Save 37% off PRO during our Black Friday Sale! »

머신러닝을 위한 기초 수학 살펴보기

2c8948aaaa1a7047e0dc3cd869877879?s=47 mingrammer
August 11, 2017

머신러닝을 위한 기초 수학 살펴보기

머신러닝을 위한 매우 기초적인 수학과 이를 응용한 선형 회귀 학습 예제

2c8948aaaa1a7047e0dc3cd869877879?s=128

mingrammer

August 11, 2017
Tweet

Transcript

  1. ݠन۞׬ਸਤೠӝୡࣻ೟࢓ಝࠁӝ (FUUJOHTUBSUFEUPMFBSOUIFMJOFBSBMHFCSBXJUIQZUIPO 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 ੉ߣࣁ࣌਷઱۽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 ࣻ೟ *UEFQFOETPOjCVU

    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 ୶ୌঌҊ્ܻ ঐഐࢸ҅ ঑୷ঌҊ્ܻ %ݽ؛݂ ѱ੐ূ૓ ୭ࣗ࠺ਊঌҊ્ܻ ೐۽ࣁझझாે݂

    Ӓې೗୊ܻ ഛܫݽ؛ ҊബਯҊࢿמ҅࢑ࢸ҅ ݠन۞׬ ؘ੉ఠ߬੉झ नഐ୊ܻ
  9. ࣻ೟੄ ೙ਃࢿ ݠन۞׬ ߑޙ੗ࣻ҅ஏ ୶ୌঌҊ્ܻ ঐഐࢸ҅ ঑୷ঌҊ્ܻ %ݽ؛݂ ѱ੐ূ૓ ୭ࣗ࠺ਊঌҊ્ܻ

    ೐۽ࣁझझாે݂ Ӓې೗୊ܻ ഛܫݽ؛ ҊബਯҊࢿמ҅࢑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؀ࣻ೟ ഛܫҗా҅ ഛܫҗా҅ ޷੸࠙೟ 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 ഛܫҗా҅ ޷੸࠙೟ ࢶഋ؀ࣻ೟ ؘ੉ఠ಴അ ҅࢑੄ബਯࢿ ୭੸ച ౠࢿ୶୹ ഛܫ࠙ನ ୶ۿ߂৘ஏ оࢸѨૐ ೧ࢳ೟੸੽Ӕ ӝ਎ӝ҅࢑ ಞ޷࠙ ੿ӏച 0 1 0 ... 0 ⎡ ⎣ ⎤ ⎦
  14. ࢶഋ؀ࣻ೟੉ۆ? ߭ఠҕр 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 ⎡ ⎣ ⎤ ⎦ ߭ఠো࢑ ೯۳ো࢑ ରਗ ࢶഋߑ੿ध ݠन۞׬ ঐഐച ੿ࠁѨ࢝ ੉޷૑೐۽ࣁय ؀ӏݽ୊ܻ
  15. ਋ܻח ࢶഋ؀ࣻܳ ׮ܖӝ ਤ೧ Numpyܳ ࢎਊ೤פ׮   ৈӝח౵੉௑੉૑݅ ࣽࣻ1ZUIPO਷ખוܿ

     /VNQZח௏যо$'PSUSBOӝ߈੉ۄࡅܴ  ࡅܳࡺ݅ইפۄߓৌਸബਯ੸ਵ۽୊ܻ೧ݫݽܻب؏ࢎਊೣ  пઙಞܻೠҊࣻળੋఠಕ੉झ৬بҳٜਸઁҕ NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ
  16. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ (vector) ↟ ߭ఠ ҕрীࢲ੄ਗࣗܳ಴അ ↟߭ఠחпਗࣗ੄ؘ੉ఠఋੑ੉زੌ ↟ࠁాBSSBZ۽಴അ

    OVNQZBSSBZ
  17. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ (vector) x = x 1 x

    2 ... x n ⎡ ⎣ ⎤ ⎦ x = x 1 x 2 ... x n ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ೯߭ఠ SPXWFDUPS ৌ߭ఠ DPMVNOWFDUPS
  18. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ (vector)

  19. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ߭ఠ ো࢑ ↟ؔࣅ BEEJUJPO  ↟ࡓࣅ TVCUSBDUJPO

     ↟झணۄғ 4DBMBS1SPEVDU  ↟ࢿ࠙ғ &MFNFOUXJTF.VMUJQMJDBUJPO  ↟ղ੸ *OOFS1SPEVDU ߭ఠח׮਺੄ো࢑ٜਸࣻ೯ೡࣻ੓਺
  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 4DBMBS1SPEVDU  ↟ࢿ࠙ғ

    &MFNFOUXJTF.VMUJQMJDBUJPO  ↟ղ੸ *OOFS1SPEVDU 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) ↟NYO੄ഋకܳо૗ ↟п೯ৌਸ߭ఠ۽಴അоמ ↟ࠁాରਗBSSBZ۽಴അ

  25. NumPy۽ ࢶഋ؀ࣻ೟ ׮ܞࠁӝ ೯۳ ো࢑ ↟ؔࣅ BEEJUJPO  ↟ࡓࣅ TVCUSBDUJPO

     ↟झணۄғ 4DBMBS1SPEVDU  ↟ࢿ࠙ғ &MFNFOUXJTF.VMUJQMJDBUJPO  ↟೯۳ғ .BUSJY.VMUJQMJDBUJPO ೯۳਷׮਺੄ো࢑ٜਸࣻ೯ೡࣻ੓਺
  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 4DBMBS1SPEVDU  ↟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੄ѐ֛ٜਸഝਊ೧рױೠ ࢶഋഥӈݽ؛ਸٜ݅যࠁѷणפ׮

  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 ױੌؘ੉ఠ
  47. ࢶഋ ഥӈ ҳഅ೧ࠁӝ y = β 0 x 0 +

    β 1 x 1 y i = x i0 β 0 + x i1 β 1 ױੌؘ੉Tఠ ׮઺ؘ੉ఠ઺Jߣ૩ؘ੉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 ױੌؘ੉ఠ ׮઺ؘ੉ఠ઺Jߣ૩ؘ੉ఠ Jߣ૩ؘ੉ఠ߭ఠ಴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 ೯۳ಞ޷࠙→ 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 →
  66. Next (more LA and Mathematics) ↟઱ࢿ࠙࠙ࢳ 1$"  ↟ױੌч࠙೧ 47%

     ↟-6࠙೧ ↟ҊਬчҊਬ߭ఠ ↟಴ળച ↟j ↟߬੉૑উా҅ ↟ഛܫӏ஗ ↟ࢠ೒݂ߑध ↟୭؀਋بஏ੿ ↟j ↟೯۳޷੸࠙೟ ↟Ӓۄ٣঱౟ ↟j
  67. хࢎ೤פ׮ MinJae Kwon (@mingrammer) Getting started to learn the linear

    algebra with python 2017.08.12