머신러닝을 위한 기초 수학 살펴보기

머신러닝을 위한 매우 기초적인 수학과 이를 응용한 선형 회귀 학습 예제

Transcript

1. ݠन۞׬ਸ
   ਤೠ
   ӝୡ
   ࣻ೟
   ࢓ಝࠁӝ (FUUJOH
   TUBSUFE
   UP
   MFBSO
   UIF
   MJOFBS
   BMHFCSB
   XJUI
   QZUIPO ӂ޹੤
2. ݠन۞׬ਸ ਤೠ ӝୡ ࣻ೟ ࢓ಝࠁӝ MinJae Kwon (@mingrammer) 2017.08.12 (Getting started to learn the linear algebra with python)
3. Name ӂ޹੤ (MinJae Kwon) Nickname @mingrammer Email k239507@gmail.com Who Game Server Engineer @ SundayToz Blog https://mingrammer.com Facebook https://facebook.com/mingrammer Github https://github.com/mingrammer Eng Blog https://medium.com/@mingrammer
4. 2. ࢶഋ؀ࣻ೟੉ۆ? 4. ୶о ӝୡ ࣻ೟ ࢓ಝࠁӝ Contents 5. ࢶഋ ഥӈ ҳഅ೧ࠁӝ 1. ࣻ೟੄ ೙ਃࢿ 3. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ 6. Next (more LA and Mathematics)
5. ࣻ೟੄ ೙ਃࢿ ੉ߣ
   ࣁ࣌਷
   ઱۽
   ӝୡ
   ࢶഋ؀ ࣻ೟ਸ
   ׮ܖ޲۽
   
   
   ׮਺
   ࣻधٜ੉
   ੊ࣼೞ૑
   ঋ਷
   ٜ࠙ਸ
   ؀࢚ਵ۽
   ೤פ׮ W ←W −α ∂L ∂W E = − 1 N t nk log(y nk ) k ∑ n ∑ d(u ! u ! T ) = 2u !
6. ࣻ೟੄ ೙ਃࢿ ਢ ѐߊ জ ѐߊ API ѐߊ ࣻ೟ T(x) ∂ ∂θ f (x,θ)dx ∫ −log(t)y(t) ∑ x∇f (x) 1 σ 2π e −(x−µ)2 2σ 2 −∞ ∞ ∫
7. ࣻ೟੄ ೙ਃࢿ ਢ ѐߊ জ ѐߊ API ѐߊ ࣻ೟ *U
   EFQFOET
   PO
   j
   CVU T(x) ∂ ∂θ f (x,θ)dx ∫ −log(t)y(t) ∑ x∇f (x) 1 σ 2π e −(x−µ)2 2σ 2 −∞ ∞ ∫
8. ࣻ೟੄ ೙ਃࢿ ߑޙ੗
   ࣻ
   ҅ஏ ୶ୌ
   ঌҊ્ܻ ঐഐ
   ࢸ҅ ঑୷
   ঌҊ્ܻ %
   ݽ؛݂ ѱ੐
   ূ૓ ୭ࣗ
   ࠺ਊ
   ঌҊ્ܻ ೐۽ࣁझ
   झாે݂ Ӓې೗
   ୊ܻ ഛܫ
   ݽ؛ ҊബਯҊࢿמ
   ҅࢑
   ࢸ҅ ݠन۞׬ ؘ੉ఠ߬੉झ नഐ
   ୊ܻ
9. ࣻ೟੄ ೙ਃࢿ ݠन۞׬ ߑޙ੗
   ࣻ
   ҅ஏ ୶ୌ
   ঌҊ્ܻ ঐഐ
   ࢸ҅ ঑୷
   ঌҊ્ܻ %
   ݽ؛݂ ѱ੐
   ূ૓ ୭ࣗ
   ࠺ਊ
   ঌҊ્ܻ ೐۽ࣁझ
   झாે݂ Ӓې೗
   ୊ܻ ഛܫ
   ݽ؛ ҊബਯҊࢿמ
   ҅࢑
   ࢸ҅ ؘ੉ఠ߬੉झ नഐ
   ୊ܻ
10. ࣻ೟੄ ೙ਃࢿ .BDIJOF
    -FBSOJOH
    "MHPSJUINT 5SBJO
    %BUB .PEFMT 7BMJEBUJPO
    %BUB 0VUQVUT /FX
    %BUB
11. ࣻ೟੄ ೙ਃࢿ 6 7 8 ... 5 7 5 6 ... 3 8 4 1 ... 4 ... ... ... ... 2 0 1 5 4 3 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ W = W −α ∂L ∂W 0 0 1 ... 0 1 0 0 ... 0 0 1 0 ... 0 ... ... ... ... 0 0 0 0 0 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 0 1 0 ... 0 1 0 0 ... 0 0 1 0 ... 0 ... ... ... ... 0 0 0 1 0 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 4 1 5 ... 8 ⎡ ⎣ ⎤ ⎦ 1 2 (y k − t k )2 ∑ y k = eak eai ∑ 0.5 0.4 ... ... 0.8 0.1 −0.3 ... ... 0.2 ... ... ... ... 0.1 ... ... ... ... 0.43 0.03 0.23 0.1 0.3 0.13 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 0 1 0 ... 0 ⎡ ⎣ ⎤ ⎦ Y = X ⋅W + B
12. ࣻ೟੄ ೙ਃࢿ 6 7 8 ... 5 7 5 6 ... 3 8 4 1 ... 4 ... ... ... ... 2 0 1 5 4 3 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ W = W −α ∂L ∂W 0 0 1 ... 0 1 0 0 ... 0 0 1 0 ... 0 ... ... ... ... 0 0 0 0 0 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 0 1 0 ... 0 1 0 0 ... 0 0 1 0 ... 0 ... ... ... ... 0 0 0 1 0 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 4 1 5 ... 8 ⎡ ⎣ ⎤ ⎦ 1 2 (y k − t k )2 ∑ y k = eak eai ∑ 0.5 0.4 ... ... 0.8 0.1 −0.3 ... ... 0.2 ... ... ... ... 0.1 ... ... ... ... 0.43 0.03 0.23 0.1 0.3 0.13 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ Y = X ⋅W + B ࢶഋ؀ࣻ೟ ࢶഋ؀ࣻ೟ ࢶഋ؀ࣻ೟ ഛܫҗ
    ా҅ ഛܫҗ
    ా҅ ޷੸࠙೟ 0 1 0 ... 0 ⎡ ⎣ ⎤ ⎦
13. ࣻ೟੄ ೙ਃࢿ 6 7 8 ... 5 7 5 6 ... 3 8 4 1 ... 4 ... ... ... ... 2 0 1 5 4 3 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ W = W −α ∂L ∂W 0 0 1 ... 0 1 0 0 ... 0 0 1 0 ... 0 ... ... ... ... 0 0 0 0 0 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 0 1 0 ... 0 1 0 0 ... 0 0 1 0 ... 0 ... ... ... ... 0 0 0 1 0 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 4 1 5 ... 8 ⎡ ⎣ ⎤ ⎦ 1 2 (y k − t k )2 ∑ y k = eak eai ∑ 0.5 0.4 ... ... 0.8 0.1 −0.3 ... ... 0.2 ... ... ... ... 0.1 ... ... ... ... 0.43 0.03 0.23 0.1 0.3 0.13 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ Y = X ⋅W + B ഛܫҗ
    ా҅ ޷੸࠙೟ ࢶഋ؀ࣻ೟ ؘ੉ఠ
    ಴അ ҅࢑੄
    ബਯࢿ ୭੸ച ౠࢿ
    ୶୹ ഛܫ
    ࠙ನ ୶ۿ
    ߂
    ৘ஏ оࢸ
    Ѩૐ ೧ࢳ೟੸
    ੽Ӕ ӝ਎ӝ
    ҅࢑ ಞ޷࠙ ੿ӏച 0 1 0 ... 0 ⎡ ⎣ ⎤ ⎦
14. ࢶഋ؀ࣻ೟੉ۆ? ߭ఠ
    ҕр x 11 x 12 x 13 x 14 x 15 x 21 x 22 x 23 x 24 x 25 x 31 x 32 x 33 x 34 x 35 x 41 x 42 x 43 x 44 x 45 x 51 x 52 x 53 x 54 x 55 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ T y 1 y 2 y 3 y 4 y 5 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ −3 −2 6 ⎡ ⎣ ⎤ ⎦ 2 2 8 ⎡ ⎣ ⎤ ⎦ ߭ఠ
    ো࢑ ೯۳
    ো࢑ ରਗ ࢶഋ
    ߑ੿ध ݠन۞׬ ঐഐച ੿ࠁ
    Ѩ࢝ ੉޷૑
    ೐۽ࣁय ؀ӏݽ
    ୊ܻ
15. ਋ܻח ࢶഋ؀ࣻܳ ׮ܖӝ ਤ೧ Numpyܳ ࢎਊ೤פ׮ 
    ৈӝח
    ౵੉௑੉૑݅
    ࣽࣻ
    1ZUIPO਷
    ખ
    
    וܿ
     /VNQZח
    ௏যо
    $
    
    'PSUSBO
    ӝ߈੉ۄ
    ࡅܴ
     ࡅܳ
    ࡺ݅
    ইפۄ
    ߓৌਸ
    ബਯ੸ਵ۽
    ୊ܻ೧
    ݫݽܻب
    ؏
    ࢎਊೣ
     пઙ
    ಞܻೠ
    Ҋࣻળ
    ੋఠಕ੉झ৬
    بҳٜਸ
    ઁҕ NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
16. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ (vector) ↟ ߭ఠ
    ҕрীࢲ੄
    ਗࣗܳ
    ಴അ
    ↟߭ఠח
    п
    ਗࣗ੄
    ؘ੉ఠ
    ఋੑ੉
    زੌ
    ↟ࠁా
    BSSBZ۽
    ಴അ
    OVNQZBSSBZ
17. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ (vector) x = x 1 x 2 ... x n ⎡ ⎣ ⎤ ⎦ x = x 1 x 2 ... x n ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ೯߭ఠ
    SPX
    WFDUPS ৌ߭ఠ
    DPMVNO
    WFDUPS
18. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ (vector)
19. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ ো࢑ ↟ؔࣅ
    BEEJUJPO
    ↟ࡓࣅ
    TVCUSBDUJPO
    ↟झணۄғ
    4DBMBS
    1SPEVDU
    ↟ࢿ࠙ғ
    &MFNFOUXJTF
    .VMUJQMJDBUJPO
    ↟ղ੸
    *OOFS
    1SPEVDU ߭ఠח
    ׮਺੄
    ো࢑ٜਸ
    ࣻ೯ೡ
    ࣻ
    ੓਺
20. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ ো࢑ 1 ↟ؔࣅ
    BEEJUJPO
    ↟ࡓࣅ
    TVCUSBDUJPO v + u = (v 1 + u 1 ,...,v n + u n ) v − u = (v 1 − u 1 ,...,v n − u n )
21. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ ো࢑ 1
22. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ ো࢑ 2 ↟झணۄғ
    4DBMBS
    1SPEVDU
    ↟ࢿ࠙ғ
    &MFNFOUXJTF
    .VMUJQMJDBUJPO
    ↟ղ੸
    *OOFS
    1SPEVDU v⊗u = (v 1 u 1 ,...,v n u n ) av = (av 1 ,...,av n ) v⋅u = v i u i i=1 n ∑
23. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ ো࢑ 2
24. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ೯۳ (Matrix) ↟N
    Y
    O੄
    ഋకܳ
    о૗
    ↟п
    ೯ৌਸ
    ߭ఠ۽
    ಴അ
    оמ
    ↟ࠁా
    ରਗ
    BSSBZ۽
    ಴അ
25. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ೯۳ ো࢑ ↟ؔࣅ
    BEEJUJPO
    ↟ࡓࣅ
    TVCUSBDUJPO
    ↟झணۄғ
    4DBMBS
    1SPEVDU
    ↟ࢿ࠙ғ
    &MFNFOUXJTF
    .VMUJQMJDBUJPO
    ↟೯۳ғ
    .BUSJY
    .VMUJQMJDBUJPO ೯۳਷
    ׮਺੄
    ো࢑ٜਸ
    ࣻ೯ೡ
    ࣻ
    ੓਺
26. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ೯۳ ো࢑ 1 ↟ؔࣅ
    BEEJUJPO
    ↟ࡓࣅ
    TVCUSBDUJPO X +Y = x 11 + y 11 ... x 1n + y 1n ... ... ... x m1 + y m1 ... x mn + y mn ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ X −Y = x 11 − y 11 ... x 1n − y 1n ... ... ... x m1 − y m1 ... x mn − y mn ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥
27. ೯۳ ো࢑ 1 NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
28. ೯۳ ো࢑ 2 ↟झணۄғ
    4DBMBS
    1SPEVDU
    ↟ࢿ࠙ғ
    &MFNFOUXJTF
    .VMUJQMJDBUJPO aX = ax 11 ... ax 1n ... ... ... ax m1 ... ax mn ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ X ⊗Y = x 11 y 11 ... x 1n y 1n ... ... ... x m1 y m1 ... x mn y mn ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
29. ೯۳ ো࢑ 2 NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
30. ೯۳ ো࢑ 3 x 11 x 12 x 13 x 14 x 21 x 22 x 23 x 24 x 31 x 32 x 33 x 34 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ೯۳ғ
    .BUSJY
    .VMUJQMJDBUJPO = y 11 y 12 y 13 y 21 y 22 y 23 y 31 y 32 y 33 y 41 y 42 y 43 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ x 11 y 11 + x 12 y 21 + x 13 y 31 + x 14 y 41 ... ... ... ... ... ... ... ... ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ 
    Y
     
    Y
     
    Y
     = Y NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
31. ೯۳ ো࢑ 3 NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
32. ੹஖ (Transpose) NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ XT = x 11 x 12 x 13 x 14 x 21 x 22 x 23 x 24 x 31 x 32 x 33 x 34 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ T = x 11 x 12 x 13 x 21 x 22 x 23 x 31 x 32 x 33 x 41 x 42 x 43 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ xT = x 1 x 2 ... x n ⎡ ⎣ ⎤ ⎦ T = x 1 x 2 ... x n ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥
33. ੹஖ (Transpose) NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
34. ױਤ ೯۳ (Identity Matrix) NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ I n = 1 0 0 ... 0 0 1 0 ... 0 0 0 1 ... 0 ... ... ... ... 0 0 0 0 0 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
35. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ױਤ ೯۳ (Identity Matrix)
36. ৉೯۳ (Inverse Matrix) XX−1 = I n = X−1X NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ৉೯۳਷ ೦࢚ ઓ੤ೞ૑ח ঋ਺
37. ৉೯۳ (Inverse Matrix) NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
38. ୶о ӝୡ ࣻ೟ ࢓ಝࠁӝ ੿ӏച 1 y i = x i x i ∑ ੹୓ sumਵ۽ ա׃ਵ۽ॄ [0, 1] ҳрਵ۽ ੿ӏച
39. ୶о ӝୡ ࣻ೟ ࢓ಝࠁӝ ੿ӏച 1
40. ӝఋ ӝୡ ࣻ೟ ࢓ಝࠁӝ ੿ӏച 2 Xi = X i − E(X) σ E(X) = 1 N X i i=1 N ∑ σ = 1 N (X i − E(X))2 i=1 N ∑ ಴ળ ੿ӏ ࠙ನܳ ഝਊ೧ ಣӐ = 0, ࠙࢑ = 1۽ ੿ӏച
41. ӝఋ ӝୡ ࣻ೟ ࢓ಝࠁӝ ੿ӏച 2
42. ӝఋ ӝୡ ࣻ೟ ࢓ಝࠁӝ ޷࠙ ߂ Ӓۄ٣঱౟ 1 2 3 0 0 1 ... 0 1 0 0 ... 0 0 1 0 ... 0 ... ... ... ... 0 0 0 0 0 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 0 1 0 ... 0 1 0 0 ... 0 0 1 0 ... 0 ... ... ... ... 0 0 0 1 0 0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ৘ஏ ݽ؛ীࢲ੄ Ѿҗчҗ पઁ Ѿҗчҗ੄ рӓ੄ ૑಴ੋ ର੉ “ࣚप"ਸ ઴੉ӝ ਤೣ ࣚप ೣࣻ Ӓې೐
43. ӝఋ ӝୡ ࣻ೟ ࢓ಝࠁӝ ಞ޷࠙ f (x) = g(x 1 )+...+ g(x n ) ∂ f (x) ∂x 1 = ∂g(x 1 ) ∂x 1 ׮߸ࣻ ҕр ഑਷ ೣࣻীࢲ ౠ੿ ߸ࣻܳ ؀࢚ਵ۽ ޷࠙ ݠन ۞׬ীࢶ ࠁా ೯۳ਸ ؀࢚ਵ۽ೠ ೯۳ ಞ޷࠙ ࢎਊ ∂L ∂X = ∂L ∂x 11 ... ∂L ∂x 1n ... ... ... ∂L ∂x m1 ... ∂L ∂x mn ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
44. ࢶഋ ഥӈ ҳഅ೧ࠁӝ ਤ੄
    ѐ֛ٜਸ
    ഝਊ೧
    рױೠ
    ࢶഋ
    ഥӈ
    ݽ؛ਸ
    ٜ݅য
    ࠁѷणפ׮
45. ࢶഋ ഥӈ ҳഅ೧ࠁӝ ୭੸੄ ࢶഋ ࢚ҙ ҙ҅ܳ ಴അೞח ૒ࢶਸ ଺ਵ۰Ҋ ೣ → ୭੸੄ ߬ఋܳ ೟ण y = β 0 x 0 + β 1 x 1 y i = x i T β
46. ࢶഋ ഥӈ ҳഅ೧ࠁӝ y = β 0 x 0 + β 1 x 1 ױੌ
    ؘ੉ఠ
47. ࢶഋ ഥӈ ҳഅ೧ࠁӝ y = β 0 x 0 + β 1 x 1 y i = x i0 β 0 + x i1 β 1 ױੌ
    ؘ੉Tఠ ׮઺
    ؘ੉ఠ઺
    Jߣ૩
    ؘ੉ఠ
48. ࢶഋ ഥӈ ҳഅ೧ࠁӝ y = β 0 x 0 + β 1 x 1 y i = x i T β y i = x i0 β 0 + x i1 β 1 ױੌ
    ؘ੉ఠ ׮઺
    ؘ੉ఠ઺
    Jߣ૩
    ؘ੉ఠ
    Jߣ૩
    ؘ੉ఠ
    ߭ఠ
    ಴അ
49. ࢶഋ ഥӈ ҳഅ೧ࠁӝ Y = Xβ Y = y 1 y 2 ... y n ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ X = x 1 T x 2 T ... x n T ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ β = β 0 β 1 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ੌ߈ചػ
    ׮઺
    ؘ੉ఠ੄
    ೯۳
    ಴അ
50. ࢶഋ ഥӈ ҳഅ೧ࠁӝ 1.0 1.1 1.2 ... 10.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
51. ࢶഋ ഥӈ ҳഅ೧ࠁӝ 1.0 1.1 1.2 ... 10.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 0.1 0.11 0.12 ... 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
52. ࢶഋ ഥӈ ҳഅ೧ࠁӝ y = ax + b = b + ax y 1 = b + ax 1 y 2 = b + ax 2
53. ࢶഋ ഥӈ ҳഅ೧ࠁӝ 1 0.1 1 0.11 1 0.12 1 ... 1 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
54. ࢶഋ ഥӈ ҳഅ೧ࠁӝ r 1 r 2 r 3 ... r 100 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 1 0.1 1 0.11 1 0.12 1 ... 1 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
55. ࢶഋ ഥӈ ҳഅ೧ࠁӝ r 1 r 2 r 3 ... r 100 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 1 x i1 1 x i2 1 x i3 ... ... 1 x i20 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 1 0.1 1 0.11 1 0.12 1 ... 1 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
56. ࢶഋ ഥӈ ҳഅ೧ࠁӝ Ӓۄ٣঱౟ ࢸ҅ 1 0.1 1 0.11 1 0.12 ... ... 1 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ w 0 w 1 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥
57. ࢶഋ ഥӈ ҳഅ೧ࠁӝ Ӓۄ٣঱౟ ࢸ҅ 1 0.1 1 0.11 1 0.12 ... ... 1 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ w 0 w 1 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ y 1 y 2 y 3 ... y 20 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ − w 0 + 0.1w 1 w 0 + 0.11w 1 w 0 + 0.12w 1 ... w 0 +1.0w 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ T
58. ࢶഋ ഥӈ ҳഅ೧ࠁӝ Ӓۄ٣঱౟ ࢸ҅ 1 0.1 1 0.11 1 0.12 ... ... 1 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ w 0 w 1 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ y 1 y 2 y 3 ... y 20 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ − w 0 + 0.1w 1 w 0 + 0.11w 1 w 0 + 0.12w 1 ... w 0 +1.0w 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ T 1 20 error i 2 i=1 20 ∑ = 1 20 (y i − e i )2 i=1 20 ∑
59. ࢶഋ ഥӈ ҳഅ೧ࠁӝ Ӓۄ٣঱౟ ࢸ҅ 1 0.1 1 0.11 1 0.12 ... ... 1 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ w 0 w 1 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ y 1 y 2 y 3 ... y 20 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ − w 0 + 0.1w 1 w 0 + 0.11w 1 w 0 + 0.12w 1 ... w 0 +1.0w 1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ T 1 20 error i 2 i=1 20 ∑ = 1 20 (y i − e i )2 i=1 20 ∑ ∂(mse) ∂W = [error][x]
60. ࢶഋ ഥӈ ҳഅ೧ࠁӝ Ӓۄ٣঱౟ ࢸ҅ ∂(mse) ∂W ೯۳
    ಞ޷࠙
    → ೯۳੄ п ਗࣗী ؀೧ ಞ޷࠙
61. ࢶഋ ഥӈ ҳഅ೧ࠁӝ Ӓۄ٣঱౟ ࢸ҅ ∂(mse) ∂w 0 = ∂( (y i − (w 0 + x i w 1 ))2 ) ∑ ∂w 0 = (y i − (w 0 + x i w 1 ))⋅1 ∑ ∂(mse) ∂w 1 = ∂( (y i − (w 0 + x i w 1 ))2 ) ∑ ∂w 1 = (y i − (w 0 + x i w 1 ))⋅ x i ∑
62. ࢶഋ ഥӈ ҳഅ೧ࠁӝ Ӓۄ٣঱౟ ࢸ҅ ∂(mse) ∂W = [ y i − (w 0 + x i w 1 ) ∑ ] 1 0.1 1 0.11 1 0.12 ... ... 1 1.0 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ = [error][x]
63. ࢶഋ ഥӈ ҳഅ೧ࠁӝ पઁ ೟ण ױ҅ W ←W −α ∂(mse) ∂W
64. ࢶഋ ഥӈ ҳഅ೧ࠁӝ ೟ण Ӓې೐ <ഥ>
    &SSPS
     <ഥ>
    &SSPS
     <ഥ>
    &SSPS
     <ഥ>
    &SSPS
    
65. ࢶഋ ഥӈ ҳഅ೧ࠁӝ ୭ઙ ೟ण Ѿҗ &SSPS
     β = −2.152736 11.075026 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ y k = x k T β →
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67. хࢎ೤פ׮ MinJae Kwon (@mingrammer) Getting started to learn the linear algebra with python 2017.08.12