RidgeRegression.ipynb

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    "# Ridge Regression\n",
    "\n",
    "## Rückblick Lineare Regression\n",
    "\n",
    "Lineare Regression: $\\mathbf{y}=𝑏+w_1\\mathbf{x}$\n",
    "\n",
    "$\\mathbf{x} \\in \\mathbb{R}^n$: Einflussgröße (Feature)  \n",
    "$\\mathbf{y} \\in \\mathbb{R}^n$: Zielvariable (Target)  \n",
    "$n$: Anzahl der Trainingsinstanzen  \n",
    "$b,w_1 \\in \\mathbb{R}$: Gewichte/Parameter  \n",
    "\n",
    "Linear Regression Straffunktion (Loss) ist definiert als:  \n",
    "\n",
    "$\\mathcal{L}(\\mathbf{w})= \\sum_{i=1}^n \\left[y_i - (b - \\mathbf{w}^T \\mathbf{x}_i) \\right]^2$  \n",
    "\n",
    "Zum lernen der unbekannten Gewichte $\\mathbf{w}$ muss man die Straffunktion $\\mathcal{L}$ minimieren. \n",
    "\n",
    "### Simuliere und Plotte Daten"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Importiere Python Libraries\n",
    "%matplotlib inline\n",
    "import pylab as pl\n",
    "import seaborn as sns\n",
    "sns.set(font_scale=1.7)\n",
    "\n",
    "from plotly.offline import init_notebook_mode, iplot\n",
    "from plotly.graph_objs import *\n",
    "import plotly.tools as tls\n",
    "#Set to True\n",
    "init_notebook_mode(connected=True)\n",
    "\n",
    "import scipy as sp\n",
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from sklearn.linear_model import LinearRegression, Ridge\n",
    "from sklearn.pipeline import Pipeline\n",
    "from ipywidgets import *\n",
    "from IPython.display import display\n",
    "\n",
    "#Funktion zum Plotten der Daten\n",
    "def plot_data(X,y,model=None,interactive=False):\n",
    "    fig = pl.figure(figsize=(10,6))\n",
    "    pl.plot(X,y,'o',markersize=10)\n",
    "    pl.xlabel(\"x\")\n",
    "    pl.ylabel(\"y\")\n",
    "    pl.title(\"\")\n",
    "    pl.ylim([-1.1,1.1])\n",
    "    pl.xlim([-3.1,3.1])\n",
    "    pl.xticks([-3,-2,-1,0,1,2,3],[\"50\",\"60\",\"70\",\"80\",\"90\",\"100\",\"110\"])\n",
    "    pl.yticks([-1,-0.5,0,0.5,1],[\"200k\",\"400k\",\"600k\",\"800k\",\"1M\"])\n",
    "    if not model==None:\n",
    "        X_new=sp.linspace(-3, 3, 100).reshape(100, 1)\n",
    "        y_new = model.predict(X_new)\n",
    "        pl.plot(X_new,y_new,\"r-\",linewidth=4,label=\"Learned Regression Fit\")\n",
    "        pl.legend()\n",
    "    if interactive:\n",
    "        plotly_fig = tls.mpl_to_plotly(fig)\n",
    "        iplot(plotly_fig, show_link=False)\n",
    "\n",
    "\n",
    "#Funktion um Beispieldaten zu simulieren\n",
    "def generate_data():\n",
    "    sp.random.seed(42)\n",
    "    X = sp.arange(-3,3,1.0/20.0).reshape(-1,1)\n",
    "    y = sp.sin(0.2*sp.pi*X+0.1*sp.random.randn(X.shape[0],1))\n",
    "    return X,y\n",
    "\n",
    "def generate_polynomial_features(X,degree=1,return_transformer=True):\n",
    "    transformer = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    X_poly = transformer.fit_transform(X)\n",
    "    if return_transformer:\n",
    "        return X_poly, transformer\n",
    "    else:\n",
    "        return X_poly\n",
    "\n",
    "#Generiere Daten\n",
    "X,y = generate_data()\n",
    "print X.shape\n",
    "#Plotte Daten\n",
    "plot_data(X,y,interactive=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lerne Lineare Regression auf Daten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anzahl der Trainingsinstanzen:\t120\n",
      "Anzahl der Features:\t\t1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Python/2.7/site-packages/plotly/matplotlylib/renderer.py:384: UserWarning:\n",
      "\n",
      "Bummer! Plotly can currently only draw Line2D objects from matplotlib that are in 'data' coordinates!\n",
      "\n",
      "/Library/Python/2.7/site-packages/plotly/matplotlylib/renderer.py:481: UserWarning:\n",
      "\n",
      "I found a path object that I don't think is part of a bar chart. Ignoring.\n",
      "\n"
     ]
    },
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     "metadata": {},
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   ],
   "source": [
    "#Lerne Lineare Regression\n",
    "print \"Anzahl der Trainingsinstanzen:\\t%d\"%(X.shape[0])\n",
    "print \"Anzahl der Features:\\t\\t%d\"%(X.shape[1])\n",
    "model = LinearRegression()\n",
    "model.fit(X,y)\n",
    "#Plotte Daten und die gelernte Funktion\n",
    "plot_data(X,y,model,interactive=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:orange\">**Model beschreibt die zugrundeliegenden Daten nur schlecht -> Model ist Unterangepasst!**</span>\n",
    "\n",
    "### Polynomiale Regression\n",
    "\n",
    "Polynomiale Regression durch hinzufügen von Features höherer Ordnung, z.B. Polynom des 100. Grades:   \n",
    "\n",
    "$\\mathbf{y} = b + w_1 \\mathbf{x}_1 + w_2 \\mathbf{x}_1^2 + w_3 \\mathbf{x}_1^3 + \\dots + + w_2 \\mathbf{x}_1^{100} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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SNyZWuJ3DQv3Qr5M34hLSoADAA2ps8uiqonFzg8bGBqwiI8ntqWeQGEVJpwkh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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ebdcf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Funktion um eine Polynomielle Regression unterschiedlichen Grades zu plotten\n",
    "def render_polynomial_regression(degree=150):\n",
    "    #Lerne Lineare Regression auf polynomiellen Features\n",
    "    transformer = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    scaler = StandardScaler()\n",
    "    model = LinearRegression()\n",
    "\n",
    "    #Polynomielle Regression mit Feature Scaling\n",
    "    polynomial_regression = Pipeline((\n",
    "        ('make_poly_features',transformer),\n",
    "        (\"scale_features\",scaler),\n",
    "        (\"run_linreg\",model),\n",
    "    ))\n",
    "\n",
    "    polynomial_regression.fit(X,y)\n",
    "    #Plotte Daten und die gelernte Funktion\n",
    "    plot_data(X,y,polynomial_regression)\n",
    "    pl.show()\n",
    "\n",
    "#Render einen Interaktiven Plot\n",
    "#interact(render_polynomial_regression,degree=IntSlider(min=1,max=300,value=100,\n",
    "#                                                       description=\"Grad des Polynoms:\"));\n",
    "render_polynomial_regression(degree=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:orange\">**Model beschreibt die Daten zu gut --> Model ist Üeberangepasst und führt zu einer schlechten Generalisierung!**</span>\n",
    "\n",
    "## Einführung in Ridge Regression\n",
    "\n",
    "Ridge Regression Loss ist definiert als:  \n",
    "\n",
    "$\\mathcal{L}_{Ridge}(\\mathbf{w})=\\frac{1}{n}\\sum_{i=1}^n \\left[y_i - (b - \\mathbf{w}^T \\mathbf{x}_i) \\right]^2 + \\underbrace{\\alpha \\Vert \\mathbf{w}\\Vert_2^2}_{Strafterm}$  \n",
    "\n",
    "Zum lernen der unbekannten Gewichte $\\mathbf{w}$ muss man die Straffunktion $\\mathcal{L}_{Ridge}$ minimieren. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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   "source": [
    "#Lerne Ridge Regression auf polynomiellen Features mit alpha=1.1\n",
    "ridge_regression = Pipeline((\n",
    "    ('make_poly_features',PolynomialFeatures(degree=100, include_bias=False)),\n",
    "    (\"scale_features\",StandardScaler()),\n",
    "    (\"run_ridgereg\",Ridge(alpha=1.1)),\n",
    "))\n",
    "\n",
    "ridge_regression.fit(X,y)\n",
    "\n",
    "plot_data(X,y,ridge_regression,interactive=True)"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:green\">**Optimale Abwägung zwischen zu einfachem und zu komplexem Model durch L2-Regularisierung!\n",
    "**</span>\n",
    "\n",
    "### Effekt von $\\alpha$ auf die Gewichte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    "#Funktion um den Effekt von alpha auf die Gewichte zu illustrieren\n",
    "def plot_effect_of_alpha(interactive=False):\n",
    "    coefs = []\n",
    "    alphas = sp.logspace(5,-6,200)\n",
    "    poly_feat = PolynomialFeatures(degree=10, include_bias=False)\n",
    "    scaler = StandardScaler()\n",
    "    for alpha in alphas:\n",
    "        model = Ridge(alpha=alpha)\n",
    "        ridge_regression = Pipeline((\n",
    "            ('make_poly_features',poly_feat),\n",
    "            (\"scale_features\",scaler),\n",
    "            (\"run_ridgereg\",model),\n",
    "        ))\n",
    "\n",
    "        ridge_regression.fit(X,y)\n",
    "\n",
    "        X_new=sp.linspace(-3, 3, 100).reshape(100, 1)\n",
    "        y_new = ridge_regression.predict(X_new)\n",
    "        coefs.append(model.coef_.flatten()[1:])\n",
    "    fig = pl.figure(figsize=(10,6))\n",
    "    ax = pl.gca()\n",
    "    ax.plot(alphas, coefs,linewidth=3)\n",
    "    ax.set_xscale('log')\n",
    "    if interactive:\n",
    "        pl.xlabel(\"alpha\")\n",
    "    else:\n",
    "        pl.xlabel('$\\\\alpha$')\n",
    "    pl.ylabel('Gewichte')\n",
    "    pl.axis('tight')\n",
    "    if interactive:\n",
    "        pl.xticks(fontsize=13)\n",
    "        plotly_fig = tls.mpl_to_plotly(fig)\n",
    "        iplot(plotly_fig, show_link=False)\n",
    "    else:\n",
    "        pl.show()\n",
    "#Plot Effect of Alpha\n",
    "plot_effect_of_alpha(interactive=True);"
   ]
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