From 95df6f31fb884a8ffdf80775b5b79fecbbef507f Mon Sep 17 00:00:00 2001 From: mhjensen Date: Sat, 7 Sep 2019 18:10:12 +0200 Subject: [PATCH] to do in reg --- doc/pub/Regression/ipynb/Regression.ipynb | 543 +++++++++++++++------- doc/src/Regression/Regression.do.txt | 7 + 2 files changed, 372 insertions(+), 178 deletions(-) diff --git a/doc/pub/Regression/ipynb/Regression.ipynb b/doc/pub/Regression/ipynb/Regression.ipynb index ca9ad0e44..bbfdcaf0e 100644 --- a/doc/pub/Regression/ipynb/Regression.ipynb +++ b/doc/pub/Regression/ipynb/Regression.ipynb @@ -379,9 +379,7 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", @@ -886,9 +884,7 @@ { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "# matrix inversion to find beta\n", @@ -907,9 +903,7 @@ { "cell_type": "code", "execution_count": 3, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "fit = np.linalg.lstsq(X, Energies, rcond =None)[0]\n", @@ -926,9 +920,7 @@ { "cell_type": "code", "execution_count": 4, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "Masses['Eapprox'] = ytilde\n", @@ -958,9 +950,7 @@ { "cell_type": "code", "execution_count": 5, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "def R2(y_data, y_model):\n", @@ -977,9 +967,7 @@ { "cell_type": "code", "execution_count": 6, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "print(R2(Energies,ytilde))" @@ -995,9 +983,7 @@ { "cell_type": "code", "execution_count": 7, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "def MSE(y_data,y_model):\n", @@ -1017,9 +1003,7 @@ { "cell_type": "code", "execution_count": 8, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "def RelativeError(y_data,y_model):\n", @@ -1396,9 +1380,7 @@ { "cell_type": "code", "execution_count": 9, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "# Common imports\n", @@ -1517,9 +1499,7 @@ { "cell_type": "code", "execution_count": 10, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import os\n", @@ -1636,9 +1616,7 @@ { "cell_type": "code", "execution_count": 11, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", @@ -1658,9 +1636,7 @@ { "cell_type": "code", "execution_count": 12, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "from sklearn.datasets import load_boston\n", @@ -1682,9 +1658,7 @@ { "cell_type": "code", "execution_count": 13, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names)\n", @@ -1702,9 +1676,7 @@ { "cell_type": "code", "execution_count": 14, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "# check for missing values in all the columns\n", @@ -1721,9 +1693,7 @@ { "cell_type": "code", "execution_count": 15, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "# set the size of the figure\n", @@ -1744,9 +1714,7 @@ { "cell_type": "code", "execution_count": 16, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "# compute the pair wise correlation for all columns \n", @@ -1766,9 +1734,7 @@ { "cell_type": "code", "execution_count": 17, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "plt.figure(figsize=(20, 5))\n", @@ -1796,9 +1762,7 @@ { "cell_type": "code", "execution_count": 18, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "X = pd.DataFrame(np.c_[boston['LSTAT'], boston['RM']], columns = ['LSTAT','RM'])\n", @@ -1815,9 +1779,7 @@ { "cell_type": "code", "execution_count": 19, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "from sklearn.model_selection import train_test_split\n", @@ -1841,9 +1803,7 @@ { "cell_type": "code", "execution_count": 20, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LinearRegression\n", @@ -1882,9 +1842,7 @@ { "cell_type": "code", "execution_count": 21, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "# plotting the y_test vs y_pred\n", @@ -2662,11 +2620,41 @@ }, { "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. -1. 2.]\n", + " [ 1. 0. 1.]\n", + " [ 1. 2. -1.]\n", + " [ 1. 1. 0.]]\n", + "[[ 4. 2. 2.]\n", + " [ 2. 6. -4.]\n", + " [ 2. -4. 6.]]\n", + "test U\n", + "[[-2.22044605e-16 -1.66533454e-16 3.88578059e-16]\n", + " [-1.66533454e-16 4.44089210e-16 -2.49800181e-16]\n", + " [ 3.88578059e-16 -2.49800181e-16 0.00000000e+00]]\n", + "test VT\n", + "[[ 1.11022302e-16 -5.55111512e-17 2.22044605e-16]\n", + " [-5.55111512e-17 -4.44089210e-16 -5.27355937e-16]\n", + " [ 2.22044605e-16 -5.27355937e-16 4.44089210e-16]]\n", + "[[-1.18404906e-16 8.16496581e-01 -5.77350269e-01]\n", + " [-7.07106781e-01 4.08248290e-01 5.77350269e-01]\n", + " [ 7.07106781e-01 4.08248290e-01 5.77350269e-01]]\n", + "[1.00000000e+01 6.00000000e+00 9.10898112e-32]\n", + "[[ 3.33066907e-17 -7.07106781e-01 7.07106781e-01]\n", + " [ 8.16496581e-01 4.08248290e-01 4.08248290e-01]\n", + " [ 5.77350269e-01 -5.77350269e-01 -5.77350269e-01]]\n", + "[[-3.65939208e+30 3.65939208e+30 3.65939208e+30]\n", + " [ 3.65939208e+30 -3.65939208e+30 -3.65939208e+30]\n", + " [ 3.65939208e+30 -3.65939208e+30 -3.65939208e+30]]\n" + ] + } + ], "source": [ "import numpy as np\n", "# SVD inversion\n", @@ -2676,10 +2664,10 @@ " numpy and scipy.linalg at the cost of being slower.\n", " '''\n", " U, s, VT = np.linalg.svd(A)\n", - "# print('test U')\n", - "# print( (np.transpose(U) @ U - U @np.transpose(U)))\n", - "# print('test VT')\n", - "# print( (np.transpose(VT) @ VT - VT @np.transpose(VT)))\n", + " print('test U')\n", + " print( (np.transpose(U) @ U - U @np.transpose(U)))\n", + " print('test VT')\n", + " print( (np.transpose(VT) @ VT - VT @np.transpose(VT)))\n", " print(U)\n", " print(s)\n", " print(VT)\n", @@ -2695,8 +2683,8 @@ "print(X)\n", "A = np.transpose(X) @ X\n", "print(A)\n", - "# Brute force inversion of super-collinear matrix\n", - "#B = np.linalg.inv(A)\n", + "#Brute force inversion of super-collinear matrix\n", + "# = np.linalg.inv(A)\n", "#print(B)\n", "C = SVDinv(A)\n", "print(C)" @@ -3244,9 +3232,7 @@ { "cell_type": "code", "execution_count": 23, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "# Importing various packages\n", @@ -3269,9 +3255,7 @@ { "cell_type": "code", "execution_count": 24, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", @@ -4517,9 +4501,7 @@ { "cell_type": "code", "execution_count": 25, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "from numpy import *\n", @@ -4659,11 +4641,37 @@ }, { "cell_type": "code", - "execution_count": 26, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Runtime: 2.52646 sec\n", + "Bootstrap Statistics :\n", + "original bias std. error\n", + " 100.037 14.9654 100.037 0.1486\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:34: MatplotlibDeprecationWarning: scipy.stats.norm.pdf\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import *\n", "from numpy.random import randint, randn\n", @@ -4719,11 +4727,20 @@ }, { "cell_type": "code", - "execution_count": 27, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", @@ -4950,11 +4967,30 @@ }, { "cell_type": "code", - "execution_count": 28, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error: 0.013121574014892718\n", + "Bias^2: 0.01207364942687296\n", + "Var: 0.0010479245880197668\n", + "0.013121574014892718 >= 0.01207364942687296 + 0.0010479245880197668 = 0.013121574014892726\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", @@ -5021,11 +5057,96 @@ }, { "cell_type": "code", - "execution_count": 29, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Polynomial degree: 0\n", + "Error: 0.3473449261227775\n", + "Bias^2: 0.34442891766377043\n", + "Var: 0.0029160084590072123\n", + "0.3473449261227775 >= 0.34442891766377043 + 0.0029160084590072123 = 0.3473449261227776\n", + "Polynomial degree: 1\n", + "Error: 0.08320869315180461\n", + "Bias^2: 0.08079415054390511\n", + "Var: 0.002414542607899522\n", + "0.08320869315180461 >= 0.08079415054390511 + 0.002414542607899522 = 0.08320869315180464\n", + "Polynomial degree: 2\n", + "Error: 0.09343098322594835\n", + "Bias^2: 0.09094327576313585\n", + "Var: 0.0024877074628124806\n", + "0.09343098322594835 >= 0.09094327576313585 + 0.0024877074628124806 = 0.09343098322594832\n", + "Polynomial degree: 3\n", + "Error: 0.04412863340553516\n", + "Bias^2: 0.042755464308461874\n", + "Var: 0.0013731690970732757\n", + "0.04412863340553516 >= 0.042755464308461874 + 0.0013731690970732757 = 0.04412863340553515\n", + "Polynomial degree: 4\n", + "Error: 0.04470908847589709\n", + "Bias^2: 0.0424098690304356\n", + "Var: 0.0022992194454615083\n", + "0.04470908847589709 >= 0.0424098690304356 + 0.0022992194454615083 = 0.04470908847589711\n", + "Polynomial degree: 5\n", + "Error: 0.028280188155767848\n", + "Bias^2: 0.02561877117843377\n", + "Var: 0.0026614169773340616\n", + "0.028280188155767848 >= 0.02561877117843377 + 0.0026614169773340616 = 0.02828018815576783\n", + "Polynomial degree: 6\n", + "Error: 0.022825849262112577\n", + "Bias^2: 0.01954964607404347\n", + "Var: 0.0032762031880691185\n", + "0.022825849262112577 >= 0.01954964607404347 + 0.0032762031880691185 = 0.022825849262112587\n", + "Polynomial degree: 7\n", + "Error: 0.018582105566171653\n", + "Bias^2: 0.014625470925816387\n", + "Var: 0.00395663464035527\n", + "0.018582105566171653 >= 0.014625470925816387 + 0.00395663464035527 = 0.018582105566171656\n", + "Polynomial degree: 8\n", + "Error: 0.012597458957966583\n", + "Bias^2: 0.011479046694580953\n", + "Var: 0.0011184122633856243\n", + "0.012597458957966583 >= 0.011479046694580953 + 0.0011184122633856243 = 0.012597458957966578\n", + "Polynomial degree: 9\n", + "Error: 0.012803744241853824\n", + "Bias^2: 0.011306151277137294\n", + "Var: 0.001497592964716532\n", + "0.012803744241853824 >= 0.011306151277137294 + 0.001497592964716532 = 0.012803744241853826\n", + "Polynomial degree: 10\n", + "Error: 0.013143772803260793\n", + "Bias^2: 0.011356632052761354\n", + "Var: 0.0017871407504994265\n", + "0.013143772803260793 >= 0.011356632052761354 + 0.0017871407504994265 = 0.01314377280326078\n", + "Polynomial degree: 11\n", + "Error: 0.021091756600533057\n", + "Bias^2: 0.010495297378127714\n", + "Var: 0.010596459222405338\n", + "0.021091756600533057 >= 0.010495297378127714 + 0.010596459222405338 = 0.02109175660053305\n", + "Polynomial degree: 12\n", + "Error: 0.016326775936490116\n", + "Bias^2: 0.012231620673703427\n", + "Var: 0.004095155262786696\n", + "0.016326775936490116 >= 0.012231620673703427 + 0.004095155262786696 = 0.016326775936490123\n", + "Polynomial degree: 13\n", + "Error: 0.023820520928716643\n", + "Bias^2: 0.013913695942313559\n", + "Var: 0.009906824986403082\n", + "0.023820520928716643 >= 0.013913695942313559 + 0.009906824986403082 = 0.023820520928716643\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", @@ -5037,7 +5158,7 @@ "\n", "np.random.seed(2018)\n", "\n", - "n = 40\n", + "n = 100\n", "n_boostraps = 100\n", "maxdegree = 14\n", "\n", @@ -5120,11 +5241,47 @@ }, { "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "============================\n", + "Underfitting vs. Overfitting\n", + "============================\n", + "\n", + "This example demonstrates the problems of underfitting and overfitting and\n", + "how we can use linear regression with polynomial features to approximate\n", + "nonlinear functions. The plot shows the function that we want to approximate,\n", + "which is a part of the cosine function. In addition, the samples from the\n", + "real function and the approximations of different models are displayed. The\n", + "models have polynomial features of different degrees. We can see that a\n", + "linear function (polynomial with degree 1) is not sufficient to fit the\n", + "training samples. This is called **underfitting**. A polynomial of degree 4\n", + "approximates the true function almost perfectly. However, for higher degrees\n", + "the model will **overfit** the training data, i.e. it learns the noise of the\n", + "training data.\n", + "We evaluate quantitatively **overfitting** / **underfitting** by using\n", + "cross-validation. We calculate the mean squared error (MSE) on the validation\n", + "set, the higher, the less likely the model generalizes correctly from the\n", + "training data.\n", + "\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\"\"\"\n", "============================\n", @@ -5239,11 +5396,19 @@ }, { "cell_type": "code", - "execution_count": 31, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/lib/python3.7/site-packages/matplotlib/__init__.py:886: MatplotlibDeprecationWarning: \n", + "examples.directory is deprecated; in the future, examples will be found relative to the 'datapath' directory.\n", + " \"found relative to the 'datapath' directory.\".format(key))\n" + ] + } + ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", @@ -5354,10 +5519,8 @@ }, { "cell_type": "code", - "execution_count": 32, - "metadata": { - "collapsed": false - }, + "execution_count": 5, + "metadata": {}, "outputs": [], "source": [ "X = np.zeros((n, L ** 2))\n", @@ -5420,10 +5583,8 @@ }, { "cell_type": "code", - "execution_count": 33, - "metadata": { - "collapsed": false - }, + "execution_count": 6, + "metadata": {}, "outputs": [], "source": [ "X_train_own = np.concatenate(\n", @@ -5438,11 +5599,23 @@ }, { "cell_type": "code", - "execution_count": 34, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "ename": "LinAlgError", + "evalue": "singular matrix", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mLinAlgError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mols_inv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mscl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mbeta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mols_inv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train_own\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mols_inv\u001b[0;34m(x, y)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mols_inv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mscl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0mbeta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mols_inv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train_own\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/usr/local/lib/python3.7/site-packages/scipy/linalg/basic.py\u001b[0m in \u001b[0;36minv\u001b[0;34m(a, overwrite_a, check_finite)\u001b[0m\n\u001b[1;32m 972\u001b[0m \u001b[0minv_a\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minfo\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgetri\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlu\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpiv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlwork\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlwork\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moverwrite_lu\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 973\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0minfo\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 974\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"singular matrix\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 975\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0minfo\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 976\u001b[0m raise ValueError('illegal value in %d-th argument of internal '\n", + "\u001b[0;31mLinAlgError\u001b[0m: singular matrix" + ] + } + ], "source": [ "def ols_inv(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n", " return scl.inv(x.T @ x) @ (x.T @ y)\n", @@ -5525,10 +5698,8 @@ }, { "cell_type": "code", - "execution_count": 35, - "metadata": { - "collapsed": false - }, + "execution_count": 8, + "metadata": {}, "outputs": [], "source": [ "def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n", @@ -5538,10 +5709,8 @@ }, { "cell_type": "code", - "execution_count": 36, - "metadata": { - "collapsed": false - }, + "execution_count": 9, + "metadata": {}, "outputs": [], "source": [ "beta = ols_svd(X_train_own,y_train)" @@ -5556,10 +5725,8 @@ }, { "cell_type": "code", - "execution_count": 37, - "metadata": { - "collapsed": false - }, + "execution_count": 10, + "metadata": {}, "outputs": [], "source": [ "J = beta[1:].reshape(L, L)" @@ -5574,11 +5741,20 @@ }, { "cell_type": "code", - "execution_count": 38, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig = plt.figure(figsize=(20, 14))\n", "im = plt.imshow(J, **cmap_args)\n", @@ -5642,10 +5818,8 @@ }, { "cell_type": "code", - "execution_count": 39, - "metadata": { - "collapsed": false - }, + "execution_count": 12, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", @@ -5750,10 +5924,8 @@ }, { "cell_type": "code", - "execution_count": 40, - "metadata": { - "collapsed": false - }, + "execution_count": 13, + "metadata": {}, "outputs": [], "source": [ "X = np.zeros((n, L ** 2))\n", @@ -5782,10 +5954,8 @@ }, { "cell_type": "code", - "execution_count": 41, - "metadata": { - "collapsed": false - }, + "execution_count": 14, + "metadata": {}, "outputs": [], "source": [ "clf = skl.LinearRegression().fit(X_train, y_train)" @@ -5800,10 +5970,8 @@ }, { "cell_type": "code", - "execution_count": 42, - "metadata": { - "collapsed": false - }, + "execution_count": 15, + "metadata": {}, "outputs": [], "source": [ "J_sk = clf.coef_.reshape(L, L)" @@ -5818,11 +5986,20 @@ }, { "cell_type": "code", - "execution_count": 43, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig = plt.figure(figsize=(20, 14))\n", "im = plt.imshow(J_sk, **cmap_args)\n", @@ -5877,9 +6054,7 @@ { "cell_type": "code", "execution_count": 44, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "_lambda = 0.1\n", @@ -5930,9 +6105,7 @@ { "cell_type": "code", "execution_count": 45, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n", @@ -5966,9 +6139,7 @@ { "cell_type": "code", "execution_count": 46, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "lambdas = np.logspace(-4, 5, 10)\n", @@ -6031,9 +6202,7 @@ { "cell_type": "code", "execution_count": 47, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "fig = plt.figure(figsize=(20, 14))\n", @@ -6078,7 +6247,25 @@ ] } ], - "metadata": {}, + "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": "3.7.3" + } + }, "nbformat": 4, "nbformat_minor": 2 } diff --git a/doc/src/Regression/Regression.do.txt b/doc/src/Regression/Regression.do.txt index 646c4abf9..5c759419c 100644 --- a/doc/src/Regression/Regression.do.txt +++ b/doc/src/Regression/Regression.do.txt @@ -2558,6 +2558,13 @@ The difference is non-negative definite since each component of the matrix product is non-negative definite. This means the variance we obtain with the standard OLS will always for $\lambda > 0$ be larger than the variance of $\bm{\beta}$ obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below. + +!split +===== Resampling methods ===== + +Discuss types of error and how we proceed in doing so. + + !split ===== Cross-validation =====