{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 機械学習の分類の話\n", "\n", "分類(Classification)は、教師あり学習の1つで、予測対象はカテゴリなどの離散的な値を予測します。 \n", "具体的には、メールがスパムかどうかや、画像に映っているのがどういった物体か、といったバイナリで表現できる値を予測する場合にモデルを作ります。\n", "\n", "基本的に、入力データをベクトル $x$ (例えば `[1, 3, 4, 8]` )と考えた時に、予測対象のカテゴリ $y$ ( ham/spam )を出力します。 \n", "入力ベクトルは整数や小数のベクトルの場合が多いですが、「晴れ」「雨」などといったカテゴリ情報も適当な数値に変換して扱うことが多いです。 \n", "同様に出力されたカテゴリは、-1や1などの整数で表現することが多いです。\n", "\n", "このnotebookでは、分類について以下のモデルを紹介します。\n", "\n", "- **パーセプトロン**(Perceptron)\n", "- **ロジスティック回帰**(Logistic Regression)\n", "- **SVM**(Support Vector Machine, サポートベクターマシン)\n", "- **ニューラルネットワーク**(Neural Network)\n", "- **k-NN**(k近傍法, k Nearest Neighbor)\n", "- **決定木**(Decision Tree)\n", " - **ランダムフォレスト**(Random Forest)\n", " - **GBDT**(Gradient Boosted Decision Tree)\n", "\n", "パーセプトロン、ロジスティック回帰、SVM、ニューラルネットワークの4つは、 \n", "2つのクラスを分類する面(**決定境界**(Dicision Boundary)と言います)を表現する関数を学習します。 \n", "k-NNは最近傍法とも呼ばれ、学習済みのデータから距離が近いデータを元に判断をします。 \n", "決定木、ランダムフォレスト、GBDTは、木構造のルールを学習します。\n", "\n", "また、このnotebookでは詳しく扱いませんが、この他にもテキスト分類などでよく使われる \n", "**ナイーブベイズ**(Naive Bayes)や、音声認識で伝統的に使われてきた**HMM**(Hidden Markov Model)などがあります。 \n", "これらのモデルは、データの背景に隠れた確率分布を推測することで、データをモデル化する手法です。 \n", "\n", "それでは、個々のアルゴリズムについて説明しましょう。\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. パーセプトロン\n", "\n", "\n", "

パーセプトロンのイメージ図

\n", "\n", " **パーセプトロン** (単純パーセプトロンと呼ぶこともあります)は、 \n", "入力ベクトル(例えば $x$ とします)と \n", "学習した重みベクトル(例えば $w$ とします)を \n", "掛けあわせた値を足しあわせて、その値が0以上の時はクラス1、0未満の時はクラス2と分類するというシンプルなモデルです。\n", "\n", "重みベクトルを配列 `w` 、入力ベクトルを配列 `x` としてとても簡単な擬似コードで書くとこうなります。\n", "\n", "```py\n", "def predict(x, w):\n", " s = np.dot(x, w)\n", " if s >= 0:\n", " return 1\n", " else\n", " return -1\n", "```\n", "\n", "実際には、\n", "\n", "```py\n", "w[0] * 1 + w[1] * x[1] + w[2] * x[2]\n", "```\n", "\n", "の合計値が正なのか負なのかでクラスを判断をします。\n", "\n", "この例では、データが2次元であるという設定で書いています。 \n", "もちろん、入力ベクトル `x` が3次元以上(ベクトルの要素が3以上)になっても構いません。 \n", "重みベクトル `w` が3つ要素があるのは、 `w[0]` はバイアスと呼ばれる変数 `x[1], x[2]` とは独立な重みを表現しているからです。\n", "\n", "この重みベクトル `w` を学習するのが目標です。\n", "\n", "### パーセプトロンの特徴、あるいは線形分離可能とは\n", "\n", "パーセプトロンの特徴としては、以下のような特徴があります。\n", "\n", "- 線形分離可能な問題のみ解ける\n", "- オンライン学習で学習する\n", "- 予測性能はそこそこで、学習は速い\n", "- 過学習には弱い\n", "\n", "パーセプトロンは**線形分離可能**(Linearly Separable)な問題のみ解くことができます。 \n", "線形分離可能とは、データをある直線でスパっと2つに分けられるデータのことを言います。\n", "\n", "少しコードで説明しましょう。 \n", "\n", "以下の2つのセルのコードは、ダミーデータの生成とそのプロットのためのコードです。 \n", "細かい所は気にしなくても良いですが、 \n", "- `df`には直線で分離できる(=線形分離可能)ダミーデータ\n", "- `df_xor`は直線では分離できない(=線形分離不可能)ダミーデータ\n", "\n", "を格納しているということを覚えておいて下さい。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from sklearn.svm import SVC\n", "from sklearn.tree import DecisionTreeClassifier\n", "from sklearn.ensemble import RandomForestClassifier\n", "from sklearn.linear_model import LogisticRegression, Perceptron\n", "from sklearn.neighbors import KNeighborsClassifier\n", "from sklearn.cross_validation import train_test_split\n", "import pandas as pd\n", "import numpy as np\n", "from numpy.random import normal as rnorm\n", "from matplotlib.colors import ListedColormap\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "plt.rcParams['font.size'] = 16\n", "\n", "def plot_result(clf, clf_name, df): \n", " X = df[['x','y']]\n", " Y = df['label']\n", " X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=.4, random_state=40)\n", " n_classes = len(Y.unique())\n", " cm = plt.cm.RdBu\n", " plot_colors = \"rbym\"\n", " plot_markers = \"o^v*\"\n", " plot_step = 0.02\n", " \n", " x_min, x_max = X.ix[:, 0].min() - .5, X.ix[:, 0].max() + .5\n", " y_min, y_max = X.ix[:, 1].min() - .5, X.ix[:, 1].max() + .5\n", " xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),\n", " np.arange(y_min, y_max, plot_step))\n", " \n", " clf.fit(X_train,y_train) \n", " score = clf.score(X_test, y_test)\n", "\n", " Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z.reshape(xx.shape)\n", " cs = plt.contourf(xx, yy, Z, cmap=cm, alpha=.5)\n", "\n", " # 学習用の点をプロット\n", " for i, color, m in zip(range(n_classes), plot_colors, plot_markers):\n", " plt.scatter(X[Y==i].x, X[Y==i].y, c=color, label=i, cmap=cm, marker=m, s=80)\n", "\n", " plt.text(xx.max() - .3, yy.min() + .3, ('%.2f' % score).lstrip('0'),\n", " size=15, horizontalalignment='right') \n", " plt.title(clf_name)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# 線形分離可能\n", "N = 50\n", "p1 = pd.DataFrame(np.hstack((rnorm(loc=2.0, scale=0.5, size=(N,1)), \n", " rnorm(loc=2.0, scale=0.5, size=(N,1)))),\n", " columns=['x','y'])\n", "p1['label'] = 0\n", "p2 = pd.DataFrame(np.hstack((rnorm(loc=1.0, scale=0.5, size=(N,1)), \n", " rnorm(loc=1.0, scale=0.5, size=(N,1)))),\n", " columns=['x','y'])\n", "p2['label'] = 1\n", "df = pd.concat([p1, p2])\n", "\n", "# XORパターン(線形分離不可能)\n", "N = 50\n", "p1 = pd.DataFrame(np.hstack((rnorm(loc=1.0, scale=1.0, size=(N,1)), \n", " rnorm(loc=1.0, scale=1.0, size=(N,1)))),\n", " columns=['x','y'])\n", "p1['label'] = 0\n", "p2 = pd.DataFrame(np.hstack((rnorm(loc=-1.0, scale=1.0, size=(N,1)), \n", " rnorm(loc=1.0, scale=1.0, size=(N,1)))),\n", " columns=['x','y'])\n", "p2['label'] = 1\n", "p3 = pd.DataFrame(np.hstack((rnorm(loc=-1.0, scale=1.0, size=(N,1)), \n", " rnorm(loc=-1.0, scale=1.0, size=(N,1)))),\n", " columns=['x','y'])\n", "p3['label'] = 0\n", "p4 = pd.DataFrame(np.hstack((rnorm(loc=1.0, scale=1.0, size=(N,1)), \n", " rnorm(loc=-1.0, scale=1.0, size=(N,1)))),\n", " columns=['x','y'])\n", "p4['label'] = 1\n", "df_xor = pd.concat([p1,p2,p3,p4])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "それでは、準備ができたのでパーセプトロンがどのようにデータを分離するのかを見てみましょう。\n", "\n", "次のコードでプロットされる、1つ目のデータは単純に直線で分離ができる(線形分離可能)なデータ、 \n", "2つ目がいわゆる[XOR](https://ja.wikipedia.org/wiki/%E6%8E%92%E4%BB%96%E7%9A%84%E8%AB%96%E7%90%86%E5%92%8C)と言われる線形分離不可能なデータです。 \n", "(図右下の数字は正解率です)\n", "\n", "このように、パーセプトロンは直線で分類することしかできないので、上の図しか分類できていないですね。" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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P8IiKRCIoAv0I75g6lRrPVPDXji4QAerchqnqRjNu1ixqaq/C4OOH48dydtfO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\n", 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UBleTWOdkK8W+LhnnIHGjzUwZO2MGbyztSCCs8u4UeW/msjOrbCeWdKXvzMjO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\nkauJonzv+5QfeG5OxqRJjRbwDYBMtMl8ZaLMZOx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf = Perceptron()\n", "\n", "plot_result(clf, 'Perceptron', df)\n", "plt.show()\n", "plot_result(clf, 'Perceptron (XOR)', df_xor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "この分類する直線を少し専門的な言い方で**超平面**(Hyperplane)と言います。(ここでの意味合いとしては決定境界と同じです) \n", "二次元の時は直線ですが、三次元だと平面になります。高次元空間での平面ということで超平面と言います。\n", "\n", "逆に2つ目の図のように、直線で分けられないデータのことを線形分離できないので線形分離不可能(あるいは非線形線形分離可能)なデータといいます。\n", "よく例としてあげられるのは排他的論理和(XOR)のデータが挙げられます。\n", "\n", "2つ目の図のようにXORは、原点を中心として右上と左下が1つのクラス、右下と左上が1つのクラスになるようにデータが存在します。 \n", "そのため、1本の直線を引くだけでは2つのクラスを適切に分離することはできません。 \n", "この、「1本の直線を引くだけで2つのクラスを分離できない」のが線形分離不可能ということです。\n", "\n", "パーセプトロンは非線形な分離はできないので、決定境界は直線になっています。 \n", "なので、XORは分離することができていませんね。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 学習するということ\n", "\n", "では、どうやって適切な重みを推定すればいいのでしょうか? \n", "真の値とのズレである誤差を表す関数を**損失関数**(Loss Function}または誤差関数(Error Function)といいます。\n", "\n", "例えば、誤差の二乗を損失関数とすると、\n", "\n", "$損失関数=(真の値-予測値)^2$\n", "\n", "となります。\n", "\n", "以下に二乗誤差の図の例を示します。" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy.plotting import plot\n", "from sympy import *\n", "\n", "x, y = symbols(\"x y\")\n", "f = x **2\n", "plot(f, (x, -3, 3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "実際にはパーセプトロンの損失関数は、`w`が重みベクトル、`x`が入力ベクトル、`y`の正解ラベル(1か-1)としたとき、\n", "\n", "```py\n", "max(0, -ywx)\n", "```\n", "\n", "となります。\n", "\n", "この損失関数を**ヒンジ損失**(Hinge Loss)といいます。 \n", "次の図を見るとわかりますが、蝶つがい(ヒンジ)のように見えることからこの名前が付いています。" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(-4, 4, 0.1)\n", "y = np.maximum(0, -x)\n", "fig = plt.plot(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "さらに、パーセプトロンの目的関数は\n", "\n", "$目的関数=損失関数$\n", "\n", "となり、目的関数を最小化することが、誤りの少ない最適な分類ができる状態になると言えます。 \n", "こうなる重みを得ることが「学習をする」ということになります。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 確率的勾配法で重み学習する\n", "\n", "\n", "では、どのように重みを推定すればよいのでしょうか。 \n", "重みの最適化には**確率的勾配降下法**(Stocastic Gradient Descent, SGD)と呼ばれる方法がよく使われます。 \n", "\n", "この方法では、目的関数の山の上から少しずつ谷に向かってで降りることで、最適な重みを得ることができます。 \n", "実際には、谷の場所は直接は見えない状態で周囲の限られた範囲しか見えません。 \n", "\n", "次の図での白丸のように、坂の傾きが大きい下り方向に向かって一歩一歩矢印の先進んでいき、重みを修正します。 \n", "そして、目的関数が最も小さいところにたどり着けば、その重みが最適な値となります。(これを解が収束すると言います。)\n", "\n", "\n", "\n", "ちなみに、山を逆にすると目的関数を最大化することになるので、山登り法とも呼ばれます。\n", "\n", "どれくらいの幅で修正するかのパラメータを学習率(Learning Rate)と言います。 \n", "修正する幅は $学習率×山の傾き$ で決まります。 \n", "学習率が大きい値だと速く収束するかもしれませんが、谷を行き過ぎて最適な解に収束しない場合もあります。 \n", "学習率が小さい場合は、収束するまでに必要な繰り返し回数が増えるため、学習時間が長くなります。 \n", "\n", "シンプルな方法では学習率が固定のまま学習しますが、後述するニューラルネットワークではこの設計が肝になってくることもあり、 \n", "動的に変化させる様々な工夫が提案されています。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 掛けあわせた値を活性化関数にかける\n", "\n", "さて、パーセプトロンの予測値は重みベクトルと入力ベクトルを掛けた結果の正負で判定しましたね。 \n", "これは掛けあわせた結果を、**ステップ関数**(Step Function)という関数に通しているとも言えます。 \n", "ステップ関数とは次の図のような関数で、入力の値を+1または-1にしてくれます。 \n", "特に、パーセプトロンにおけるステップ関数のような、出力値を非線形変換する関数を**活性化関数**(Activation Function)と呼びます。 \n", "\n", "通常のステップ関数は0か1を出力しますが、パーセプトロンによる2クラス分類は、 \n", "計算のしやすさから2つのクラスを-1、+1とすることが多いです。\n", "\n", "\n", "\n", "パーセプトロンは、その後の様々なアルゴリズムに影響を与えた、歴史的に重要なアルゴリズムです。\n", "\n", "引き続き、パーセプトロンの仲間のアルゴリズムについて学んでいきましょう。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ロジスティック回帰\n", "\n", "\n", "

ロジスティック回帰のイメージ図

\n", "\n", "**ロジスティック回帰** は、回帰という名前とは裏腹に分類のためのモデルです。 \n", "イメージ図はパーセプトロンとよく似ていますが、活性化関数が少し違います。\n", "\n", "パーセプトロンとよく似ていますが、以下のような特徴があります。\n", "\n", "- 出力とは別に、その出力のクラスに所属する確率値が出せる\n", "- 学習はオンライン学習でもバッチ学習でも可能\n", "- 予測性能はまずまず、学習速度は速い\n", "- 過学習を防ぐための正則化項が加わっている\n", "\n", "特に出力の確率値が出せるという特徴のため、広告のクリック予測にもよく使われています。\n", "\n", "ロジスティック回帰は、パーセプトロンと同じく線形分離可能な分類器のため、決定境界は直線になります。 \n", "以下に、実際の分類例を示します。" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WQn5cNwlatkcWFTEBOAKrGcBPaarE9yKW0lwCrKIYw0ha1C8x59GDYh4BHreP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\nC/QBzgdGAr2BOfaxfKAcOAOoA+aTo7/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Qv+ev4r4/2WiVTBUUSWQpf7llY1Lp9vkSoeLEk0FjxEkXzdPARcAY4GchRB/L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\nvwgbI90omniG9ujMig1bKTl1FHUvL0rrvUbrISgXTRmOUZ8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf = LogisticRegression()\n", "plot_result(clf, 'LogisticRegression', df)\n", "plt.show()\n", "plot_result(clf, 'LogisticRegression (XOR)', df_xor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### パーセプトロンとの違い\n", "\n", "パーセプトロンとの違いは、\n", "\n", "- 活性化関数がシグモイド関数(Sigmoid Function)(ロジスティック・シグモイド関数(Logistic sigmoid funcrtion)とも言います)であること\n", "- 損失関数が交差エントロピー損失(Cross-entropy Loss)であること\n", "- **正則化項**(Regularization Term)(または**罰則項**(Penalty Term)とも呼ばれます)が加わっているためパーセプトロンより過学習を防ぎやすいこと\n", "- オンラインでもバッチでも学習可能なこと\n", "\n", "が挙げられます。\n", "\n", "### シグモイド関数\n", "\n", "シグモイド関数は以下に示すような形状をしています。 \n", "入力が0の時は0.5をとり、値小さくなるほど0に、大きくなるほど1に近づく関数です。 \n", "ちなみに、シグモイド関数を一般化したものがロジスティック関数と呼ばれており、ロジスティック回帰の由来となっています。" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = 1 / (1+exp(-x))\n", "plot(f, (x, -5, 5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 正則化項が決定境界をなめらかにする\n", "\n", "**正則化**(Regularization)は、学習時にペナルティを与えることで決定境界をなめらかにする働きを持ちます。 \n", "入力データに対して最適化する際に正則化項を加える事で、既知のデータの影響を受けすぎないようにします。 \n", "つまり、未知のデータに対するあそびを作ることができるのです。\n", "\n", "既知のデータに対して最適化をし過ぎると、ノイズののった変なデータに対しても対応しようと頑張りすぎてしまいます。 \n", "こういったデータに対しても、正則化をすることで強く影響を受けすぎないことが可能となります。\n", "\n", "正則化項を加えると目的関数は以下のように表現できます。\n", "\n", "$目的関数 = 損失関数 + 正則化項$\n", "\n", "この目的関数を最小化するパラメータを推定することで、ロジスティック回帰を学習できます。\n", "パーセプトロンと同じく確率的勾配降下法を使うことで最適化できます。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SVM\n", "\n", "\n", "

SVMのイメージ図

\n", "\n", "\n", "SVMは、分類問題を解くときに非常に良く利用されているモデルです。 \n", "パーセプトロンを拡張したモデルと考えることができ、線形分離不可能な問題も解くことができます。 \n", "様々なアルゴリズムやライブラリが開発されており、高速な学習ができます。 \n", "\n", "以下のような特徴があります。\n", "\n", "- **マージン最大化** をすることで、なめらかな超平面を学習できる\n", "- カーネル(Kernel)と呼ばれる方法を使い、非線形なデータを分離できる\n", "- 線形カーネルなら次元数の多い疎なデータも学習可能\n", "- バッチ学習でもオンライン学習でも可能\n", "\n", "損失関数はパーセプトロンと同じく、ヒンジ損失を使います。 \n", "厳密にはパーセプトロンとは、横軸との交点の場所が違います。 \n", "グラフとして書くと以下のようになります。" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Q6LJ+6CGpu1uaMiWENpAKTiYCFbNnSzt3hi7rgwdjTwO8h6AGBpkzR7r//rD8cYR7GiER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\nAEgcQQ0AiSOoASBxBDUAJI6gBoDE/T9e2Qd+GjOvjwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(-4, 4, 0.1)\n", "y = np.maximum(0, 1-x)\n", "plt.plot(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### SVMの特徴その1:マージン最大化\n", "\n", "SVMの特徴は大きく2つあります。\n", "\n", "1つ目の特徴は、マージン最大化をすることで、正則化項と同じように過学習を抑える事ができます。\n", "\n", "\n", "

SVMのイメージ図(再掲)

\n", "\n", "\n", "マージン最大化は、イメージ図のように超平面をどのように引けば、2クラスそれぞれ最も近いデータ(これをサポートベクターと言います)までの距離が最大化できるかを考えます。 \n", "サポートベクターから等距離となるように超平面を引けば、未知のデータに対して余裕のある超平面が得ることができます。\n", "\n", "サポートベクターと超平面までの距離(これを**マージン**といいます)が \n", "最大になるような超平面の引き方を決めることで、既知のデータに対して最もあそびが生まれます。 \n", "このおかげで、データに特化し過ぎない余裕のある決定境界を得ることが出来ます。 \n", "\n", "最適化手法は様々あり詳細は割愛しますが、バッチ学習のためのアルゴリズムもオンライン学習も両方あります。 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### SVMの特徴その2:カーネルトリック\n", "\n", "2つ目の特徴は、カーネルと呼ばれるテクニックです。\n", "\n", "これは線形分離不可能なデータでも、カーネルと呼ばれる関数を使ってデータをより高次元空間に変換することで、 \n", "線形分離可能にするという方法です。 \n", "以下のイメージ図を見てみると、1次元では線形分離できなかったのが、2次元に変換をすることで、線形分離可能になっています。 \n", "\n", "\n", "

カーネルトリックのイメージ

\n", "\n", "カーネルには、\n", "- **線形カーネル**(Linear Kernel)\n", "- **多項式カーネル**(Polynomial Kernel)\n", "- **RBFカーネル**(Radial Basis Function Kernel, 動的基底関数カーネル)\n", "\n", "などがあります。 \n", "\n", "次の4つの図に、線形カーネルとRBFカーネルの時の決定境界を示します。 \n", "特に、線形カーネル(XOR)とRBFカーネル(XOR)の図を見比べるとわかるように、RBFカーネルの方がXORに対して適切に分離できているのがわかります。\n", "\n", "線形カーネルは処理の速さから主にテキストなどの高次元で疎なベクトルのデータに、RBFカーネルは画像や音声信号などの密なデータによく使われます。" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Zs+v+XHXC8XTu0DHNd9lc5AU4XyBAe2O41Ji0V78oZ+nM2uOa9ys8SGfXNtV9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\nn1Vb4O5mj/kar2HLx2t58+X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cWl/HqndnNqm6NzL8Mm/G08x97B5uW7mMpd4GPFIgGUnAP4JFc2c1KXyVzpTU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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf = SVC(kernel='linear')\n", "plot_result(clf, 'SVM (linear)', df)\n", "plt.show()\n", "plot_result(clf, 'SVM (linear, XOR)', df_xor)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Nxd3adR7FfahYuwQvxF/dwryXniMQOB94GvgDsInmWZPPANcSCFwR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\n+8t8+n8AHhVrRVGUfENj1oqiKB5AxVp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UT+u7sdNLwkI18WjdhIZftm9eH9RH9W5ykQwKzNMw+jPtpae46YFH4/gEwolV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\nCOOCCnzcB/wD2Oh/9QXu8G8zwxBnJRiGSJbweL1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf = SVC(kernel='rbf')\n", "plot_result(clf, 'SVM (RBF)', df)\n", "plt.show()\n", "plot_result(clf, 'SVM (RBF, XOR)', df_xor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ニューラルネットワーク\n", "\n", "\n", "

ニューラルネットワークのイメージ図

\n", "\n", "\n", "**ニューラルネットワーク**(Neural Network)は多層パーセプトロンとも呼ばれ、パーセプトロンを1つのノードとして階層上に重ねたもののことです。 \n", "脳の神経モデルを模倣しているためこの名前になっています。\n", "\n", "ニューラルネットワークはいろいろな形状がありますが、一番基本的な3階層のフィードフォワード型ニューラルネットワークを考えます。 \n", "入力層、中間層、出力層という順番に入力と重みを掛けあわせて計算していき、出力層に分類したいクラスだけノードを用意します。 \n", "入力層、出力層の数に応じて中間層(隠れ層とも言います)の数を用意します。\n", "\n", "活性関数には、初期はステップ関数が、その後シグモイド関数が良く利用されてきました。 \n", "近年では深層学習では**ReLU**(Rectified Linear Unit)が性能が良いためよく使われています。   \n", "ReLUは以下のようなグラフになります。" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(-4, 4, 0.1)\n", "y = np.maximum(0, x)\n", "fig = plt.plot(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ニューラルネットワークの場合パーセプトロンとは異なり、非線形関数を活性化関数として利用したものを多段に重ねるため、決定境界は直線でないものも描けます。\n", "\n", "ニューラルネットワークの決定境界は、詳しくは西尾泰和さんの[TensorFlow Playgroundの解説記事](http://d.hatena.ne.jp/nishiohirokazu/20160414/1460602667)を見ると良いでしょう。 \n", "(執筆当時はscikit-learnにNNの実装がなかった...)\n", "\n", "### ニューラルネットワークの学習法\n", "\n", "フィードフォワード型のニューラルネットワークは、**誤差逆伝播法**(バックプロパゲーション, Backpropagation)と呼ばれる方法で学習します。 \n", "ランダムに初期化した重みの値を使って出力値をネットワークの順方向に計算し、 \n", "計算した値と正解となる値との誤差をネットワークの逆方向に計算して重みを修正します。 \n", "そして、重みの修正量が規定値以下になるか決められたループ回数を繰り返したら学習を打ち切ります。\n", "\n", "### ニューラルネットワークの特徴\n", "\n", "ニューラルネットワークには以下のような特徴があります。\n", "\n", "- 非線形なデータを分離できる\n", "- 学習に時間がかかる\n", "- パラメータの数が多いので、過学習しやすい\n", "- 重みの初期値に依存して、局所最適解にはまりやすい\n", "\n", "ニューラルネットワークの中間層の層を増やすと、誤差逆伝播法では学習ができない問題があります。 \n", "それを解決して深いネットワークも学習できるようにしたのが深層学習です。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## k-NN(k近傍法)\n", "\n", "k-NN(k近傍法)は、未知のデータのクラスを近くの既知データのクラスの多数決で決めるという、最近傍探索のアルゴリズムの1つです。 \n", "kは投票する個数のことを意味し、 $k=3$ のときはデータに最も近い3点のうち、得票数が多いクラスに所属しているとみなします。 \n", "\n", "\n", "

k-NNのイメージ図

\n", "\n", "\n", "\n", "イメージ図の例を見てみましょう。 \n", "新しいデータである□が、○と△のどちらのクラスかということを考えます。 \n", "□の周囲3つのデータを見ると○になることがわかります。 \n", "もちろん、kの数を変えると所属するクラスは容易に変わります。 \n", "\n", "kを3としてダミーデータで分類をした図が以下の2つになります。 \n", "XORの例を見てもわかるように、決定境界は直線にはなりません。" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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gbbccb0s74DyaRD1NJFjbVGCu2p+rflLC5a79g2m0eathNJoL/+enTV5zXr9u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\na+2I4k9r/WXDXzcopd4FKjAqQ35h2aD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MFv/89OPNgIfjsoyO9O15BT3yVjLSYWeA5/05aMa9X8/eZLY/ry6nqIgA1dFJ0ajQFzvN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\nW71WosyY4bNuNT1O7MWwj1Y6tt3JOKd/tJKrcrh+KuadMJB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf = KNeighborsClassifier(3)\n", "plot_result(clf, 'k-NN', df)\n", "plt.show()\n", "plot_result(clf, 'k-NN (XOR)', df_xor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### k-NNの特徴\n", "\n", "k-NNには以下のような特徴があります。\n", "\n", "- インクリメンタルに1つずつ学習する\n", "- 単純な方法だと全データとの距離計算をする必要があるため、予測計算に時間が掛かる\n", "- kの数によるがそこそこの予測性能\n", "\n", "### kの決め方\n", "\n", "kの数は交差検証で決めます。 \n", "この時、どのデータが「近い」のかというのを決めるためには、「距離」を定義する必要があります。\n", "\n", "多く用いられるのは2つの点を結んだ直線の長さであるユークリッド距離(Euclidean Distance}ですが、分散を考慮する**マハラノビス距離**(Mahalanobis Distance)が用いられることも有ります。 \n", "ユークリッド距離は、点の座標を表すベクトル$a$とベクトル$b$があったとき、\n", "\n", "```py\n", "np.sqrt(sum(x - y)**2 for x, y in zip(a, b))\n", "```\n", "\n", "で求めることが出来ます。 \n", "(実際には、NumPyを使って@{np.linalg.norm(a - b)}で求めたほうが高速です。)\n", "\n", "### k-NNの使いドコロ\n", "\n", "自然言語処理のときなど、疎なデータの場合は次元の呪いのため予測性能がでないことが多いです。  \n", "こうしたときには、後述する次元削減手法で次元圧縮をすると性能が改善することが知られています。\n", "\n", "k-NNはシンプルでな手法のため、気軽に試すのには良い方法です。  \n", "また、距離さえ定義できれば応用が効くので、例えばElasticsearchなどの全文検索エンジンのスコアを距離とみなしてk-NNを使うなどもできます。  \n", "計算時間がかかる問題については、近似的に近傍探索をするなどいくつかの手法がでています。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 決定木、ランダムフォレスト、GBDT\n", "\n", "\n", "

決定木のイメージ図

\n", "\n", "\n", "決定木は、木の根から順番に条件分岐をたどっていき、葉に到達すると予測結果を返すモデルです。 \n", "**不純度**(Impurity)と呼ばれる基準を使って、分割する前と後でできるだけ違うクラスが混ざらなくなるように分岐条件を学習していきます。 \n", "具体的には**情報ゲイン**(Information Gain)や**ジニ係数**(Gini coefficient)などの基準を不純度として使い、不純度が下がるようにデータを分割します。 \n", "決定木を使うことで、データからうまく分類できるようなIF-THENルールのツリーを、イメージ図のように得ることができるのです。\n", "\n", "\n", "### 決定木の特徴\n", "\n", "決定木の特徴をまとめると、以下のようになります。\n", "\n", "- 学習したモデルを人間が見て解釈しやすい\n", "- 入力データの正規化がいらない\n", "- カテゴリー変数や欠損値などを入力しても内部で処理してくれる\n", "- 特定の条件下では過学習しやすい傾向にある\n", "- 非線形分離可能だが、線形分離可能な問題は不得意\n", "- クラスごとのデータ数に偏りのあるデータは不得意\n", "- データの小さな変化に対して結果が大きく変わりやすい\n", "- 予測性能はまずまず\n", "- バッチ学習でしか学習できない\n", "\n", "決定木の大きな特徴としては、学習したモデルを可視化して解釈しやすいという点があげられます。 \n", "これは、学習結果としてIF-THENルールが得られるため、工場のセンサー値から製品の故障を予測したい場合、どのセンサーが異常の原因なのかといったように、 \n", "この分類結果に至った条件が得られることが求められるシーンには有効でしょう。 \n", "\n", "パーセプトロンやロジスティック回帰とは異なり、線形分離不可能なデータも分類できます。 \n", "一方で線形分離可能な問題はそこまで得意ではありません。\n", "\n", "また、データを条件分岐で分けていくという性質上、木の深さが深くなると学習に使えるデータ数が少なくなるため、過学習しやすくなる傾向にあります。 \n", "これについては、木の深さを少なくしたり**枝刈り**(剪定, pruning)することである程度防ぐことが出来ます。 \n", "特徴の数が多い時も過学習しやすくなるため、事前に次元削減や特徴選択をしておくと良いでしょう。 \n", "\n", "ダミーデータに対する決定境界を見ても、線形分離可能な単純な例の方が過学習気味になっているのがわかります。" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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L3gLgt/0utrV/oCxoYDbhWHKRMLWjRa6L61qGm/2Xc3ZvFgeVSA0ItyoOwKJp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\nCyEle6mumrY1UsC1lgI9BRg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4VfMm4jOqDLhP5uI3xgOBKN67RV7Uc0ajvGwvJcvnEfB/HVzn9w2mqKAjP21a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\njcL+wslq3ASovmGzV/OGty58CqV2416iZvVwQ0P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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf = DecisionTreeClassifier()\n", "plot_result(clf, 'Decision Tree', df)\n", "plt.show()\n", "plot_result(clf, 'Decision Tree (XOR)', df_xor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 決定木を複数作って統合する、ランダムフォレスト\n", "\n", "決定木を応用した手法に、**ランダムフォレスト**(Random Forest)や**Gradient Boosted Decision Tree**(GBDT)があります。\n", "\n", "ランダムフォレストは、利用する特徴量の組み合わせを色々用意して、性能がよかった学習器複数の予測結果を多数決で統合します。 \n", "複数の木を独立に学習できるため並列で学習できます。 \n", "また、決定木の枝刈りをしないため主なパラメータは2つと後述するGBDTと比べて少ないですが、過学習しやすい傾向にあります。 \n", "\n", "予測性能は決定木より高く、パラメータ数が少ないためチューニングも比較的簡単で手頃です。 \n", "決定境界を見てもわかるように、決定木ベースのアルゴリズムのため傾向は似ています。\n" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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443rQtrCItoVFjDuuB/1G/JlzBg13fByVe3SctcsyXXjJTrSxw27V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\npZTygP8Pdz7eG+jX0YkAAAAASUVORK5CYII=\n", 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jpB37Kiggra6jBHwVEGrJXxGN244+w6H7+O82lb6TSE0D4vSfIkTp2pGHPCv3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\n7rNJFMvqgu2RZ48I2hOpFaNWacwNLImNicgQEfFYeC0Nc/4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clf = RandomForestClassifier()\n", "plot_result(clf, 'Random Forest', df)\n", "plt.show()\n", "plot_result(clf, 'Random Forest (XOR)', df_xor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 直列的に複数の木を学習するGBDT\n", "\n", "ランダムフォレストが並列的に学習して予測結果を利用するのに対して、 \n", "GBDTはサンプリングしたデータに対して直列的に浅い木を学習していく勾配ブースティング法(Gradient Boosting)を使うアルゴリズムです。\n", "\n", "予測した値と実際の値のズレを目的変数として考慮することで、弱点を補強しながら複数の学習器が学習されます。\n", "直列で学習するため時間がかかること、ランダムフォレストと比べてもパラメータが多いためチューニングにコストがかかりますが、予測性能はランダムフォレストよりも高いです。 \n", "\n", "[XGBoost](https://github.com/dmlc/xgboost)という高速なライブラリが出たこともあり大規模なデータでも処理しやすく、コンペサイトのKaggleでも人気です。 \n", "特にXGBoostは確率的な最適化をしているため、大規模データにも高速に処理できます。\n", "\n", "### アンサンブル学習とは\n", "\n", "ランダムフォレストやGBDTのように、複数の学習結果を組み合わせる手法を**アンサンブル学習**(Ensemble Learning)といいます。\n", "アンサンブル学習は通常、ロジスティック回帰やルールが1つだけの決定木などの \n", "シンプルな学習器(弱学習器(Week Learner)といいます)を複数組み合わせて学習をします。\n", "\n", "単純な決定木は、データの追加を行うと学習結果が大きく変わるのに対して、ランダムフォレストなどは学習結果が安定しやすくなるといったメリットもあります。\n", "また、予測性能もアンサンブルをしたほうがより良くなることが知られています。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 参考文献\n", "\n", "- http://scikit-learn.org/stable/auto_examples/linear_model/plot_sgd_loss_functions.html\n", "- [jgbos's notebook](http://nbviewer.jupyter.org/github/jgbos/iPython-Notebooks/blob/master/Comparing%20machine%20learning%20classifiers%20based%20on%20their%20hyperplanes%20or%20decision%20boundaries.ipynb) \n", "- http://scikit-learn.org/dev/auto_examples/neural_networks/plot_mlp_alpha.html" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "\"クリエイティブ・コモンズ・ライセンス\"
この 作品 は クリエイティブ・コモンズ 表示 - 非営利 - 継承 4.0 国際 ライセンスの下に提供されています。" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }