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機械学習のための数学 〜微分・偏微分の計算, 勾配降下法(最急降下法)〜

kkeeth
December 15, 2016

機械学習のための数学 〜微分・偏微分の計算, 勾配降下法(最急降下法)〜

機械学習を学ぶ上で必要となる「微分・偏微分」と、単純パーセプトロンを学ぶ上で必要となる「勾配降下法(最急降下法)」を理解し、実際に計算ができることが目標です。

kkeeth

December 15, 2016
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  1. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    機械学習のための数学
    微分・偏微分の計算,
    勾配降下法(最急降下法)

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  2. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分

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  3. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分とは

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  4. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数?導関数?

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  5. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数とは

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  6. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数とは
    What’s !?

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  7. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(補足)
    この値を
    極限という

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  8. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(具体例)

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  9. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(具体例)
    因数分解!

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  10. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(具体例)

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  11. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(具体例)
    約分して

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  12. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(具体例)

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  13. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(具体例)

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  14. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(具体例)

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  15. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数(具体例)
    この値は何を
    意味する?

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  16. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数の意味

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  17. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数の意味

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  18. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数の意味

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  19. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数の意味
    微分係数の値と一致

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  20. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分係数の意味
    微分係数は, 点aにおける
    接線の傾きを表す!

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  21. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    導関数とは

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  22. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    導関数(求め方)

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  23. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    導関数(具体例)

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  24. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分練習問題

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  25. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分練習問題(回答)

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  26. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分練習問題(回答)

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  27. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    微分練習問題(回答)

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  28. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    関数の四則演算に対する微分

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  29. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    関数の四則演算に対する微分

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  30. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    関数の四則演算に対する微分(具体例)

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  31. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    偏微分

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  32. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    偏…微分?

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  33. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    そう, 偏った微分.

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  34. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    偏微分とは

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  35. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    偏微分(具体例)
    実際に計算してみよう!

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  36. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    偏微分(具体例)

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  37. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    勾配降下法(最急降下法)

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  38. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    勾配降下法(最急降下法)

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  39. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    もちろんこいつ!
    勾配降下法(最急降下法)

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  40. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    勾配降下法(最急降下法)
    これはグラフ全体が分かって
    いるから分かる!

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  41. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    じゃあ、全体が分からない
    ときはどうする?
    勾配降下法(最急降下法)

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  42. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    勾配降下法(最急降下法)

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  43. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    こいつに
    注目!
    こいつに注目!
    勾配降下法(最急降下法)

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  44. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    この点での
    傾きは正!
    この点での
    傾きは負!
    勾配降下法(最急降下法)

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  45. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    この点は
    負の方向
    に!
    勾配降下法(最急降下法)
    この点は
    正の方向に!

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  46. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    この点は
    負の方向に!
    この点は
    正の方向に!
    勾配降下法(最急降下法)
    緑の点を傾きに比例した
    距離だけ動かしてみる

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  47. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    勾配降下法(最急降下法)

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  48. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    勾配降下法(最急降下法)

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  49. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    勾配降下法(最急降下法)

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  50. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    勾配降下法(最急降下法)
    この勾配降下法には
    弱点がある…(次回)

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  51. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    以上です。

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  52. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    ありがとうございました!

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  53. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    付録

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  54. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    関数の極限の厳密な定義

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  55. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    導関数一覧

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  56. Copyright© 2016 Leprachaun Corp. All Rights Reserved
    合成関数の微分

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