From 14144f2728ca2822e349bda68ccaf0c27d81f83b Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Tue, 12 Sep 2023 16:19:03 +0200 Subject: [PATCH] small updates --- doc/src/week36/programs/franke.py | 8 +- doc/src/week36/programs/franketest.py | 64 ++++ .../week37/programs/codeexamplesscaling.ipynb | 275 ++++++++++-------- 3 files changed, 220 insertions(+), 127 deletions(-) create mode 100644 doc/src/week36/programs/franketest.py diff --git a/doc/src/week36/programs/franke.py b/doc/src/week36/programs/franke.py index 4044e773a..2e46cc3cc 100644 --- a/doc/src/week36/programs/franke.py +++ b/doc/src/week36/programs/franke.py @@ -1,3 +1,5 @@ + +# tod make plot import numpy as np import pandas as pd import matplotlib.pyplot as plt @@ -35,13 +37,13 @@ def create_X(x, y, n ): # Making meshgrid of datapoints and compute Franke's function -n = 5 -N = 1000 +n = 2 +N = 2 x = np.sort(np.random.uniform(0, 1, N)) y = np.sort(np.random.uniform(0, 1, N)) z = FrankeFunction(x, y) X = create_X(x, y, n=n) - +print(X) # We split the data in test and training data X_train, X_test, y_train, y_test = train_test_split(X, z, test_size=0.2) diff --git a/doc/src/week36/programs/franketest.py b/doc/src/week36/programs/franketest.py new file mode 100644 index 000000000..743b9c9b4 --- /dev/null +++ b/doc/src/week36/programs/franketest.py @@ -0,0 +1,64 @@ +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +from sklearn.model_selection import train_test_split +from sklearn import linear_model + + +def MSE(y_data,y_model): + n = np.size(y_model) + return np.sum((y_data-y_model)**2)/n + +def FrankeFunction(x,y): + term1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2)) + term2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1)) + term3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2)) + term4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2) + return term1 + term2 + term3 + term4 + + +def create_X(x, y, n ): + if len(x.shape) > 1: + x = np.ravel(x) + y = np.ravel(y) + + N = len(x) + l = int((n+1)*(n+2)/2) # Number of elements in beta + X = np.ones((N,l)) + + for i in range(1,n+1): + q = int((i)*(i+1)/2) + for k in range(i+1): + X[:,q+k] = (x**(i-k))*(y**k) + + return X + + +# Making meshgrid of datapoints and compute Franke's function +# fourth-order poly, intercept included above +n = 5 +N = 1000 +x = np.sort(np.random.uniform(0, 1, N)) +y = np.sort(np.random.uniform(0, 1, N)) +z = FrankeFunction(x, y) +X = create_X(x, y, n=n) + +# We split the data in test and training data +X_train, X_test, y_train, y_test = train_test_split(X, z, test_size=0.2) + +# matrix inversion to find beta, note no centering scaling and intercept column included +OLSbeta = np.linalg.pinv(X_train.T @ X_train) @ X_train.T @ y_train +print(OLSbeta) +# and then make the prediction +ytildeOLS = X_train @ OLSbeta +print("Training MSE for OLS") +print(MSE(y_train,ytildeOLS)) +ypredictOLS = X_test @ OLSbeta +print("Test MSE OLS") +print(MSE(y_test,ypredictOLS)) + + + + + + diff --git a/doc/src/week37/programs/codeexamplesscaling.ipynb b/doc/src/week37/programs/codeexamplesscaling.ipynb index 407aea948..5a7561123 100644 --- a/doc/src/week37/programs/codeexamplesscaling.ipynb +++ b/doc/src/week37/programs/codeexamplesscaling.ipynb @@ -3,9 +3,7 @@ { "cell_type": "markdown", "id": "11ec219f", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "\n", @@ -15,9 +13,7 @@ { "cell_type": "markdown", "id": "f5df87ed", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "# Scaling examples with own code and the library Scikit-Learn\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n", @@ -30,9 +26,7 @@ { "cell_type": "markdown", "id": "95d166ea", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## This note contains code examples with a simple scaling\n", "\n", @@ -55,13 +49,35 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "eef9ae09", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.79934087 0.47179152 5.01549939]\n", + "[1.79909592 0.47176716 5.01550546]\n", + " \n", + "test MSE of OLS:\n", + "1.13943111290393\n", + " \n", + "test MSE of Ridge\n", + "1.1395235273363686\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "%matplotlib inline\n", "\n", @@ -132,9 +148,7 @@ { "cell_type": "markdown", "id": "c368bb8d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "In this example we do not include the intercept and we scale the data by subtracting the mean values. This follows the discussion in the [lecture material](https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#more-on-rescaling-data).\n", "see also the weekly slides [for week 36](https://compphysics.github.io/MachineLearning/doc/pub/week36/html/._week36-bs029.html).\n", @@ -152,9 +166,7 @@ { "cell_type": "markdown", "id": "9ba5c048", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\beta_0, \\beta_1, ... , \\beta_{p-1}) = \\frac{1}{n}\\sum_{i=0}^{n} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij}\\beta_j\\right)^2,.\n", @@ -164,9 +176,7 @@ { "cell_type": "markdown", "id": "be61f447", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Recall also that we use the squared value. This expression can lead to an\n", "increased penalty for higher differences between predicted and\n", @@ -181,9 +191,7 @@ { "cell_type": "markdown", "id": "2efa5b58", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial C}{\\partial \\beta_j} = 0,\n", @@ -193,9 +201,7 @@ { "cell_type": "markdown", "id": "cd3b54c0", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "for all $j$. For $\\beta_0$ we have" ] @@ -203,9 +209,7 @@ { "cell_type": "markdown", "id": "1a141a26", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial C}{\\partial \\beta_0} = -\\frac{2}{n}\\sum_{i=0}^{n-1} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij} \\beta_j\\right).\n", @@ -215,9 +219,7 @@ { "cell_type": "markdown", "id": "5c2a9db1", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Multiplying away the constant $2/n$, we obtain" ] @@ -225,9 +227,7 @@ { "cell_type": "markdown", "id": "f279815d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\sum_{i=0}^{n-1} \\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} \\sum_{j=1}^{p-1} X_{ij} \\beta_j.\n", @@ -237,9 +237,7 @@ { "cell_type": "markdown", "id": "f77462b8", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Let us specialize first to the case where we have only two parameters $\\beta_0$ and $\\beta_1$.\n", "Our result for $\\beta_0$ simplifies then to" @@ -248,9 +246,7 @@ { "cell_type": "markdown", "id": "8ef3d129", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "n\\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} X_{i1} \\beta_1.\n", @@ -260,9 +256,7 @@ { "cell_type": "markdown", "id": "d7ca1b4a", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We obtain then" ] @@ -270,9 +264,7 @@ { "cell_type": "markdown", "id": "6859a8d9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\beta_1\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1}.\n", @@ -282,9 +274,7 @@ { "cell_type": "markdown", "id": "a018b414", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "If we define" ] @@ -292,9 +282,7 @@ { "cell_type": "markdown", "id": "9f3fd8e8", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mu_{\\boldsymbol{x}_1}=\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1},\n", @@ -304,9 +292,7 @@ { "cell_type": "markdown", "id": "df1038ff", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "and the mean value of the outputs as" ] @@ -314,9 +300,7 @@ { "cell_type": "markdown", "id": "c979cecf", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mu_y=\\frac{1}{n}\\sum_{i=0}^{n-1}y_i,\n", @@ -326,9 +310,7 @@ { "cell_type": "markdown", "id": "1380fd5d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "we have" ] @@ -336,9 +318,7 @@ { "cell_type": "markdown", "id": "40e7054e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\beta_0 = \\mu_y - \\beta_1\\mu_{\\boldsymbol{x}_1}.\n", @@ -348,9 +328,7 @@ { "cell_type": "markdown", "id": "f785b8c5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "In the general case with more parameters than $\\beta_0$ and $\\beta_1$, we have" ] @@ -358,9 +336,7 @@ { "cell_type": "markdown", "id": "1b94b3e7", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\frac{1}{n}\\sum_{i=0}^{n-1}\\sum_{j=1}^{p-1} X_{ij}\\beta_j.\n", @@ -370,9 +346,7 @@ { "cell_type": "markdown", "id": "1346bbb5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We can rewrite the latter equation as" ] @@ -380,9 +354,7 @@ { "cell_type": "markdown", "id": "044dc319", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\sum_{j=1}^{p-1} \\mu_{\\boldsymbol{x}_j}\\beta_j,\n", @@ -392,9 +364,7 @@ { "cell_type": "markdown", "id": "1ae565fb", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "where we have defined" ] @@ -402,9 +372,7 @@ { "cell_type": "markdown", "id": "2fe619e9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mu_{\\boldsymbol{x}_j}=\\frac{1}{n}\\sum_{i=0}^{n-1} X_{ij},\n", @@ -414,9 +382,7 @@ { "cell_type": "markdown", "id": "025a9267", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "the mean value for all elements of the column vector $\\boldsymbol{x}_j$.\n", "\n", @@ -426,9 +392,7 @@ { "cell_type": "markdown", "id": "22131558", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\boldsymbol{\\beta}) = (\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta})^T(\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta}).\n", @@ -438,9 +402,7 @@ { "cell_type": "markdown", "id": "ab3ab42d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "If we minimize with respect to $\\boldsymbol{\\beta}$ we have then" ] @@ -448,9 +410,7 @@ { "cell_type": "markdown", "id": "ca424c8e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X})^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}},\n", @@ -460,9 +420,7 @@ { "cell_type": "markdown", "id": "2367454f", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "where $\\boldsymbol{\\tilde{y}} = \\boldsymbol{y} - \\overline{\\boldsymbol{y}}$\n", "and $\\tilde{X}_{ij} = X_{ij} - \\frac{1}{n}\\sum_{k=0}^{n-1}X_{kj}$.\n", @@ -473,9 +431,7 @@ { "cell_type": "markdown", "id": "2cf181e1", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X} + \\lambda I)^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}}.\n", @@ -485,22 +441,44 @@ { "cell_type": "markdown", "id": "b20efe04", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Now we try to implement this." ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "id": "5b3cfc82", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.47179152 5.01549939]\n", + "[0.47176783 5.01542292]\n", + "1.7993408651198877\n", + "1.7995707762668065\n", + " \n", + "test MSE of OLS:\n", + "1.1394311129039245\n", + " \n", + "test MSE of Ridge\n", + "1.1395084586525954\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "np.random.seed(2018)\n", @@ -569,9 +547,7 @@ { "cell_type": "markdown", "id": "9f177d5f", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Finally, instead of using our own function we repeat the same example\n", "using the **standardscaler** functionality of the library\n", @@ -580,13 +556,37 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "id": "9130dfd9", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.47179152 5.01549939]\n", + "[0.47176783 5.01542292]\n", + "1.799340865119893\n", + "1.7995707762668047\n", + " \n", + "test MSE of OLS\n", + "1.1394311129039263\n", + " \n", + "test MSE of Ridge\n", + "1.1395084586525954\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from sklearn import linear_model\n", "np.random.seed(2018)\n", @@ -638,13 +638,40 @@ "print(MSE(y_test,ytilde_test_Ridge))\n", "plt.scatter(x,y,label='Data')\n", "plt.plot(x, X @ RegRidge.coef_ + RegRidge.intercept_ , label=\"Ridge_Fit\")\n", + "\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7e81070c", + "metadata": {}, + "outputs": [], + "source": [] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.10" + } + }, "nbformat": 4, "nbformat_minor": 5 }