫϨαΠίϩͷͷ͕֬ͲΕ͘Β͍ʹ
ͳΔ͔ͷ֬
ͷಛΛԡ͑͞Δͱ͍ΖΜͳσʔλʹର͢Δ༧ଌਪ ఆʹʹཱͪ·͢ ֬ ϕʔλ֬ͷग़͢͞Λௐઅ͢Δ֬
ڞࣄલಛఆͷؔͷੵʹରͯ͠ɺࣄޙͷࣜ ͷܗ͕ಉ͡ࣄલͷ͜ͱɻ ڞࣄલº͕ɺࣄޙͷܗͱಉ͡ʹͳΔ͜ͱΛ ར༻͢Δ͜ͱͰɺࣄޙฏۉͷެࣜΛద༻ͨ͠ΓɺϥϯμϜ αϯϓϦϯάͱݺΕΔख๏Λద༻͘͢͠Δ͜ͱ͕Ͱ͖ Δ σʔλΛਫ૿ͯ͠͠શମͷΛਪఆ͢Δํ๏ ɻ ֬
p ( ✓ | x ) / p ( x | ✓ ) p ( ✓ ) ࣄલ ࣄޙ ϕʔλ㲌ϕϧψʔΠºϕʔλͳͲ
جຊతͳΈ ͋Δϊʔυʹ͓͚ΔೖྗͷΛ׆ੑԽؔͱݺΕΔҙ ͷؔʹΑͬͯɺม͠ɺ࣍ͷೖྗ ग़ྗ ͱ͢Δ ͋ΔϊʔυʹมԽ͕ى͖ͨ࣌ʹશͯͷύϥϝʔλʹٴ΅͢ ӨڹΛࠩͷ࿈Ͱද͢ɻ χϡʔϥϧωοτ x1
x2 x3 f (x)=w1x1+w2x2+w3x3 y= ( f ( x )) y w1 w2 w3
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༗໊ͳຊ
ࣗવݴޠॲཧ͓͢͢Ίຊ
࣮͓͢͢Ίຊ