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道具としての機械学習:直感的概要とその実際

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2017年3月9日 @ 北大・地球環境科学研究院
「地球流体データ解析・数値計算ワークショップ 」
https://www.gfd-dennou.org/library/davis/workshop/2017-03-08/

地球流体電脳倶楽部
https://www.gfd-dennou.org/index.html

Published in: Technology
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道具としての機械学習:直感的概要とその実際

  1. 1. 道具としての機械学習:   直感的概要とその実際 北北海道⼤大学  情報科学研究科  瀧川  ⼀一学
  2. 2. ⾃自⼰己紹介 北北⼤大で学ぶ  (10年年)  内訳:  ⼤大学4,⼤大学院2+3,研究員1 😊⾳音響信号の分離離技術  (多変量量解析・統計的信号処理理) 北北⼤大で働く  (5年年)  内訳:  特任助教2.5,  准教授2.5   😆離離散構造を伴う機械学習、科学への機械学習の適⽤用 化学研究所・バイオインフォマティクスセンター   薬学研究科・医薬創成情報科学専攻 京⼤大で働く  (7年年)内訳:  助教7 😊⽣生命科学データからの知識識発⾒見見・計算⽣生物学
  3. 3. 現在の所属  (2017年年3⽉月) 北北海道⼤大学・情報科学研究科 http://art.ist.hokudai.ac.jp 参考)  1974  Turing  Award  Lecture  “Computer  Programming  as  an  Art”  (Don  Knuth) ⼤大規模知識識処理理研究室:  湊  真⼀一  教授・瀧川(准教授)・⽯石畠正和  特任助教 ScienceとEngineeringを   つなぐ「Art」を求めて https://doi.org/10.1145/361604.361612
  4. 4. 1.離離散構造を伴う機械学習   •グラフ集合上の機械学習  (グラフに値をとる確率率率変数上の機械学習)   •グラフデータからのデータマイニング  (グラフマイニング)   •ネットワーク構造を持つ因⼦子を伴う機械学習・データマイニング   •組合せ構造を伴う機械学習・データマイニング   2.科学データに対する機械学習   •有機低分⼦子の物性予測のための多次元配列列上の深層学習   •物性・活性の機械学習による予測と評価   •科学データの機械学習における記述⼦子の設計・学習・評価   3.バイオインフォマティクスおよび分⼦子⽣生物学   •代謝反応系の遺伝⼦子ネットワークの遺伝⼦子発現モデル   •低分⼦子化合物-‐‑‒標的ネットワークの特徴づけと予測   •分⼦子⽣生物学研究におけるバイオインフォマティクス解析   4.その他 現在の主な研究項⽬目
  5. 5. 本⽇日の話題 ① データ社会とデータ駆動科学   ② 機械学習って何ができるの?   ③ 機械学習ってどう使うの?   ④ これだけは知らないと誤⽤用につながる注意点   ⑤ まとめと蛇⾜足
  6. 6. ①  データ社会とデータ駆動科学
  7. 7. 質問その1 以下の7つのGoogleサービスをいままでに
 ⼀一つも使ったことがない⼈人はいますか? • Google検索索   • Gmail   • Android   • Google  Maps   • YouTube   • Google  Chrome   • Google  Play
  8. 8. 質問その2 以下の7つのGoogleサービスにいままでに
 ⼀一回もお⾦金金を払ったことがない⼈人はいますか? • Google検索索   • Gmail   • Android   • Google  Maps   • YouTube   • Google  Chrome   • Google  Play
  9. 9. なぜ無料料で使えるものが多いのか • この7つは⽉月間の実利利⽤用者数が10億を超える   • 維持だけでも莫⼤大なお⾦金金がかかるはず Google社  (アルファベット社) 2015年年の売上⾼高:749億8900ドル(約9兆円) うち、広告売上⾼高:673億9000ドル(約8兆1000億円) 😳
  10. 10. 機械学習のニーズ:すべてがデータになる社会 インターネット・スマートデバイス・IoTが関与する業態 • 対象の詳細なデータを⼤大規模に収集することが可能   • 得られるデータを有効利利⽤用しなくてはならない
 →  広告/商品推薦、マーケティング、消費者⾏行行動理理解 「情報技術  (分析担当者の仕事の⾃自動化)」の必要性 • 効率率率化:そもそも⼈人⼿手でさばける規模を超えている   • 合理理化:“マイサイド・バイアス  (確証バイアス)”
         ⼈人はデータに⾃自分の⾒見見たいものを⾒見見てしまう
  11. 11. 広告、マーケティング、消費者⾏行行動理理解…? 真理理。しかし、新しい技術はまず最も⼿手軽に稼げると ころに導⼊入されるもの。最初に印刷技術で印刷された ものは「聖書・宗教冊⼦子」「政治論論説」「ポルノ」 ʻ‘The  best  minds  of  my  generation  are  thinking   about  how  to  make  people  click  ads…  That  sucks.ʼ’      Jeff  Hammerbacher 機械学習を始めとする情報利利活⽤用技術はかなり汎⽤用的な ものであり、まだまだ広い適⽤用可能性を持つ!
  12. 12. データ⼤大氾濫濫と情報過多 • このトレンドは科学研究の世界にも到来 • とにかく⾝身の回りでいろいろな情報がデータになり
 もはや⼈人⼿手では利利活⽤用できない… • “Data  Deluge”  (データの⼤大氾濫濫)   • ”Information  Overload”  (情報過多) 😫 😱 • 計測機器の⾼高精度度・⾼高効率率率・⼤大規模化   • ⽣生命科学分野などのオープンデータベース   • ◯◯インフォマティクスの重要性の増⼤大
  13. 13. 科学は「データの⾒見見⽅方」と無縁ではいられない! • こんなビルをたてても安全なの?   • オスプレイは安全なの?   • この薬を飲めば私の病気は治るの?   • この健康⾷食品⾷食べていれば⻑⾧長⽣生きできるの?   • この⾷食品たべればダイエットできるの?   • この化粧品つけていればすこしでも若若くいられるの?   • 原⼦子⼒力力は安全なの?   • 福島へかえりたいけど安全なの?   • このくらい⼤大きな堤防⽴立立てればもう安⼼心なの? 科学というものには、本来限界があって、広い意味での再現可能の   現象を、⾃自然界から抜き出して、それを統計学的に究明していく、   そういう性質の学問なのである。「科学の⽅方法(中⾕谷宇吉郎郎)」
  14. 14. データ駆動科学  (Data-‐‑‒Driven  Sciences) The grand aim of science is to cover the greatest number of experimental facts by logical deduction from the smallest number of hypotheses or axioms. ─── Albert Einstein experimental factshypotheses/axioms deduction induction (or abduction) ここは現在は優れた科学者(⼈人間)がセンスでやっている   (と⾔言うか、これこそが科学者の腕の⾒見見せ所?)
  15. 15. データ駆動科学  (Data-‐‑‒Driven  Sciences) The grand aim of science is to cover the greatest number of experimental facts by logical deduction from the smallest number of hypotheses or axioms. ─── Albert Einstein experimental factshypotheses/axioms deduction induction (or abduction) 「facts」が蓄積されてくれば、このinductionが機能しうる (優れた科学者の経験と勘はその試⾏行行錯誤で醸成される?)
  16. 16. データ駆動科学の理理想と現実 • “Garbage  in,  Garbage  out”
 →「データで駆動」なのでデータがゴミなら、結果もゴミ   • 多くの実問題はいわゆるビッグデータとは関係がない
 →データ駆動科学では良良くみるとスモールデータ問題が⼤大半
   (⼀一部業態を除き使えるビッグデータの収集は超⾼高コスト)   • データを無⽬目的にたくさん収集しても普通何も解決しない
 →仮説を持たない⼤大量量のデータ(インターネットやオミクス)
   からどんな知識識が得られるのか? データ駆動科学の成功を左右するのは本質的には(モデルや⼿手法 ではなく)「データそれ⾃自⾝身の質、量量、カバレッジ」。だが…
  17. 17. ?? ?? ?? 現在までに調べられた物質 可能な新物質の候補 物性 … 1  2        n 物質1 … 1  2        n 物質2 … 1  2        n 物質N … 1  2        n 候補1 … 1  2        n 候補2 … 1  2        n 候補M… 物性 物性 個別に第⼀一   原理理計算 標準的探索索 … < Schrödinger   ⽅方程式を解く 事例例:シミュレーションと相補的な技術へ
  18. 18. B その利利活⽤用(予測) 法則性A 既知データに潜む   法則性の⾃自動的獲得 ⽬目指すゴール:  データ駆動型の帰納的探索索技術の確⽴立立 Q:  どのようなやり⽅方が筋がよく、⾼高速で⾼高精度度な予測を与えるのか? “演繹的” “帰納的” ?? ?? ?? 現在までに調べられた物質 可能な新物質の候補 物性 … 1  2        n 物質1 … 1  2        n 物質2 … 1  2        n 物質N … 1  2        n 候補1 … 1  2        n 候補2 … 1  2        n 候補M… 物性 物性 個別に第⼀一   原理理計算 標準的探索索 … < Schrödinger   ⽅方程式を解く 事例例:シミュレーションと相補的な技術へ
  19. 19. ②  機械学習って何ができるの?
  20. 20. 機械学習とは? 「機械が経験から学習する」機能を実現する情報技術 機械  =  コンピュータプログラム 経験  =  データ 学習  =  いくつかタイプがある • 教師あり学習:お⼿手本から学習   • 教師なし学習:データ⾃自⾝身のパターンを学習   • 強化学習:試⾏行行錯誤で学習
  21. 21. もう少し詳しく…「学習」のタイプ •  教師あり学習  (supervised)
 ⼊入⼒力力と出⼒力力のたくさんの⾒見見本から⼊入⼒力力→出⼒力力の計算を学習   •  教師なし学習  (unsupervised)
 与えられたデータのみで何とかする学習
 例例)  似ているものをグループ化,  次元削減,  埋め込み,  多様体学習   •  半教師あり学習  (semisupervised)
 上⼆二つの間くらいで⾊色々設定がある
 (教師なしのデータが混じってる、グループ化に⾒見見本ついてる、etc)   •  強化学習  (reinforcement)
 試⾏行行錯誤してみて成功失敗のフィードバックで学習
 例例)  ⾚赤ちゃんの歩⾏行行の学習、運動やゲームプレイの上達   今⽇日はこれを説明
  22. 22. 機械学習とは? Q.「機械学習」って⼈人⼯工知能ですか? • この素朴な質問は⾮非常に微妙なところをついている。   • 「機械学習」も「⼈人⼯工知能」も分野横断的な対象で
 使う⼈人によって意味しているものが結構異異なる。   • 「機械学習」「多変量量解析」「データサイエンス」 「データマイニング」「確率率率モデル」「因果推論論」… A. 機械学習は⼈人⼯工知能を実現するために必要だと考えら れている要素技術の⼀一つ。
 関⼼心は狭義には「学習の仕組み」に特化している。
  23. 23. 実問題を⽣生きるために:論論理理推論論から統計へ • その昔「知能」とは単純に「論論理理的思考」を意味した   • ⼈人間が「知能」がないとできないと思っていたタスク の多くは思ったほど論論理理的ではないことが判明   • すべてを論論理理で厳密に推論論(or  形式化)しようとすると すぐ組合せ爆発やフレームや暗黙知(常識識)や⾃自⼰己⾔言及 などの問題が⽣生じて実問題が全然解けない   • 蓄積されたデータに潜む法則性を経験則として取り出 して、それをフル活⽤用するほうが実問題が解ける!
  24. 24. 事例例:⼿手書き⽂文字認識識 ⼊入⼒力力した⼿手書き⽂文字の画像を⼊入⼒力力すると、その⽂文字を出⼒力力 してくれるようなコンピュータプログラムをつくりたい コンピュータ   プログラム …しかし、どういうコードを書けばいいのだろう? ⼈人間にはたやすくできる処理理だけど、そもそも我々 ⾃自⾝身どうやってこの作業をやっているのか理理路路整然 とは説明できん… 「め」
  25. 25. コンピュータ   プログラム ⼊入⼒力力 出⼒力力 計算(computation) 会社の給料料計算も、銀⾏行行の⼝口座管理理も、ミサイルの   弾道計算も、スマホアプリも、プレステのゲームも 「計算」部のロジックは⼈人間が考え、通常は
 プログラミング⾔言語を⽤用いてがしがし記述する コンピュータプログラムをつくるとは
  26. 26. 教師つき学習:お⼿手本からの学習 コンピュータプログラムを作るには⼊入⼒力力から出⼒力力を 得る⼿手順がカンペキにわかってなければいけない。 コンピュータ   プログラム ⼊入⼒力力 出⼒力力 でも、実際には肝⼼心の⼿手順がよく分からないことが多い ?将棋の盤⾯面 勝てる確率率率 ?現在の脳波 ⾒見見ている映像 ?フランス語 ⽇日本語 ?⾳音声信号 テキスト
  27. 27. 教師つき学習  =  新しいプログラミングの形 教師つき学習  =  ⼊入出⼒力力の多量量の⾒見見本から計算部 のロジックを⾃自動的に構築する技術
  28. 28. 教師つき学習のしくみ:統計的法則性の活⽤用 ⼀一つの事例例だけ⾒見見てもわからないが多くの事例例に共通して   浮かび上がってくる統計的な法則性を使う (現在の)機械学習  =  データの抽象化  =  データ中の統計的 法則性を機械(コンピュータ)に学習させる理理論論 他の例例)  スマホのカメラかざしたら⼈人の顔がうつっている
 箇所に枠が表⽰示される機能をどうプログラムする?
  29. 29. 統計的に浮かび上がる法則性
  30. 30. 統計的に浮かび上がる法則性 5 6.25 7.5 8.75 10 90112.5135157.5180 ● ● ●● ● ● ● ● ●● ● ●
  31. 31. 統計的に浮かび上がる法則性 5 6.25 7.5 8.75 10 90112.5135157.5180 ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●
  32. 32. 統計的に浮かび上がる法則性 5 6.25 7.5 8.75 10 90112.5135157.5180 ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
  33. 33. 統計的に浮かび上がる法則性 5 6.25 7.5 8.75 10 90112.5135157.5180 ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●
  34. 34. 統計的に浮かび上がる法則性 5 6.25 7.5 8.75 10 90112.5135157.5180 ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●
  35. 35. 統計的に浮かび上がる法則性 5 6.25 7.5 8.75 10 90112.5135157.5180 ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
  36. 36. 統計的に浮かび上がる法則性 5 6.25 7.5 8.75 10 90112.5135157.5180 ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
  37. 37. 統計的に浮かび上がる法則性 5 6.25 7.5 8.75 10 90112.5135157.5180 ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 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