diff --git a/doc/pub/week38/html/._week38-bs001.html b/doc/pub/week38/html/._week38-bs001.html index af8f75e3e..3d6301961 100644 --- a/doc/pub/week38/html/._week38-bs001.html +++ b/doc/pub/week38/html/._week38-bs001.html @@ -422,6 +422,7 @@ MathJax.Hub.Config({ diff --git a/doc/pub/week38/html/._week38-bs014.html b/doc/pub/week38/html/._week38-bs014.html index 6e43634a1..fa21e3ef4 100644 --- a/doc/pub/week38/html/._week38-bs014.html +++ b/doc/pub/week38/html/._week38-bs014.html @@ -544,6 +544,9 @@ $$ \lambda \vert\vert \boldsymbol{\beta} \vert\vert_1 = \lambda \sum_{j=1}^{p-1}\vert\beta_j\vert. $$ +

+It means that, when scaling the design matrix and the outputs/targets, by subtracting the mean values, we have an optimization problem which is not penalized by the intercept. The MSE value can then be smaller since it focuses only on the remaining quantities. If we however bring back the intercept, we will get a MSE which then contains the intercept. +

diff --git a/doc/pub/week38/html/._week38-bs016.html b/doc/pub/week38/html/._week38-bs016.html index f43f780bc..7f0b084f4 100644 --- a/doc/pub/week38/html/._week38-bs016.html +++ b/doc/pub/week38/html/._week38-bs016.html @@ -506,11 +506,15 @@ plt.show()

We see here, when compared to the code which includes explicitely the intercept column, that our MSE value is actually smaller. This is -because the regularization term does not include the intercept value \( \beta_0 \) in the -fitting. This applies to Lasso regularization as well. +because the regularization term does not include the intercept value +\( \beta_0 \) in the fitting. This applies to Lasso regularization as +well. It means that our optimization is now done only with the +centered matrix and/or vector that enter the fitting procedure. Note +also that the problem with the intercept occurs mainly in these type +of polynomial fitting problem.

-If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting. +The next example is indeed an example where all these discussions about the role of intercept are not present.

diff --git a/doc/pub/week38/html/week38-reveal.html b/doc/pub/week38/html/week38-reveal.html index 47d2e6b21..9d28f2209 100644 --- a/doc/pub/week38/html/week38-reveal.html +++ b/doc/pub/week38/html/week38-reveal.html @@ -163,6 +163,7 @@ MathJax.Hub.Config({

@@ -795,6 +796,9 @@ $$ \lambda \vert\vert \boldsymbol{\beta} \vert\vert_1 = \lambda \sum_{j=1}^{p-1}\vert\beta_j\vert. $$

 
+ +

+It means that, when scaling the design matrix and the outputs/targets, by subtracting the mean values, we have an optimization problem which is not penalized by the intercept. The MSE value can then be smaller since it focuses only on the remaining quantities. If we however bring back the intercept, we will get a MSE which then contains the intercept. @@ -970,11 +974,15 @@ plt.show()

We see here, when compared to the code which includes explicitely the intercept column, that our MSE value is actually smaller. This is -because the regularization term does not include the intercept value \( \beta_0 \) in the -fitting. This applies to Lasso regularization as well. +because the regularization term does not include the intercept value +\( \beta_0 \) in the fitting. This applies to Lasso regularization as +well. It means that our optimization is now done only with the +centered matrix and/or vector that enter the fitting procedure. Note +also that the problem with the intercept occurs mainly in these type +of polynomial fitting problem.

-If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting. +The next example is indeed an example where all these discussions about the role of intercept are not present. diff --git a/doc/pub/week38/html/week38-solarized.html b/doc/pub/week38/html/week38-solarized.html index c55e90506..480bb1016 100644 --- a/doc/pub/week38/html/week38-solarized.html +++ b/doc/pub/week38/html/week38-solarized.html @@ -346,6 +346,7 @@ MathJax.Hub.Config({

@@ -924,6 +925,9 @@ $$ \lambda \vert\vert \boldsymbol{\beta} \vert\vert_1 = \lambda \sum_{j=1}^{p-1}\vert\beta_j\vert. $$ +

+It means that, when scaling the design matrix and the outputs/targets, by subtracting the mean values, we have an optimization problem which is not penalized by the intercept. The MSE value can then be smaller since it focuses only on the remaining quantities. If we however bring back the intercept, we will get a MSE which then contains the intercept. +











@@ -1098,11 +1102,15 @@ plt.show()

We see here, when compared to the code which includes explicitely the intercept column, that our MSE value is actually smaller. This is -because the regularization term does not include the intercept value \( \beta_0 \) in the -fitting. This applies to Lasso regularization as well. +because the regularization term does not include the intercept value +\( \beta_0 \) in the fitting. This applies to Lasso regularization as +well. It means that our optimization is now done only with the +centered matrix and/or vector that enter the fitting procedure. Note +also that the problem with the intercept occurs mainly in these type +of polynomial fitting problem.

-If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting. +The next example is indeed an example where all these discussions about the role of intercept are not present.











diff --git a/doc/pub/week38/html/week38.html b/doc/pub/week38/html/week38.html index 0eb03ac64..f09aa8f50 100644 --- a/doc/pub/week38/html/week38.html +++ b/doc/pub/week38/html/week38.html @@ -351,6 +351,7 @@ MathJax.Hub.Config({

@@ -929,6 +930,9 @@ $$ \lambda \vert\vert \boldsymbol{\beta} \vert\vert_1 = \lambda \sum_{j=1}^{p-1}\vert\beta_j\vert. $$ +

+It means that, when scaling the design matrix and the outputs/targets, by subtracting the mean values, we have an optimization problem which is not penalized by the intercept. The MSE value can then be smaller since it focuses only on the remaining quantities. If we however bring back the intercept, we will get a MSE which then contains the intercept. +











@@ -1103,11 +1107,15 @@ plt.show()

We see here, when compared to the code which includes explicitely the intercept column, that our MSE value is actually smaller. This is -because the regularization term does not include the intercept value \( \beta_0 \) in the -fitting. This applies to Lasso regularization as well. +because the regularization term does not include the intercept value +\( \beta_0 \) in the fitting. This applies to Lasso regularization as +well. It means that our optimization is now done only with the +centered matrix and/or vector that enter the fitting procedure. Note +also that the problem with the intercept occurs mainly in these type +of polynomial fitting problem.

-If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting. +The next example is indeed an example where all these discussions about the role of intercept are not present.











diff --git a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz index f2ebad607..51d029e51 100644 Binary files a/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz and b/doc/pub/week38/ipynb/ipynb-week38-src.tar.gz differ diff --git a/doc/pub/week38/ipynb/week38.ipynb b/doc/pub/week38/ipynb/week38.ipynb index 4ec6c9c80..d836998bd 100644 --- a/doc/pub/week38/ipynb/week38.ipynb +++ b/doc/pub/week38/ipynb/week38.ipynb @@ -24,6 +24,8 @@ "\n", "* Thursday: Summary of regression methods and discussion of project 1. Start Logistic Regression\n", "\n", + "* [Video of Lecture September 23](https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureSeptember23.mp4?vrtx=view-as-webpage)\n", + "\n", "* Friday: Logistic Regression and Optimization methods\n", "\n", "## Thursday September 23\n", @@ -234,7 +236,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "%matplotlib inline\n", @@ -395,7 +400,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "#Model training, we compute the mean value of y and X\n", @@ -503,7 +511,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "X = X - np.mean(X,axis=0)" @@ -710,43 +721,12 @@ }, { "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "True beta: [2, 0.5, 3.7]\n", - "Fitted beta: [2.08376632 0.19569961 3.97898392]\n", - "Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]\n", - "MSE with intercept column\n", - "0.004113634617443137\n", - "MSE with intercept column from SKL\n", - "0.0041136346174431284\n", - "Manual intercept: 2.083766322923905\n", - "Fitted beta (wiothout intercept): [0.19569961 3.97898392]\n", - "Sklearn intercept: 2.0837663229239025\n", - "Sklearn fitted beta (without intercept): [0.19569961 3.97898392]\n", - "MSE with Manual intercept\n", - "4.34619572316926\n", - "MSE with Sklearn intercept\n", - "0.004113634617443135\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "

" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", @@ -824,7 +804,7 @@ "ypredictOwn = X @ beta\n", "ypredictSKL = skl.predict(X)\n", "print(f\"MSE with Manual intercept\")\n", - "print(MSE(y,ypredictOwn))\n", + "print(MSE(y,ypredictOwn+intercept))\n", "print(f\"MSE with Sklearn intercept\")\n", "print(MSE(y,ypredictSKL))\n", "\n", @@ -849,7 +829,7 @@ "meaning that the MSE can be penalized by the value of the\n", "intercept. Not including the intercept in the fit, means that the\n", "regularization term does not include $\\beta_0$. For different values\n", - "of $\\lambda$, this may lead to differeing MSE values.\n", + "of $\\lambda$, this may lead to differeing MSE values. \n", "\n", "To remind the reader, the regularization term, with the intercept in Ridge regression is given by" ] @@ -899,6 +879,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "It means that, when scaling the design matrix and the outputs/targets, by subtracting the mean values, we have an optimization problem which is not penalized by the intercept. The MSE value can then be smaller since it focuses only on the remaining quantities. If we however bring back the intercept, we will get a MSE which then contains the intercept. \n", + "\n", "## Code Examples\n", "\n", "Armed with this wisdom, we attempt first to simply set the intercept equal to **False** in our implementation of Ridge regression for our well-known vanilla data set." @@ -906,113 +888,12 @@ }, { "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Beta values for own Ridge implementation\n", - "[ 1.03032441e+00 6.28336218e-02 -6.24175744e-01 5.21169159e-02\n", - " 2.80847477e-01 2.12552073e-01 8.13220609e-02 -1.69634577e-02\n", - " -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n", - " -9.80609614e-03 1.08299273e-02 2.41882037e-02 2.93492130e-02\n", - " 2.64742912e-02 1.63249532e-02 -5.01831250e-05 -2.15098090e-02]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[ 0.00000000e+00 6.21437387e-02 -6.21799480e-01 4.97375876e-02\n", - " 2.80186212e-01 2.13204296e-01 8.21806408e-02 -1.64261842e-02\n", - " -6.49525927e-02 -7.40621002e-02 -5.97380172e-02 -3.53631498e-02\n", - " -1.00892602e-02 1.06457090e-02 2.41129954e-02 2.93712126e-02\n", - " 2.65682547e-02 1.64586608e-02 8.86820374e-05 -2.13996549e-02]\n", - "MSE values for own Ridge implementation\n", - "4.3632959273186007e-07\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "4.538437249567689e-07\n", - "Beta values for own Ridge implementation\n", - "[ 1.03630548 -0.01963611 -0.37900111 -0.07062318 0.12182967 0.16343471\n", - " 0.13003291 0.07490892 0.02365049 -0.01449782 -0.03814292 -0.04909093\n", - " -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724 0.01348565\n", - " 0.02976145 0.04543942]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[ 0. -0.02347793 -0.37069922 -0.07332612 0.11841713 0.16193346\n", - " 0.1301137 0.07578485 0.02473008 -0.01354652 -0.03746205 -0.048708\n", - " -0.04998023 -0.04397732 -0.03302123 -0.01896364 -0.00321213 0.01320154\n", - " 0.02954601 0.04532178]\n", - "MSE values for own Ridge implementation\n", - "5.194042826640948e-06\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "5.7536602621083615e-06\n", - "Beta values for own Ridge implementation\n", - "[ 1.04220758 -0.10931453 -0.17641709 -0.06020587 0.02208512 0.05789007\n", - " 0.06491736 0.05785343 0.04537385 0.03196357 0.01969145 0.00934499\n", - " 0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n", - " -0.01708852 -0.01708781]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[ 0. -0.12806426 -0.15525674 -0.05487426 0.0191961 0.05293494\n", - " 0.0605132 0.05479386 0.04368354 0.03139359 0.01993241 0.01011079\n", - " 0.00212882 -0.00410226 -0.00879058 -0.01217801 -0.0144992 -0.01596432\n", - " -0.01675341 -0.01701673]\n", - "MSE values for own Ridge implementation\n", - "2.094082198961287e-05\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "2.891180548496722e-05\n", - "Beta values for own Ridge implementation\n", - "[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855 0.00312361\n", - " 0.01463049 0.01975848 0.02123176 0.02068067 0.01905883 0.01691985\n", - " 0.01458337 0.01223198 0.00996754 0.00784393 0.00588657 0.00410387\n", - " 0.00249435 0.00105081]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[ 0. -0.13729887 -0.08409267 -0.03383964 -0.00374257 0.01182892\n", - " 0.01878432 0.02095086 0.02056419 0.01888753 0.01662493 0.01416442\n", - " 0.01171602 0.00938921 0.00723663 0.0052788 0.00351837 0.00194828\n", - " 0.00055647 -0.00067131]\n", - "MSE values for own Ridge implementation\n", - "0.00031535148309579146\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "6.344515538040109e-05\n", - "Beta values for own Ridge implementation\n", - "[ 8.38916861e-01 1.31276579e-01 8.97497404e-03 -1.72271878e-02\n", - " -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n", - " -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n", - " -1.84923989e-03 -8.13661243e-04 7.46984697e-06 6.56636616e-04\n", - " 1.16805821e-03 1.56912044e-03 1.88168312e-03 2.12318726e-03]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[ 0. -0.05814585 -0.04390414 -0.02861232 -0.01777492 -0.01046009\n", - " -0.00550644 -0.00210846 0.00024979 0.00189794 0.00305065 0.00385122\n", - " 0.00439783 0.00475926 0.00498468 0.00510982 0.00516093 0.00515753\n", - " 0.00511424 0.00504205]\n", - "MSE values for own Ridge implementation\n", - "0.01507238889517716\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "0.0008213907109028524\n", - "Beta values for own Ridge implementation\n", - "[0.37396662 0.14174745 0.0764924 0.04892055 0.03447512 0.02586427\n", - " 0.02024962 0.01633913 0.01347916 0.0113104 0.0096208 0.00827728\n", - " 0.00719176 0.00630331 0.00556826 0.0049544 0.00443743 0.0039987\n", - " 0.0036237 0.003301 ]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[ 0. -0.00952707 -0.00855426 -0.00684557 -0.00542639 -0.00433676\n", - " -0.00350466 -0.00286296 -0.00236187 -0.0019659 -0.00164965 -0.0013947\n", - " -0.00118745 -0.0010177 -0.0008777 -0.00076148 -0.00066442 -0.00058287\n", - " -0.00051397 -0.00045544]\n", - "MSE values for own Ridge implementation\n", - "0.2640931530791003\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "0.0031252083411001537\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", @@ -1052,7 +933,7 @@ " lmb = lambdas[i]\n", " OwnRidgeBeta = np.linalg.pinv(X_train.T @ X_train+lmb*I) @ X_train.T @ y_train\n", " # Note: we include the intercept column and no scaling\n", - " RegRidge = linear_model.Ridge(lmb)#,fit_intercept=False)\n", + " RegRidge = linear_model.Ridge(lmb,fit_intercept=False)\n", " RegRidge.fit(X_train,y_train)\n", " # and then make the prediction\n", " ytildeOwnRidge = X_train @ OwnRidgeBeta\n", @@ -1095,138 +976,12 @@ }, { "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Beta values for own Ridge implementation\n", - "[ 3.43579948e-02 -5.43330971e-01 -3.10141414e-03 2.47116868e-01\n", - " 2.18613217e-01 1.02054837e-01 -4.25617662e-04 -5.90475506e-02\n", - " -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n", - " 1.11482289e-02 2.88529063e-02 3.67047975e-02 3.38135733e-02\n", - " 2.02198702e-02 -3.46383924e-03 -3.63025821e-02]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03 2.47116868e-01\n", - " 2.18613217e-01 1.02054837e-01 -4.25617658e-04 -5.90475506e-02\n", - " -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n", - " 1.11482289e-02 2.88529063e-02 3.67047975e-02 3.38135733e-02\n", - " 2.02198702e-02 -3.46383925e-03 -3.63025821e-02]\n", - "Intercept from own implementation:\n", - "1.0330308045181225\n", - "Intercept from Scikit-Learn Ridge implementation\n", - "1.033030804518383\n", - "MSE values for own Ridge implementation\n", - "3.139255958275475e-06\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "3.139255958572018e-06\n", - "Beta values for own Ridge implementation\n", - "[-0.05807125 -0.29822833 -0.08551306 0.08156108 0.13679863 0.12333649\n", - " 0.08251519 0.03815288 0.00111756 -0.02498832 -0.04010697 -0.04566964\n", - " -0.04355837 -0.03562355 -0.02348765 -0.00848904 0.00831018 0.0260906\n", - " 0.04423486]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[-0.05807125 -0.29822833 -0.08551306 0.08156108 0.13679863 0.12333649\n", - " 0.08251519 0.03815288 0.00111756 -0.02498832 -0.04010697 -0.04566964\n", - " -0.04355837 -0.03562355 -0.02348765 -0.00848904 0.00831018 0.0260906\n", - " 0.04423486]\n", - "Intercept from own implementation:\n", - "1.0411487294305548\n", - "Intercept from Scikit-Learn Ridge implementation\n", - "1.0411487294305266\n", - "MSE values for own Ridge implementation\n", - "1.9601304850163794e-05\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "1.9601304850085328e-05\n", - "Beta values for own Ridge implementation\n", - "[-0.1416398 -0.14021063 -0.05383795 0.01367553 0.04784395 0.05796251\n", - " 0.05447415 0.044613 0.03267527 0.02098261 0.01066519 0.00217499\n", - " -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081 -0.01416528\n", - " -0.01290947]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[-0.1416398 -0.14021063 -0.05383795 0.01367553 0.04784395 0.05796251\n", - " 0.05447415 0.044613 0.03267527 0.02098261 0.01066519 0.00217499\n", - " -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081 -0.01416528\n", - " -0.01290947]\n", - "Intercept from own implementation:\n", - "1.0495569966278282\n", - "Intercept from Scikit-Learn Ridge implementation\n", - "1.0495569966278269\n", - "MSE values for own Ridge implementation\n", - "5.4959161509370406e-05\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "5.4959161509366834e-05\n", - "Beta values for own Ridge implementation\n", - "[-0.13535942 -0.08593216 -0.03568439 -0.0036367 0.01397146 0.02229529\n", - " 0.02503753 0.0245528 0.02228115 0.01908936 0.01549377 0.01179792\n", - " 0.00817631 0.00472512 0.00149311 -0.00149956 -0.00424967 -0.00676387\n", - " -0.00905423]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[-0.13535942 -0.08593216 -0.03568439 -0.0036367 0.01397146 0.02229529\n", - " 0.02503753 0.0245528 0.02228115 0.01908936 0.01549377 0.01179792\n", - " 0.00817631 0.00472512 0.00149311 -0.00149956 -0.00424967 -0.00676387\n", - " -0.00905423]\n", - "Intercept from own implementation:\n", - "1.039967668952797\n", - "Intercept from Scikit-Learn Ridge implementation\n", - "1.0399676689527975\n", - "MSE values for own Ridge implementation\n", - "7.571105947979326e-05\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "7.57110594797945e-05\n", - "Beta values for own Ridge implementation\n", - "[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706 -0.00517114\n", - " -0.00174276 0.00068734 0.00243186 0.00369758 0.00462287 0.0053018\n", - " 0.00579953 0.006162 0.00642221 0.00660427 0.00672607 0.0068011\n", - " 0.00683964]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706 -0.00517114\n", - " -0.00174276 0.00068734 0.00243186 0.00369758 0.00462287 0.0053018\n", - " 0.00579953 0.006162 0.00642221 0.00660427 0.00672607 0.0068011\n", - " 0.00683964]\n", - "Intercept from own implementation:\n", - "0.999955585168597\n", - "Intercept from Scikit-Learn Ridge implementation\n", - "0.999955585168597\n", - "MSE values for own Ridge implementation\n", - "0.0007698473260556339\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "0.000769847326055633\n", - "Beta values for own Ridge implementation\n", - "[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n", - " -0.00323332 -0.00274989 -0.0023548 -0.00202756 -0.00175331 -0.00152117\n", - " -0.001323 -0.0011526 -0.00100519 -0.00087697 -0.00076495 -0.00066668\n", - " -0.00058016]\n", - "Beta values for Scikit-Learn Ridge implementation\n", - "[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n", - " -0.00323332 -0.00274989 -0.0023548 -0.00202756 -0.00175331 -0.00152117\n", - " -0.001323 -0.0011526 -0.00100519 -0.00087697 -0.00076495 -0.00066668\n", - " -0.00058016]\n", - "Intercept from own implementation:\n", - "0.9637117593816477\n", - "Intercept from Scikit-Learn Ridge implementation\n", - "0.9637117593816477\n", - "MSE values for own Ridge implementation\n", - "0.0023813163025848865\n", - "MSE values for Scikit-Learn Ridge implementation\n", - "0.002381316302584886\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", @@ -1316,10 +1071,15 @@ "source": [ "We see here, when compared to the code which includes explicitely the\n", "intercept column, that our MSE value is actually smaller. This is\n", - "because the regularization term does not include the intercept value $\\beta_0$ in the\n", - "fitting. This applies to Lasso regularization as well.\n", + "because the regularization term does not include the intercept value\n", + "$\\beta_0$ in the fitting. This applies to Lasso regularization as\n", + "well. It means that our optimization is now done only with the\n", + "centered matrix and/or vector that enter the fitting procedure. Note\n", + "also that the problem with the intercept occurs mainly in these type\n", + "of polynomial fitting problem.\n", + "\n", + "The next example is indeed an example where all these discussions about the role of intercept are not present.\n", "\n", - "If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting.\n", "\n", "## More complicated Example: The Ising model\n", "\n", @@ -1357,8 +1117,11 @@ }, { "cell_type": "code", - "execution_count": 5, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import numpy as np\n", @@ -1470,8 +1233,11 @@ }, { "cell_type": "code", - "execution_count": 6, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "X = np.zeros((n, L ** 2))\n", @@ -1534,8 +1300,11 @@ }, { "cell_type": "code", - "execution_count": 7, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "X_train_own = np.concatenate(\n", @@ -1550,23 +1319,12 @@ }, { "cell_type": "code", - "execution_count": 8, - "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~/opt/anaconda3/lib/python3.8/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 975\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 976\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--> 977\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 978\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 979\u001b[0m raise ValueError('illegal value in %d-th argument of internal '\n", - "\u001b[0;31mLinAlgError\u001b[0m: singular matrix" - ] - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "def ols_inv(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n", " return scl.inv(x.T @ x) @ (x.T @ y)\n", @@ -1649,8 +1407,11 @@ }, { "cell_type": "code", - "execution_count": 9, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n", @@ -1660,8 +1421,11 @@ }, { "cell_type": "code", - "execution_count": 10, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "beta = ols_svd(X_train_own,y_train)" @@ -1676,8 +1440,11 @@ }, { "cell_type": "code", - "execution_count": 11, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "J = beta[1:].reshape(L, L)" @@ -1692,28 +1459,12 @@ }, { "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - ":7: UserWarning: FixedFormatter should only be used together with FixedLocator\n", - " cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "fig = plt.figure(figsize=(20, 14))\n", "im = plt.imshow(J, **cmap_args)\n", @@ -1777,8 +1528,11 @@ }, { "cell_type": "code", - "execution_count": 13, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import numpy as np\n", @@ -1883,8 +1637,11 @@ }, { "cell_type": "code", - "execution_count": 14, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "X = np.zeros((n, L ** 2))\n", @@ -1913,8 +1670,11 @@ }, { "cell_type": "code", - "execution_count": 15, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "clf = skl.LinearRegression().fit(X_train, y_train)" @@ -1929,8 +1689,11 @@ }, { "cell_type": "code", - "execution_count": 16, - "metadata": {}, + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "J_sk = clf.coef_.reshape(L, L)" @@ -1945,28 +1708,12 @@ }, { "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - ":7: UserWarning: FixedFormatter should only be used together with FixedLocator\n", - " cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "fig = plt.figure(figsize=(20, 14))\n", "im = plt.imshow(J_sk, **cmap_args)\n", @@ -2019,28 +1766,12 @@ }, { "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - ":10: UserWarning: FixedFormatter should only be used together with FixedLocator\n", - " cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "_lambda = 0.1\n", "clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)\n", @@ -2089,28 +1820,12 @@ }, { "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - ":9: UserWarning: FixedFormatter should only be used together with FixedLocator\n", - " cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n", "J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n", @@ -2142,29 +1857,12 @@ }, { "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - " 0%| | 0/10 [00:00" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "lambdas = np.logspace(-4, 5, 10)\n", "\n", @@ -2225,20 +1923,12 @@ }, { "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "execution_count": null, + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "fig = plt.figure(figsize=(20, 14))\n", "\n", @@ -2428,7 +2118,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "# Common imports\n", @@ -2499,7 +2192,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])\n", @@ -2583,7 +2279,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "\"\"\"The sigmoid function (or the logistic curve) is a\n", @@ -3002,7 +2701,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", @@ -3045,7 +2747,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", @@ -3108,7 +2813,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "cancerpd = pd.DataFrame(cancer.data, columns=cancer.feature_names)" @@ -3124,7 +2832,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "correlation_matrix = cancerpd.corr().round(1)" @@ -3147,7 +2858,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", @@ -3964,7 +3678,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "import numpy as np\n", @@ -3999,7 +3716,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "pt.axis(\"equal\")\n", @@ -4017,7 +3737,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "x = guesses[-1]\n", @@ -4034,7 +3757,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "def f1d(alpha):\n", @@ -4056,7 +3782,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "pt.axis(\"equal\")\n", @@ -4432,7 +4161,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "x = 2*np.random.rand(m,1)\n", @@ -4599,7 +4331,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "\n", @@ -4660,7 +4395,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "# Importing various packages\n", @@ -4744,7 +4482,10 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": false, + "editable": true + }, "outputs": [], "source": [ "from random import random, seed\n", @@ -4812,25 +4553,7 @@ ] } ], - "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": "3.8.5" - } - }, + "metadata": {}, "nbformat": 4, "nbformat_minor": 4 } diff --git a/doc/src/week38/week38.do.txt b/doc/src/week38/week38.do.txt index c0d0b7d77..71aa184a5 100644 --- a/doc/src/week38/week38.do.txt +++ b/doc/src/week38/week38.do.txt @@ -10,6 +10,7 @@ DATE: today ===== Plans for week 38 ===== * Thursday: Summary of regression methods and discussion of project 1. Start Logistic Regression +* "Video of Lecture September 23":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h21/forelesningsvideoer/LectureSeptember23.mp4?vrtx=view-as-webpage" * Friday: Logistic Regression and Optimization methods @@ -553,7 +554,7 @@ the way we treat the intercept may give a larger or smaller MSE, meaning that the MSE can be penalized by the value of the intercept. Not including the intercept in the fit, means that the regularization term does not include $\beta_0$. For different values -of $\lambda$, this may lead to differeing MSE values. +of $\lambda$, this may lead to differeing MSE values. To remind the reader, the regularization term, with the intercept in Ridge regression is given by !bt @@ -575,6 +576,7 @@ For Lasso regression we have \] !et +It means that, when scaling the design matrix and the outputs/targets, by subtracting the mean values, we have an optimization problem which is not penalized by the intercept. The MSE value can then be smaller since it focuses only on the remaining quantities. If we however bring back the intercept, we will get a MSE which then contains the intercept. !split ===== Code Examples ===== @@ -743,10 +745,15 @@ plt.show() We see here, when compared to the code which includes explicitely the intercept column, that our MSE value is actually smaller. This is -because the regularization term does not include the intercept value $\beta_0$ in the -fitting. This applies to Lasso regularization as well. +because the regularization term does not include the intercept value +$\beta_0$ in the fitting. This applies to Lasso regularization as +well. It means that our optimization is now done only with the +centered matrix and/or vector that enter the fitting procedure. Note +also that the problem with the intercept occurs mainly in these type +of polynomial fitting problem. + +The next example is indeed an example where all these discussions about the role of intercept are not present. -If we stay with ordinary least squares, there is no dependence on the value of the intercept when we perform the fitting. !split ===== More complicated Example: The Ising model =====