diff --git a/doc/.DS_Store b/doc/.DS_Store
index 85cde44c2..402963403 100644
Binary files a/doc/.DS_Store and b/doc/.DS_Store differ
diff --git a/doc/pub/Regression/html/._Regression-bs000.html b/doc/pub/Regression/html/._Regression-bs000.html
index 1449392b9..180fe6505 100644
--- a/doc/pub/Regression/html/._Regression-bs000.html
+++ b/doc/pub/Regression/html/._Regression-bs000.html
@@ -425,7 +425,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Sep 13, 2019
+
Dec 18, 2019
diff --git a/doc/pub/Regression/html/._Regression-bs039.html b/doc/pub/Regression/html/._Regression-bs039.html
index 5b48f4fa7..bbe17bc0d 100644
--- a/doc/pub/Regression/html/._Regression-bs039.html
+++ b/doc/pub/Regression/html/._Regression-bs039.html
@@ -437,7 +437,7 @@ with \( t \) a finite positive number.
We see that Ridge regression is nothing but the standard
OLS with a modified diagonal term added to \( \boldsymbol{X}^T\boldsymbol{X} \). The
-consequences, in particular for our discussion of the bias-variance
+consequences, in particular for our discussion of the bias-variance tradeoff
are rather interesting.
diff --git a/doc/pub/Regression/html/._Regression-bs097.html b/doc/pub/Regression/html/._Regression-bs097.html
index 3f1148439..0aa28c1f5 100644
--- a/doc/pub/Regression/html/._Regression-bs097.html
+++ b/doc/pub/Regression/html/._Regression-bs097.html
@@ -437,6 +437,9 @@ sets. However, if a method has high variance then small changes in
the training data can result in large changes in the model. In general, more
flexible statistical methods have higher variance.
+
+You may also find this recent article of interest.
+
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Sep 13, 2019
+
Dec 18, 2019
@@ -1919,7 +1919,7 @@ with \( t \) a finite positive number.
We see that Ridge regression is nothing but the standard
OLS with a modified diagonal term added to \( \boldsymbol{X}^T\boldsymbol{X} \). The
-consequences, in particular for our discussion of the bias-variance
+consequences, in particular for our discussion of the bias-variance tradeoff
are rather interesting.
@@ -3928,6 +3928,9 @@ estimate for our model should not vary too much between training
sets. However, if a method has high variance then small changes in
the training data can result in large changes in the model. In general, more
flexible statistical methods have higher variance.
+
+
+You may also find this recent article of interest.
diff --git a/doc/pub/Regression/html/Regression-solarized.html b/doc/pub/Regression/html/Regression-solarized.html
index a89648175..b97502674 100644
--- a/doc/pub/Regression/html/Regression-solarized.html
+++ b/doc/pub/Regression/html/Regression-solarized.html
@@ -305,7 +305,7 @@ MathJax.Hub.Config({
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Sep 13, 2019
+
Dec 18, 2019
@@ -1946,7 +1946,7 @@ with \( t \) a finite positive number.
We see that Ridge regression is nothing but the standard
OLS with a modified diagonal term added to \( \boldsymbol{X}^T\boldsymbol{X} \). The
-consequences, in particular for our discussion of the bias-variance
+consequences, in particular for our discussion of the bias-variance tradeoff
are rather interesting.
@@ -3840,6 +3840,9 @@ sets. However, if a method has high variance then small changes in
the training data can result in large changes in the model. In general, more
flexible statistical methods have higher variance.
+
+You may also find this recent article of interest.
+
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
-
Sep 13, 2019
+
Dec 18, 2019
@@ -1951,7 +1951,7 @@ with \( t \) a finite positive number.
We see that Ridge regression is nothing but the standard
OLS with a modified diagonal term added to \( \boldsymbol{X}^T\boldsymbol{X} \). The
-consequences, in particular for our discussion of the bias-variance
+consequences, in particular for our discussion of the bias-variance tradeoff
are rather interesting.
@@ -3845,6 +3845,9 @@ sets. However, if a method has high variance then small changes in
the training data can result in large changes in the model. In general, more
flexible statistical methods have higher variance.
+
+You may also find this recent article of interest.
+
diff --git a/doc/pub/Regression/ipynb/Regression.ipynb b/doc/pub/Regression/ipynb/Regression.ipynb
index de49dad97..f95059065 100644
--- a/doc/pub/Regression/ipynb/Regression.ipynb
+++ b/doc/pub/Regression/ipynb/Regression.ipynb
@@ -10,7 +10,7 @@
" \n",
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
"\n",
- "Date: **Sep 13, 2019**\n",
+ "Date: **Dec 18, 2019**\n",
"\n",
"Copyright 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
"\n",
@@ -379,7 +379,9 @@
{
"cell_type": "code",
"execution_count": 1,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"%matplotlib inline\n",
@@ -884,7 +886,9 @@
{
"cell_type": "code",
"execution_count": 2,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"# matrix inversion to find beta\n",
@@ -903,7 +907,9 @@
{
"cell_type": "code",
"execution_count": 3,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"fit = np.linalg.lstsq(X, Energies, rcond =None)[0]\n",
@@ -920,7 +926,9 @@
{
"cell_type": "code",
"execution_count": 4,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"Masses['Eapprox'] = ytilde\n",
@@ -950,7 +958,9 @@
{
"cell_type": "code",
"execution_count": 5,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"def R2(y_data, y_model):\n",
@@ -967,7 +977,9 @@
{
"cell_type": "code",
"execution_count": 6,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"print(R2(Energies,ytilde))"
@@ -983,7 +995,9 @@
{
"cell_type": "code",
"execution_count": 7,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"def MSE(y_data,y_model):\n",
@@ -1003,7 +1017,9 @@
{
"cell_type": "code",
"execution_count": 8,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"def RelativeError(y_data,y_model):\n",
@@ -1380,7 +1396,9 @@
{
"cell_type": "code",
"execution_count": 9,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"# Common imports\n",
@@ -1499,7 +1517,9 @@
{
"cell_type": "code",
"execution_count": 10,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import os\n",
@@ -1615,19 +1635,11 @@
},
{
"cell_type": "code",
- "execution_count": 1,
- "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"
- ]
- }
- ],
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt \n",
@@ -1645,20 +1657,11 @@
},
{
"cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])"
- ]
- },
- "execution_count": 2,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"from sklearn.datasets import load_boston\n",
"\n",
@@ -1678,8 +1681,10 @@
},
{
"cell_type": "code",
- "execution_count": 3,
- "metadata": {},
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names)\n",
@@ -1696,34 +1701,11 @@
},
{
"cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "CRIM 0\n",
- "ZN 0\n",
- "INDUS 0\n",
- "CHAS 0\n",
- "NOX 0\n",
- "RM 0\n",
- "AGE 0\n",
- "DIS 0\n",
- "RAD 0\n",
- "TAX 0\n",
- "PTRATIO 0\n",
- "B 0\n",
- "LSTAT 0\n",
- "MEDV 0\n",
- "dtype: int64"
- ]
- },
- "execution_count": 4,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"# check for missing values in all the columns\n",
"boston.isnull().sum()"
@@ -1738,20 +1720,11 @@
},
{
"cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"# set the size of the figure\n",
"sns.set(rc={'figure.figsize':(11.7,8.27)})\n",
@@ -1770,30 +1743,11 @@
},
{
"cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- ""
- ]
- },
- "execution_count": 6,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"# compute the pair wise correlation for all columns \n",
"correlation_matrix = boston.corr().round(2)\n",
@@ -1811,20 +1765,11 @@
},
{
"cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"plt.figure(figsize=(20, 5))\n",
"\n",
@@ -1850,8 +1795,10 @@
},
{
"cell_type": "code",
- "execution_count": 8,
- "metadata": {},
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"X = pd.DataFrame(np.c_[boston['LSTAT'], boston['RM']], columns = ['LSTAT','RM'])\n",
@@ -1867,20 +1814,11 @@
},
{
"cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "(404, 2)\n",
- "(102, 2)\n",
- "(404,)\n",
- "(102,)\n"
- ]
- }
- ],
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"from sklearn.model_selection import train_test_split\n",
"\n",
@@ -1902,26 +1840,11 @@
},
{
"cell_type": "code",
- "execution_count": 10,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "The model performance for training set\n",
- "--------------------------------------\n",
- "RMSE is 5.6371293350711955\n",
- "R2 score is 0.6300745149331701\n",
- "\n",
- "\n",
- "The model performance for testing set\n",
- "--------------------------------------\n",
- "RMSE is 5.137400784702911\n",
- "R2 score is 0.6628996975186953\n"
- ]
- }
- ],
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"from sklearn.linear_model import LinearRegression\n",
"from sklearn.metrics import mean_squared_error, r2_score\n",
@@ -1958,20 +1881,11 @@
},
{
"cell_type": "code",
- "execution_count": 11,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"# plotting the y_test vs y_pred\n",
"# ideally should have been a straight line\n",
@@ -2602,7 +2516,7 @@
"\n",
"We see that Ridge regression is nothing but the standard\n",
"OLS with a modified diagonal term added to $\\boldsymbol{X}^T\\boldsymbol{X}$. The\n",
- "consequences, in particular for our discussion of the bias-variance\n",
+ "consequences, in particular for our discussion of the bias-variance tradeoff \n",
"are rather interesting.\n",
"\n",
"Furthermore, if we use the result above in terms of the SVD decomposition (our analysis was done for the OLS method), we had"
@@ -2749,7 +2663,9 @@
{
"cell_type": "code",
"execution_count": 22,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -3337,7 +3253,9 @@
{
"cell_type": "code",
"execution_count": 23,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"# Importing various packages\n",
@@ -3360,7 +3278,9 @@
{
"cell_type": "code",
"execution_count": 24,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -4523,7 +4443,9 @@
{
"cell_type": "code",
"execution_count": 25,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"from numpy import *\n",
@@ -4663,37 +4585,11 @@
},
{
"cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "Runtime: 2.03806 sec\n",
- "Bootstrap Statistics :\n",
- "original bias std. error\n",
- " 99.7977 14.8857 99.7961 0.148807\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"
- }
- ],
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
"source": [
"from numpy import *\n",
"from numpy.random import randint, randn\n",
@@ -4838,7 +4734,9 @@
{
"cell_type": "code",
"execution_count": 27,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -5067,7 +4965,9 @@
{
"cell_type": "code",
"execution_count": 28,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
@@ -5136,7 +5036,9 @@
{
"cell_type": "code",
"execution_count": 29,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
@@ -5227,13 +5129,17 @@
"flexible statistical methods have higher variance.\n",
"\n",
"\n",
+ "You may also find this recent [article](https://www.pnas.org/content/116/32/15849) of interest.\n",
+ "\n",
"## Another Example from Scikit-Learn's Repository"
]
},
{
"cell_type": "code",
"execution_count": 30,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"\"\"\"\n",
@@ -5319,7 +5225,9 @@
{
"cell_type": "code",
"execution_count": 31,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"# Common imports\n",
@@ -5413,7 +5321,9 @@
{
"cell_type": "code",
"execution_count": 32,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"# Common imports\n",
@@ -5495,7 +5405,9 @@
{
"cell_type": "code",
"execution_count": 33,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -5576,7 +5488,9 @@
{
"cell_type": "code",
"execution_count": 34,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -5689,7 +5603,9 @@
{
"cell_type": "code",
"execution_count": 35,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"X = np.zeros((n, L ** 2))\n",
@@ -5753,7 +5669,9 @@
{
"cell_type": "code",
"execution_count": 36,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"X_train_own = np.concatenate(\n",
@@ -5769,7 +5687,9 @@
{
"cell_type": "code",
"execution_count": 37,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"def ols_inv(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
@@ -5854,7 +5774,9 @@
{
"cell_type": "code",
"execution_count": 38,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"def ols_svd(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
@@ -5865,7 +5787,9 @@
{
"cell_type": "code",
"execution_count": 39,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"beta = ols_svd(X_train_own,y_train)"
@@ -5881,7 +5805,9 @@
{
"cell_type": "code",
"execution_count": 40,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"J = beta[1:].reshape(L, L)"
@@ -5897,7 +5823,9 @@
{
"cell_type": "code",
"execution_count": 41,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"fig = plt.figure(figsize=(20, 14))\n",
@@ -5963,7 +5891,9 @@
{
"cell_type": "code",
"execution_count": 42,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"import numpy as np\n",
@@ -6069,7 +5999,9 @@
{
"cell_type": "code",
"execution_count": 43,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"X = np.zeros((n, L ** 2))\n",
@@ -6099,7 +6031,9 @@
{
"cell_type": "code",
"execution_count": 44,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"clf = skl.LinearRegression().fit(X_train, y_train)"
@@ -6115,7 +6049,9 @@
{
"cell_type": "code",
"execution_count": 45,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"J_sk = clf.coef_.reshape(L, L)"
@@ -6131,7 +6067,9 @@
{
"cell_type": "code",
"execution_count": 46,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"fig = plt.figure(figsize=(20, 14))\n",
@@ -6187,7 +6125,9 @@
{
"cell_type": "code",
"execution_count": 47,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"_lambda = 0.1\n",
@@ -6238,7 +6178,9 @@
{
"cell_type": "code",
"execution_count": 48,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n",
@@ -6272,7 +6214,9 @@
{
"cell_type": "code",
"execution_count": 49,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"lambdas = np.logspace(-4, 5, 10)\n",
@@ -6335,7 +6279,9 @@
{
"cell_type": "code",
"execution_count": 50,
- "metadata": {},
+ "metadata": {
+ "collapsed": false
+ },
"outputs": [],
"source": [
"fig = plt.figure(figsize=(20, 14))\n",
@@ -6380,25 +6326,7 @@
]
}
],
- "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": "3.7.4"
- }
- },
+ "metadata": {},
"nbformat": 4,
"nbformat_minor": 2
}
diff --git a/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz b/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz
index b57d74aad..384441a8e 100644
Binary files a/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz and b/doc/pub/Regression/ipynb/ipynb-Regression-src.tar.gz differ
diff --git a/doc/pub/Regression/pdf/Regression-minted.pdf b/doc/pub/Regression/pdf/Regression-minted.pdf
index 9ee6ecba2..33c8acacb 100644
Binary files a/doc/pub/Regression/pdf/Regression-minted.pdf and b/doc/pub/Regression/pdf/Regression-minted.pdf differ
diff --git a/doc/src/Regression/Regression.do.txt b/doc/src/Regression/Regression.do.txt
index f3517e5fa..357bc9a4f 100644
--- a/doc/src/Regression/Regression.do.txt
+++ b/doc/src/Regression/Regression.do.txt
@@ -1493,7 +1493,7 @@ with $t$ a finite positive number.
We see that Ridge regression is nothing but the standard
OLS with a modified diagonal term added to $\bm{X}^T\bm{X}$. The
-consequences, in particular for our discussion of the bias-variance
+consequences, in particular for our discussion of the bias-variance tradeoff
are rather interesting.
Furthermore, if we use the result above in terms of the SVD decomposition (our analysis was done for the OLS method), we had
@@ -3191,6 +3191,8 @@ the training data can result in large changes in the model. In general, more
flexible statistical methods have higher variance.
+You may also find this recent "article":"https://www.pnas.org/content/116/32/15849" of interest.
+
!split
===== Another Example from Scikit-Learn's Repository =====
!bc pycod
diff --git a/doc/src/Regression/lasso.tex b/doc/src/Regression/lasso.tex
deleted file mode 100644
index b50a098c2..000000000
--- a/doc/src/Regression/lasso.tex
+++ /dev/null
@@ -1,882 +0,0 @@
-\documentclass[11pt,british,a4paper]{article}
-%\pdfobjcompresslevel=0
-\usepackage[usenames,dvipsnames]{xcolor}
-\usepackage[includeheadfoot,margin=0.8 in]{geometry}
-\usepackage{siunitx,physics,cancel,upgreek,varioref,listings,booktabs,pdfpages,ifthen,polynom,todonotes}
-%\usepackage{minted}
-\usepackage[backend=biber]{biblatex}
-\DefineBibliographyStrings{english}{%
- bibliography = {References},
-}
-\addbibresource{sources.bib}
-\usepackage{mathtools,upgreek,bigints}
-\usepackage{babel}
-\usepackage{graphicx}
-\usepackage{float}
-\usepackage{amsmath}
-\usepackage{amssymb}
-\usepackage{tocloft}
-\usepackage[T1]{fontenc}
-%\usepackage{fouriernc}
-% \usepackage[T1]{fontenc}
-\usepackage{mathpazo}
-% \usepackage{inconsolata}
-%\usepackage{eulervm}
-%\usepackage{cmbright}
-%\usepackage{fontspec}
-%\usepackage{unicode-math}
-%\setmainfont{Tex Gyre Pagella}
-%\setmathfont{Tex Gyre Pagella Math}
-%\setmonofont{Tex Gyre Cursor}
-%\renewcommand*\ttdefault{txtt}
-\graphicspath{{figs/}}
-\usepackage[scaled]{beramono}
-\usepackage{fancyhdr}
-\usepackage[utf8]{inputenc}
-\usepackage{textcomp}
-\usepackage{lastpage}
-\usepackage{microtype}
-\usepackage[font=normalsize]{subcaption}
-\usepackage{luacode}
-\usepackage[linktoc=all, bookmarks=true, pdfauthor={Anders Johansson},pdftitle={FYS-STK4155 Project 1}]{hyperref}
-\usepackage{tikz,pgfplots,pgfplotstable}
-\usepgfplotslibrary{colorbrewer}
-\usepgfplotslibrary{external}
-\tikzset{external/system call={lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"}}
-\tikzexternalize%[prefix=tmp/, mode=list and make]
-\pgfplotsset{cycle list/Dark2}
-\pgfplotsset{compat=1.8}
-\renewcommand{\CancelColor}{\color{red}}
-\let\oldexp=\exp
-\renewcommand{\exp}[1]{\mathrm{e}^{#1}}
-
-
-\labelformat{section}{#1}
-\labelformat{subsection}{exercise~#1}
-\labelformat{subsubsection}{paragraph~#1}
-\labelformat{equation}{equation~(#1)}
-\labelformat{figure}{figure~#1}
-\labelformat{table}{table~#1}
-
-\renewcommand{\footrulewidth}{\headrulewidth}
-
-%\setcounter{secnumdepth}{4}
-\setlength{\parindent}{0cm}
-\setlength{\parskip}{1em}
-
-\definecolor{bluekeywords}{rgb}{0.13,0.13,1}
-\definecolor{greencomments}{rgb}{0,0.5,0}
-\definecolor{redstrings}{rgb}{0.9,0,0}
-\lstset{rangeprefix=!/,
- rangesuffix=/!,
- includerangemarker=false}
-\lstset{showstringspaces=false,
- basicstyle=\small\ttfamily,
- keywordstyle=\color{bluekeywords},
- commentstyle=\color{greencomments},
- numberstyle=\color{bluekeywords},
- stringstyle=\color{redstrings},
- breaklines=true,
- %texcl=true,
- language=Fortran,
- morekeywords={norm2,class,deferred}
-}
-\colorlet{DarkGrey}{white!20!black}
-\newcommand{\eqtag}[1]{\refstepcounter{equation}\tag{\theequation}\label{#1}}
-\hypersetup{hidelinks=True}
-
-\sisetup{detect-all}
-\sisetup{exponent-product = \cdot, output-product = \cdot,per-mode=symbol}
-% \sisetup{output-decimal-marker={,}}
-\sisetup{round-mode = off, round-precision=3}
-\sisetup{number-unit-product = \ }
-
-\allowdisplaybreaks[4]
-\fancyhf{}
-
-\rhead{Project 1}
-\rfoot{Page~\thepage{} of~\pageref{LastPage}}
-\lhead{FYS-STK4155}
-
-%\definecolor{gronn}{rgb}{0.29, 0.33, 0.13}
-\definecolor{gronn}{rgb}{0, 0.5, 0}
-
-\newcommand{\husk}[2]{\tikz[baseline,remember picture,inner sep=0pt,outer sep=0pt]{\node[anchor=base] (#1) {\(#2\)};}}
-\newcommand{\artanh}[1]{\operatorname{artanh}{\qty(#1)}}
-\newcommand{\matrise}[1]{\begin{pmatrix}#1\end{pmatrix}}
-\DeclareMathOperator{\Proj}{Proj}
-\DeclareMathOperator{\Col}{Col}
-\DeclareMathOperator{\sgn}{sgn}
-\DeclareMathOperator{\MSE}{MSE}
-
-\newread\infile
-
-\setcounter{tocdepth}{2}
-\numberwithin{equation}{section}
-
-\usepackage{tikz-uml}
-
-\pgfplotstableset{
- every head row/.style={before row=\toprule,after row=\midrule},
- every last row/.style={after row=\bottomrule},
- columns/Method/.style={string type, column type=l}
-}
-
-%start
-\begin{document}
-\title{FYS-STK4155: Project 1}
-\author{Anders Johansson}
-%\maketitle
-
-\begin{titlepage}
-%\includegraphics[width=\textwidth]{fysisk.pdf}
-\vspace*{\fill}
-\begin{center}
-\textsf{
- \Huge \textbf{Project 1}\\\vspace{0.5cm}
- \Large \textbf{FYS-STK4155 --- Applied data analysis and machine learning}\\
- \vspace{2cm}
- \includegraphics[width=0.45\textwidth]{figs/geography.pdf}%
- \includegraphics[width=0.45\textwidth]{figs/geography_approx.pdf}\\
- \vspace{2cm}
- Anders Johansson\\
- \today\\
-}
-\vspace{1.5cm}
-\includegraphics{uio.pdf}\\
-\vspace*{\fill}
-\end{center}
-\end{titlepage}
-\null
-\pagestyle{empty}
-\newpage
-
-\pagestyle{fancy}
-\setcounter{page}{1}
-
-\begin{abstract}
- This project uses fitting of Franke's function and geographical data to compare ordinary least squares, Ridge and LASSO regression. Resampling is done in order to get accurate estimates for variances and means. A bias-variance decomposition is derived analytically and confirmed numerically for both artificial and geographical data. The regression methods are implemented from scratch in Fortran and show good performance, although Newton's method proves to be suboptimal as a minimisation method for the LASSO cost function, due to its non-differentiability in its minimum for large values of the regularisation parameter. Ridge and LASSO regression are found to outperform ordinary least squares on test data, in particular on the geographical data where ordinary least squares suffers from severe overfitting for polynomial degrees larger than \(10\).
-\end{abstract}
-
-All files for this project are available at \url{https://github.com/anjohan/ml1}.
-
-\tableofcontents
-\clearpage
-% _ _
-% (_)_ __ | |_ _ __ ___
-% | | '_ \| __| '__/ _ \
-% | | | | | |_| | | (_) |
-% |_|_| |_|\__|_| \___/
-\section{Introduction}
-Fitting of data is an important tool in most sciences.
-The goal can be to interpolate between already measured data or predict values outside the measured range when extra experiments are infeasible, or to discover relations between quantities.
-By assuming that the data points can be modelled by a linear combination of some set of functions and minimising the error, one ends up with linear regression.
-This report explores three different linear regression methods --- ordinary least squares, which simply minimises the error, and Ridge and LASSO, which make up for their worse performance on training data by returning better predictors.
-
-The main goal of this project is to compare these three regression methods empirically by applying it to two sets of data.
-First, the regression methods are applied to a data set generated from a known function, specifically the Franke's function, which is a sum of bivariate Gaussian functions.
-Having verified the implementation of the methods, they are then applied to geographic data, namely the altitude as a function of geographic coordinates.
-
-The first part of this report goes through the basic theory of these regression methods and their implementation, as well as resampling techniques and the bias-variance decomposition.
-Then, the regression methods are applied to the Franke's function and the results are analysed with resampling. Finally, geographical data is fitted and the methods are compared over a range of polynomial degrees and regularisation parameters.
-
-% _ _
-% | |_| |__ ___ ___ _ __ _ _
-% | __| '_ \ / _ \/ _ \| '__| | | |
-% | |_| | | | __/ (_) | | | |_| |
-% \__|_| |_|\___|\___/|_| \__, |
-% |___/
-\section{Theory and methods}
-
-\subsection{Test case}
-The function to be fitted as verification of the regression methods is the famous Franke's function \(f:\qty[0,1]^2\to\mathbb{R}\) given by
-\begin{equation}
- \begin{alignedat}{2}
- f(x_1,x_2) &= \frac{3}{4}\oldexp(-\frac{(9x_1-2)^2}{4} - \frac{(9x_2-2)^2}{4})
- + \frac{3}{4}\oldexp(-\frac{(9x_1+1)^2}{49}- \frac{(9x_2+1)}{10} ) \\
- &+ \frac{1}{2}\oldexp(-\frac{(9x_1-7)^2}{4} - \frac{(9x_2-3)^2}{4})
- - \frac{1}{5}\oldexp(-(9x_1-4)^2 - (9x_2-7)^2)
- \end{alignedat}\label{eq:franke}
-\end{equation}
-and shown in~\vref{fig:franke}.
-
-\begin{figure}[H]
- \centering
- \includegraphics{franke.pdf}
- \caption{The Franke's function to be fitted, given by~\vref{eq:franke}.}\label{fig:franke}
-\end{figure}
-
-\subsection{Fitting problem statement}
-The general problem is to fit a given set of data \(D=\qty{(\vec{x}_i,y_i)}_{i=1}^N\), where \(\vec{x}_i\) are inputs of some dimensionality (\(2\) in this project) and \(y_i\) are scalar outputs.
-A set of basis functions \(\qty{\phi_j}_{j=1}^p\) is chosen, and the goal is to approximate the input data with the linear combination \(\beta_j \phi_j(\vec{x})\).
-If the data set were generated by such a linear combination, there would exist parameters \(\qty{\beta_j}\) such that \(\beta_j\phi_j(\vec{x}_i)=y_i\), which can be rewritten as the matrix equation
-\begin{equation}
- X\vec{\beta} = \vec{y},
-\end{equation}
-where \(X\in\mathbb{R}^{N\times p}\) is the matrix with elements \(x_{ij}=\phi_j(\vec{x}_i)\), and \(\vec{\beta}\) and \(\vec{y}\) are the vectors with elements \(\beta_j\) and \(y_i\).
-
-In general, it will not be possible to find parameters \(\beta_j\) which fulfill this, since the data set will not be generated from the simple basis functions.
-Consequently, one must find the \(\beta_j\)s which in some sense make \(X\vec{\beta}\) as close to \(\vec{y}\) as possible.
-The way in which to measure deviation from the perfect solution is called the \emph{cost function}, frequently written \(Q(\vec{\beta};D)\).
-Regression methods differ in the choice of cost function, while their aim is always to find the parameters \(\beta_j\) which minimise the cost function.
-
-When a regression method has been used to find \(\vec{\beta}\), predicted values are denoted \(\tilde{y}_i = X_{ij}\beta_j\), while the original, exact values are denoted \(y_i\).
-
-% _ _ _ _
-% ___ _ __ __| (_)_ __ __ _ _ __ _ _ | | ___ __ _ ___| |_
-% / _ \| '__/ _` | | '_ \ / _` | '__| | | | | |/ _ \/ _` / __| __|
-% | (_) | | | (_| | | | | | (_| | | | |_| | | | __/ (_| \__ \ |_
-% \___/|_| \__,_|_|_| |_|\__,_|_| \__, | |_|\___|\__,_|___/\__|
-% ___ __ _ _ _ __ _ _ __ ___ ___|___/
-% / __|/ _` | | | |/ _` | '__/ _ \/ __|
-% \__ \ (_| | |_| | (_| | | | __/\__ \
-% |___/\__, |\__,_|\__,_|_| \___||___/
-% |_|
-\subsection{Ordinary Least Squares}
-The ordinary least squares method is the simplest and most intuitive, since its cost function is simply the square of the error made by the fit,
-\begin{equation}
- Q(\beta;D) = \norm{\vec{y}-X\vec{\beta}}_2^2,
-\end{equation}
-where \(\norm{\cdot}_p\) denotes the usual \(p\)-norm.
-
-\subsubsection{Geometric view}
-The geometric view of the equation \(X\vec{\beta}=\vec{y}\) is to find the linear combination of the columns of \(X\) equal to \(\vec{y}\).
-This is not necessarily possible if the columns of \(X\) do not span \(\mathbb{R}^N\), which is not possible if \(p 0\\ 0, & x = 0 \\ -1, & x < 0 \end{cases}
-\end{equation}
-and proceed happily.
-
-The gradient of the cost function is thus
-\begin{equation}
- \nabla Q_\lambda = -2 X^T \qty(\vec{y} - X\vec{\beta}) + \lambda \sgn\qty(\vec{\beta}),
-\end{equation}
-and \(\nabla Q_\lambda = \vec{0}\) does unfortunately not have a closed-form solution.
-A separate minimisation algorithm must therefore be used to find the parameters \(\beta_j\) which minimise the cost function.
-The calculated gradient can be put straight into the gradient descent algorithm with a suitable step length.
-Alternatively, Newton's method can be used with the second derivative (Hessian) matrix of the cost function.
-The second derivative of the absolute value is even more problematic, which is solved by setting it equal to zero.
-
-The Hessian matrix of the LASSO cost function is thus the same as the second derivative of the ordinary least squares cost function,
-\begin{equation}
- H_{kl} = H_{lk} = \pdv{Q_\lambda}{\beta_l}{\beta_k}
- = \pdv{\beta_l}(\nabla_k Q)
- \,\husk{gradref}{=}\, \pdv{\beta_l}(-2X_{ik}\qty(y_i-X_{ij}\beta_j))
- = 2X_{ik}X_{il},
-\tikz[>=latex,overlay,remember picture,thick]{\draw[<-,gronn] (gradref) .. controls ++(0,0.75) and ++(-1,0) .. ++(1,0.75) node[anchor=west] {\small\ref{eq:olsgradcomp}};}
-\end{equation}
-which is the component form of the matrix equation
-\begin{equation}
- H = 2 X^T X.
-\end{equation}
-The gradient can now be rewritten as
-\begin{equation}
- \nabla Q_\lambda = -2 X^T \vec{y} + H\vec{\beta} + \lambda \sgn\qty(\vec{\beta}).
-\end{equation}
-\Vref*{eq:newtonstep} in Newton's method can then transformed into
-\begin{equation}
- H\qty(\vec{\beta}_{i+1} - \vec{\beta}_i) = 2X^T \vec{y} - H\vec{\beta}_i - \lambda \sgn\qty(\vec{\beta}_i)
- \implies H\vec{\beta}_{i+1} = 2X^T\vec{y} - \lambda \sgn\qty(\vec{\beta}_i). \label{eq:lassonewton}
-\end{equation}
-Since \(H=2X^T X\), this reduces to the normal equations of ordinary least squares (\vref*{eq:olsnormal}) in the case of \(\lambda=0\), as it should.
-
-Minimisation of the LASSO cost function has the benefit that the second derivative is independent of \(\vec{\beta}\).
-\(H\) can therefore be Cholesky-decomposed once, an \(\mathcal{O}\qty(p^3)\) operation, and the result can be used to solve the linear set of equations for each iteration, which is \(\mathcal{O}\qty(p^2)\) with a pre-Cholesky-decomposed matrix.
-The Cholesky-decomposition can be used instead of an LU-decomposition, reducing the number of floating point operations by a factor of two, because \(H=2X^T X\) is positive definite when \(X\) is non-singular.
-
-Evaluation of the gradient only involves matrix-vector products, which is also an \(\mathcal{O}\qty(p^2)\) operation.
-The minimisation can, therefore, be done with one initial \(\mathcal{O}\qty(p^3)\) and then only \(\mathcal{O}\qty(p^2)\) operations per iteration, while the more general problem requires both the construction and the Cholesky-decomposition of \(H\), an \(\mathcal{O}\qty(p^3)\) operation, for every single iteration.
-
-LASSO regression has been implemented by calculating the Cholesky-decomposition of \(H\) using \lstinline{dpptrf}, guessing \(\beta_j=1\) and then repeatedly solving~\vref{eq:lassonewton} using \lstinline{dpptrs} until convergence, as illustrated by the following snippet.
-\lstinputlisting[linerange={lassostart-lassoend}]{lib/lasso.f90}
-
-This implementation gives both good performance and accurate results for small values of \(\lambda\).
-Larger values, however, give rise to issues.
-The theory suggests that a large \(\lambda\) should force some of the parameters \(\beta_j\) to become zero, but the cost function is not differentiable, and certainly not double differentiable, when \(\beta_j\) is zero.
-Consequently, Newton's method struggles to converge when some \(\beta_j\)s are zero in the true minimum of the LASSO cost function.
-Smarter methods such as coordinate descent\cite{friedman} should therefore be used, as in e.g.\ scikit-learn.
-
-
-% _ _ _ _ _
-% _ __ ___ (_)_ __ (_)_ __ ___ (_)___ __ _| |_(_) ___ _ __
-%| '_ ` _ \| | '_ \| | '_ ` _ \| / __|/ _` | __| |/ _ \| '_ \
-%| | | | | | | | | | | | | | | | \__ \ (_| | |_| | (_) | | | |
-%|_| |_| |_|_|_| |_|_|_| |_| |_|_|___/\__,_|\__|_|\___/|_| |_|
-\subsection{Minimisation methods}
-The important step in a regression method, or indeed in any statistical learning method, is to minimise the cost function.
-Certain cost functions, such as those of ordinary least squares and Ridge regression, admit analytical closed-form solutions for the parameters \(\beta_j\) which minimise \(Q(\vec{\beta};D)\), while most methods, including LASSO regression and logistic regression, require usage of some general minimisation algorithm.
-
-\subsubsection{Newton's method}\label{subsubsec:newton}
-Since the gradient of the cost function, \(\nabla Q\), is a perfectly normal function from \(\mathbb{R}^p\) to \(\mathbb{R}^p\), it can be Taylor expanded around some point \(\vec{\beta}_0\).
-This Taylor expansion can then be evaluated at a point \(\vec{\beta}_0 + \delta\vec{\beta}\). To first order in \(\delta\vec{\beta}\),
-\begin{equation}
- \nabla Q\qty(\vec{\beta}_0 + \delta\vec{\beta}) = \nabla Q\qty(\vec{\beta}_0) + H\qty(\vec{\beta}_0)\delta\vec{\beta},
-\end{equation}
-where \(H(\vec{\beta}_0)\) is the derivative of \(\nabla Q\), i.e.\ the Hessian of \(Q\), evaluated at \(\beta_0\).
-Given a guess \(\beta_0\) somewhere near the minimum of \(Q\), a better estimate can be found by solving for the \(\delta\vec{\beta}\) which makes \(\nabla Q(\vec{\beta}_0 + \delta\vec{\beta}) = \vec{0}\), i.e.
-\begin{equation}
- H\qty(\vec{\beta}_0)\delta\vec{\beta} = -\nabla Q\qty(\vec{\beta}_0),
-\end{equation}
-and, in general, solving
-\begin{equation}
- H\qty(\vec{\beta}_i)\delta\vec{\beta}_i = -\nabla Q\qty(\vec{\beta}_i),\label{eq:newtonstep}
-\end{equation}
-letting \(\vec{\beta}_{i+1} = \vec{\beta}_i + \delta\vec{\beta}_i\) and continuing the process until the method has converged sufficiently.
-The above equation is a simple linear set of equations.
-
-
-\subsubsection{Gradient descent}
-Evaluating the Hessian matrix and inverting it can sometimes be infeasible, for example due to poor time complexity or being woefully undefined.
-In such cases, one can replace the Hessian \(H\) with a number \(1/\alpha\).
-\Vref{eq:newtonstep} is then rewritten as
-\begin{equation}
- \vec{\beta}_{i+1} = \vec{\beta_i} - \alpha \nabla Q\qty(\vec{\beta}_i),
-\end{equation}
-with a simple geometric interpretation:
-By going a small step in the opposite direction of the gradient, the value of the cost function will decrease and \(\vec{\beta}\) will approach the true minimum.
-A small step will guarantee convergence for a convex function at the cost of slow convergence, while a larger value may give faster convergence or not converge at all.
-
-% __
-% _ __ ___ _ __ / _| ___ _ __ _ __ ___ __ _ _ __ ___ ___
-% | '_ \ / _ \ '__| |_ / _ \| '__| '_ ` _ \ / _` | '_ \ / __/ _ \
-% | |_) | __/ | | _| (_) | | | | | | | | (_| | | | | (_| __/
-% | .__/ \___|_| |_| \___/|_| |_| |_| |_|\__,_|_| |_|\___\___|
-% |_|
-\subsection{Performance of regression methods}
-While the cost function is minimised by all regression methods, its value is not particularly meaningful.
-In particular, the cost functions in Ridge and LASSO regression depend on the parameter \(\lambda\), and a measure independent of \(\lambda\) should be used to determine the optimal \(\lambda\).
-Other functions are therefore introduced to measure the performance of a given regression method and/or a choice of parameters.
-
-The simplest measure is the mean square error,
-\begin{equation}
- \MSE\qty(\vec{\beta},D) = \frac{1}{N}\norm{\vec{y}-\vec{\tilde{y}}}_2^2 = \frac{1}{N} \sum_{i=1}^N \qty(y_i - \tilde{y}_i)^2,
-\end{equation}
-which should be as small as possible. Another measure is the \(R^2\) score, defined as
-\begin{equation}
- R^2(\vec{\beta},D) = 1 - \frac{\norm{\vec{y} - \vec{\tilde{y}}}_2^2}{\norm{\vec{y} - \bar{y}}_2^2}
- = 1 - \frac{\sum_{i=1}^N \qty(y_i - \tilde{y}_i)^2}{\sum_{i=1}^N \qty(y_i - \bar{y})^2},
-\end{equation}
-where \(\bar{y}\) is the mean of the measured values. The \(R^2\) score should be as close to \(1\) as possible.
-
-Prediction and these measures of performance can be applied to two main types of data.
-Firstly, it can be applied to the data from which \(\vec{\beta}\) was derived, which is called the training data.
-Ordinary least squares, corresponding to \(\lambda=0\) for the other methods, will, by definition, give the best results for this data set.
-Secondly, the performance can be measured for values not among the training data, called test data. Ridge and LASSO are expected to outperform ordinary least squares for small, non-zero values of \(\lambda\) for this category of data.
-
-% _ _
-% _ __ ___ ___ __ _ _ __ ___ _ __ | (_)_ __ __ _
-% | '__/ _ \/ __|/ _` | '_ ` _ \| '_ \| | | '_ \ / _` |
-% | | | __/\__ \ (_| | | | | | | |_) | | | | | | (_| |
-% |_| \___||___/\__,_|_| |_| |_| .__/|_|_|_| |_|\__, |
-% |_| |___/
-\subsection{Resampling methods}
-Resampling methods are techniques to improve the prediction accuracy and obtain estimates for quantities such as the variance of \(\vec{\beta}\) by repeatedly dividing the data set into training and test data.
-Two simple examples are \(k\)-fold cross-validation and bootstrapping.
-The former partitions the data set into \(k\) partitions.
-One of these subsets is chosen as test data on which the performance is measured, while the rest are used as training data.
-This process is the repeated \(k\) times, so that each subset is used once as test data.
-Bootstrapping, on the other hand, repeatedly creates training data sets by randomly selecting \(N\) values from the data set with replacement, while another, separate data set is used as test data each time, as illustrated by the snippet below.
-\lstinputlisting[linerange={bootstrapstart-bootstrapend}]{lib/bootstrap.f90}
-
-% _ _ _
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-% | '_ \| |/ _` / __| / _` | '_ \ / _` |
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-% __ ____ _ _ __(_) __ _ _ __ ___ ___
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-% \ V / (_| | | | | (_| | | | | (_| __/
-% \_/ \__,_|_| |_|\__,_|_| |_|\___\___|
-\subsection{Bias and variance}
-The choice of the number of basis functions, \(p\), determines the complexity of the model to which the data set is fitted.
-A higher complexity makes the model a better approximation to the training data, which is said to reduce the \emph{bias} of the model.
-On the other hand, a higher complexity may decrease the model's ability to predict reasonable values for test data, since a more complex model will be more affected by noise in the model.
-This is said to increase the model's \emph{variance}.
-The best prediction performance is therefore achieved for a complexity which balances bias and variance, which is called the bias-variance trade-off\cite{mehta}.
-
-Following~\cite{mehta}, a mathematical manifestation of the bias-variance trade-off can be derived by assuming that the measured data set \(D=\qty{\qty(\vec{x}_i,y_i)}_{i=1}^N\) is generated by a combination of some model \(f\qty(\vec{x})\) (for example Franke's function) and random noise, specifically
-\begin{equation}
- y_i = f\qty(\vec{x}_i) + \varepsilon_i \eqqcolon f_i + \varepsilon_i,
-\end{equation}
-where the variables \(\varepsilon_i\) are independent and normally distributed with variance \(\sigma^2\) around zero.
-Given a data set \(D\), a prediction \(\tilde{y}_i^D\) can be made by any of the regression methods discussed above.
-An expected mean square error can be found by averaging over all datasets \(D\) and all noises \(\vec{\varepsilon}\),
-\begin{alignat}{2}
- E_{D,\varepsilon}\qty[\norm{\vec{y}-\vec{\tilde{y}}_D}_2^2]
- &= E_{D,\varepsilon}\qty[\norm{\vec{y} - \vec{f} + \vec{f} - \vec{\tilde{y}}_D}_2^2] \label{eq:tmp}
- = E_{D,\varepsilon}\qty[\norm{\vec{y} - \vec{f}}_2^2 + \norm{\vec{f} - \vec{\tilde{y}}_D}_2^2
- + 2 \qty(\vec{y} - \vec{f})\cdot\qty(\vec{f} - \vec{\tilde{y}}_D)],
- \shortintertext{and using the linearity of the expectation value,}
- &= E_{D,\varepsilon}\qty[\norm{\vec{y} - \vec{f}}_2^2] + E_{D,\varepsilon}\qty[\norm{\vec{f} - \vec{\tilde{y}}_D}_2^2]
- + 2 E_{D,\varepsilon}\qty[\qty(\vec{y} - \vec{f})\cdot\qty(\vec{f} - \vec{\tilde{y}}_D)]\\
- &= E_{D,\varepsilon}\qty[\norm{\vec{\varepsilon}}_2^2] + E_{D,\varepsilon}\qty[\norm{\vec{f} - \vec{\tilde{y}}_D}_2^2]
- + 2 E_{D,\varepsilon}\qty[\vec{\varepsilon}\cdot\qty(\vec{f} - \vec{\tilde{y}}_D)]\\
- &= \sigma^2 + E_{D,\varepsilon}\qty[\norm{\vec{f} - \vec{\tilde{y}}_D}_2^2]
- + 2 \cancel{E_{\varepsilon}\qty[\vec{\varepsilon}]}\cdot E_{D}\qty[\qty(\vec{f} - \vec{\tilde{y}}_D)]\\
- &= \sigma^2 + E_{D}\qty[\norm{\vec{f} - \vec{\tilde{y}}_D}_2^2].
-\end{alignat}
-This expression can be further decomposed by adding and subtracting the average prediction, \(E_D\qty[\vec{\tilde{y}}_D]\),
-\begin{alignat}{2}
- E_{D}\qty[\norm{\vec{y}-\vec{\tilde{y}}_D}_2^2]
- &= \sigma^2 + E_{D}\qty[\norm{\vec{f}- E_D\qty[\vec{\tilde{y}}_D] + E_D\qty[\vec{\tilde{y}}_D] - \vec{\tilde{y}}_D}_2^2]\\
- &= \sigma^2 + \norm{\vec{f}- E_D\qty[\vec{\tilde{y}}_D]}_2^2 + E_D\qty[\norm{E_D\qty[\vec{\tilde{y}}_D] - \vec{\tilde{y}}_D}_2^2]\\
- &\phantom{{}={}} + 2E_D\qty[\qty(\vec{f}- E_D\qty[\vec{\tilde{y}}_D])\cdot\cancel{\qty(E_D\qty[\vec{\tilde{y}}_D] - \vec{\tilde{y}}_D)}]\\
- &= \sigma^2 + \norm{\vec{f}- E_D\qty[\vec{\tilde{y}}_D]}_2^2 + E_D\qty[\norm{E_D\qty[\vec{\tilde{y}}_D] - \vec{\tilde{y}}_D}_2^2].
-\end{alignat}
-The first term, \(\sigma^2\), represents the noise in the generated data, which no model can overcome.
-The second term measures the deviation of the average prediction from the true, noise-free model, which is the (squared) bias.
-Lastly, the third term measures how much the predictions vary and is called the variance.
-A complex model (large \(p\)) will minimise the second term, since a complex model will be better suited to fit the true model, \(f\), while the third term will increase with model complexity since the fitting procedure will be more sensitive to noise in the different data sets.
-
-Unfortunately, the above bias-variance decomposition requires knowledge of the exact model behind the data, \(f\).
-A more computationally practical expression could have been derived by adding and subtracting \(E_D\qty[\vec{\tilde{y}}_D]\) in~\vref{eq:tmp}, which gives the expression
-\begin{equation}
- E_{D}\qty[\norm{\vec{y}-\vec{\tilde{y}}_D}_2^2]
- = \norm{\vec{y}- E_D\qty[\vec{\tilde{y}}_D]}_2^2 + E_D\qty[\norm{E_D\qty[\vec{\tilde{y}}_D] - \vec{\tilde{y}}_D}_2^2]
-\end{equation}
-by manipulations analogous to the ones used above. This is another formulation of the bias-variance decomposition which can be used without any information about the underlying model. Dividing by \(N\) gives the average \(\MSE\) on the left-hand side.
-
-
-
-% _ _ _ _ _
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-% | | | | | | | |_) | | __/ | | | | | __/ | | | || (_| | |_| | (_) | | | |
-% |_|_| |_| |_| .__/|_|\___|_| |_| |_|\___|_| |_|\__\__,_|\__|_|\___/|_| |_|
-% |_|
-\subsection{Implementation}
-The three regression methods and bootstrapping have been implemented in a polymorphic class hierarchy in Fortran.
-An object-oriented approach ensures ease of reuse for later projects, while also simplifying certain parts of the code and organisation.
-For instance, the bootstrapping algorithm can take in a regression method object, which is guaranteed to have methods for prediction and fitting, and not care whether ordinary least squares, Ridge or LASSO regression is used. Fortran was chosen because it combines excellent performance with object-oriented capabilities and a nice syntax for numerical work.
-\tikzexternalenable
-\tikzsetnextfilename{uml}
-\begin{figure}[H]
- \centering
- \begin{tikzpicture}
- \begin{umlpackage}{Linear regression and bootstrapping}
- \umlclass[type=abstract]{regressor}{
- \lstinline{real :: X(N, p), beta(p)}\\
- \lstinline{class(basis_function) :: basis(p)}
- }{
- \lstinline{subroutine create_X(real :: x_values(N,:))}\\
- \lstinline{subroutine predict(real :: x(N,:), y(N); optional :: y_exact(N), mse, r2)}\\
- \lstinline{deferred subroutine fit(real, optional :: x_values(N,:); real :: y_values(N))}
- }
- \umlclass[below = 1cm of regressor.south, anchor=north]{ridge}{
- \lstinline{real :: lambda}
- }{}
- \umlemptyclass[left=1cm of ridge.north west, anchor=north east]{ols}
- \umlclass[right = 1cm of ridge.north east, anchor=north west]{lasso}{
- \lstinline{real :: lambda}\\
- \lstinline{real :: tolerance}
- }{}
- \umlinherit[geometry=|-|,arm1=0.3cm,arm2=0.3cm,anchor1=90,anchor2=240]{ols}{regressor}
- \umlinherit[geometry=|-|,arm1=0.3cm,arm2=0.3cm,anchor1=90,anchor2=270]{ridge}{regressor}
- \umlinherit[geometry=|-|,arm1=0.3cm,arm2=0.3cm,anchor1=90,anchor2=300]{lasso}{regressor}
-
- \umlclass[type=abstract, below=5.5cm of regressor.west,anchor=north west]{basisfunction}{}{
- \lstinline{deferred real function eval(real :: x(:))}
- }
- \umlclass[right=1cm of basisfunction.north east,anchor=north west]{polynomial2d}{
- \lstinline{integer :: x1_pow, x2_pow}
- }{}
- \umlinherit{polynomial2d}{basisfunction}
-
- \umluniassoc[pos1=2.9, mult1=1..*, geometry=|-|, anchor1=202, anchor2=165,weight=0.35]{regressor}{basisfunction}
-
- \umlclass[above=1cm of regressor.north, anchor=south]{bootstrapper}{
- \lstinline{class(regressor) :: fitter}\\
- \lstinline{real :: y_predictions(N, num_bootstraps), R2s(num_bootstraps), MSEs(num_bootstraps)}\\
- \lstinline{real :: betas(p, num_bootstraps), mean_beta(p), beta_variance(p)}
- }{
- \lstinline{subroutine bootstrap(real :: x(:,:), y(:); integer :: num_bootstraps)}
- }
- \umluniassoc[mult1=1,pos1=0.8]{bootstrapper}{regressor}
- \end{umlpackage}
- \end{tikzpicture}
- \caption{Class hierarchy of implementation. All \lstinline{real} variables are of kind \lstinline{real64} from \lstinline{iso_fortran_env}.}
-\end{figure}
-\tikzexternaldisable
-
-% _ _ __
-% __ _ _ __ __ _| |_ _ ___(_)___ ___ / _|
-% / _` | '_ \ / _` | | | | / __| / __| / _ \| |_
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-% \__,_|_| |_|\__,_|_|\__, |___/_|___/ \___/|_|
-% _ _|___/
-% _ __ ___ ___| |_| |__ ___ __| |___
-% | '_ ` _ \ / _ \ __| '_ \ / _ \ / _` / __|
-% | | | | | | __/ |_| | | | (_) | (_| \__ \
-% |_| |_| |_|\___|\__|_| |_|\___/ \__,_|___/
-\section{Analysis of methods}
-The accuracy and viability of the methods can be studied on a test case where the underlying function is known.
-Such an example is Franke's function shown in~\vref{fig:franke}.
-
-\subsection{Verification of theory and fitting}
-\begin{figure}[H]
- \centering
- \begin{subfigure}{\textwidth}
- \centering
- \includegraphics{figs/verification_OLS.pdf}
- \caption{Ordinary least squares regression.}
- \end{subfigure}
- \begin{subfigure}{\textwidth}
- \centering
- \includegraphics{figs/verification_Ridge.pdf}
- \caption{Ridge regression.}
- \end{subfigure}
-% \begin{subfigure}{\textwidth}
-% \centering
-% \includegraphics{figs/verification_LASSO.pdf}
-% \caption{LASSO regression.}
-% \end{subfigure}
- \caption{Comparison of Franke's function with noise (red) and a fifth degree polynomial approximation (multi-coloured). The colour of the polynomial approximation shows its deviation from Franke's function.~\Vref{fig:betas} shows that the parameters are significantly different for the different methods, yet the resulting approximations are approximately equal.}
-\end{figure}
-
-\begin{figure}[H]
- \centering
- \begin{tikzpicture}
- \begin{axis}[thick,
- height=3in,
- width=6in,
- grid,
- xlabel = {\(i\)},
- ylabel = {\(\beta_i\)},
- legend style={draw=none,at={(0.98,0.98)},anchor=north east},
- legend cell align=left
- ]
- \foreach \method in {OLS, Ridge}{
- \addplot+[only marks,mark=o] plot[error bars/y dir=both, error bars/y explicit] table[y error=uncertainty] {data/verification_mean_beta_\method.dat};
- \addlegendentryexpanded{\method};
- }
- \addplot+[only marks,mark=o] plot[error bars/y dir=both, error bars/y explicit] table[y error=uncertainty] {data/verification_mean_beta_sklearn.dat};
- \addlegendentryexpanded{LASSO (scikit-learn)};
- \end{axis}
- \end{tikzpicture}
- \caption{Comparison of parameters for the different regression methods when applied to Franke's function with noise and using polynomials up to fifth order. The Ridge coefficients are severely suppressed, yet~\vref{table:performance} shows that the fitting quality is virtually the same. LASSO regression (using scikit-learn) gives a sparse solution, i.e.\ some \(\beta_j\)s are exactly zero. Confidence intervals are estimated as \(\beta_j \pm 2\sigma_{\beta_j}\), where \(\sigma_{\beta_j}\) is the standard deviation of \(\beta_j\) calculated from bootstrapping.}\label{fig:betas}
-\end{figure}
-
-\begin{table}[H]
- \centering
- \caption{Measure of performance on training and test data sampled from Franke's function with noise for the different methods. Ordinary least squares should, by design, perform best on the training data, while Ridge and LASSO are expected to perform better on test data not used in the fitting due to their regularisation parameter. The advantage of regularised methods is amplified when a smaller number of points is used (\(\num{10000}\) points were used here for plotting purposes). See also~\vref{tab:biasvar}, which shows the average error on test data for many bootstrap samples.}\label{table:performance}
- \pgfplotstabletypeset[zerofill, fixed,precision=4]{./data/verification_mse_r2.dat}
-\end{table}
-
-\subsection{Bias and variance}
-According to the bias-variance decomposition, the mean squared error should be equal to the sum of the bias (squared) and the variance.
-The bias and variance are calculated from bootstrapping, and the results show good agreement with the theoretical prediction.
-\begin{table}[H]
- \centering
- \caption{Verification of the bias-variance decomposition via bootstrapping for fitting of Franke's function with noise. As expected, the sum of the bias and the variance is equal to the mean squared error, and the regularised methods perform better on test data than ordinary least squares.}\label{tab:biasvar}
- \pgfplotstabletypeset[sci, sci zerofill, precision=3]{./data/verification_bias_variance.dat}
-\end{table}
-
-\begin{figure}[H]
- \centering
- \begin{tikzpicture}
- \begin{axis}[thick,
- height=3in,
- width=6in,
- ymode=log,
- grid,
- xtick distance=1,
- xlabel = {Polynomial degree \(d\)},
- ylabel = {Error},
- legend style={draw=none,at={(0.02,0.50)},anchor=west},
- legend cell align=left
- ]
- \addplot+ table[y index=1] {data/complexity.dat};
- \addlegendentry{MSE (OLS)};
- \addplot+ table[y index=2] {data/complexity.dat};
- \addlegendentry{Bias (OLS)};
- \addplot+ table[y index=3] {data/complexity.dat};
- \addlegendentry{Variance (OLS)};
- \addplot+ table[y index=4] {data/complexity.dat};
- \addlegendentry{MSE (Ridge)};
- \addplot+ table[y index=5] {data/complexity.dat};
- \addlegendentry{Bias (Ridge)};
- \addplot+ table[y index=6] {data/complexity.dat};
- \addlegendentry{Variance (Ridge)};
- \end{axis}
- \end{tikzpicture}
- \caption{Visualisation of bias-variance trade-off. The mean squared error for test data is expected to first decrease with increasing complexity as the bias decreases towards \(\sigma^2\), and then increase as the variance becomes dominant. Additionally, the regularisation of the Ridge regressor is intended to keep the variance moderate even with a high polynomial degree.}\label{fig:biasvar}
-\end{figure}
-
-\subsection{Effect of noise}
-\begin{figure}[H]
- \centering
- \begin{tikzpicture}
- \begin{axis}[
- thick,
- width=6in,
- height=3in,
- xlabel = {\(\sigma\)},
- ylabel = {\(R^2\)},
- legend cell align=left,
- legend style={draw=none,at={(0.98,0.98)},anchor=north east},
- grid
- ]
- \addplot+ table[y index=1] {data/noise.dat};
- \addlegendentry{Training data};
- \addplot+ table[y index=2] {data/noise.dat};
- \addlegendentry{Test data};
- \end{axis}
- \end{tikzpicture}
- \caption{\(R^2\) score of Ridge regression with \(\lambda=0.001\) when normally distributed noise with a standard deviation of \(\sigma\) is added to Franke's function. \(400\) data points are used, and the performance is clearly better for the training data to which the model was fitted than novel test data. A higher number of data points reduces the overfitting, so that the prediction and its performance are less affected by noise.}
-\end{figure}
-
-\subsection{Effect of regularisation}
-\begin{figure}[H]
- \centering
- \begin{tikzpicture}
- \begin{axis}[
- thick,
- width=6in,
- height=3in,
- xmode=log,
- xlabel = {\(\lambda\)},
- ylabel = {\(R^2\)},
- legend cell align=left,
- legend style={draw=none,at={(0.02,0.40)},anchor=west},
- grid
- ]
- \addplot+ table[y index=1] {data/r2_lambda.dat};
- \addlegendentry{Training data};
- \addplot+ table[y index=2] {data/r2_lambda.dat};
- \addlegendentry{Test data};
- \end{axis}
- \end{tikzpicture}
- \caption{\(R^2\)-score as a function of the regularisation parameter \(\lambda\) for Ridge regression. \(\lambda=0\) would correspond to ordinary least squares. While ordinary least squares regression by construction gives the best performance on training data, the results show that a smart choice of \(\lambda\) can give better predicting performance since the regularisation reduces overfitting and variance.}
-\end{figure}
-
-\begin{figure}[H]
- \centering
- \begin{tikzpicture}
- \begin{axis}[
- thick,
- width=6in,
- height=3in,
- xmode=log,
- ymode=log,
- xlabel = {\(\lambda\)},
- ylabel = {Error},
- legend cell align=left,
- legend style={draw=none,at={(0.98,0.98)},anchor=north east},
- grid
- ]
- \addplot+ table[y index=1] {data/bivar_lambda.dat};
- \addlegendentry{MSE};
- \addplot+ table[y index=2] {data/bivar_lambda.dat};
- \addlegendentry{Bias};
- \addplot+ table[y index=3] {data/bivar_lambda.dat};
- \addlegendentry{Variance};
- \end{axis}
- \end{tikzpicture}
- \caption{Error, bias and variance as a function of the regularisation parameter \(\lambda\) for Ridge regression, calculated from bootstrapping. The variance, which is the error due to overfitting of the noise, gradually decreases as \(\lambda\) increases, while a too large \(\lambda\) causes the bias to increase because the severe suppression of the \(\beta_j\) coefficients makes it impossible for the polynomial expansion to approximate the model function (Franke's function).}
-\end{figure}
-
-
-\pgfplotstableread[skip first n=1]{data/beta_lambda.dat}{\betatable}
-\begin{figure}[H]
- \centering
- \begin{tikzpicture}
- \begin{axis}[
- thick,
- width=6in,
- height=3in,
- xmode=log,
- xlabel = {\(\lambda\)},
- ylabel = {\(\beta_i\)},
- legend cell align=left,
- legend style={draw=none,at={(0.98,0.98)},anchor=north east},
- grid
- ]
- \foreach \index in {1,3,...,44}{
- \addplot+ table[y index=\index, y error index={\index+1}] {\betatable};
- }
- \end{axis}
- \end{tikzpicture}
- \caption{Coefficients \(\beta_j\) as a function of the regularisation parameter \(\lambda\) for Ridge regression. Regularisation suppresses the coefficients due to the penalising \(\lambda\|\vec{\beta}\|_2^2\) term in the cost function, in order to achieve better prediction abilities due to lower variance and effect of noise. LASSO regression would set many of the coefficients to exactly zero, ref.~\vref{fig:betas}.}
-\end{figure}
-
-% _
-% __ _ ___ ___ __ _ _ __ __ _ _ __ | |__ _ _
-% / _` |/ _ \/ _ \ / _` | '__/ _` | '_ \| '_ \| | | |
-%| (_| | __/ (_) | (_| | | | (_| | |_) | | | | |_| |
-% \__, |\___|\___/ \__, |_| \__,_| .__/|_| |_|\__, |
-% |___/ |___/ |_| |___/
-\section{Geographical data}
-The previous section verified the implementation of ordinary least squares and Ridge regression (and scikit-learn's LASSO regression), as well as some theoretical predictions.
-It is now time to apply them to real-world data, such as the geographical data in the figure below.
-\begin{figure}[H]
- \centering
- \includegraphics{figs/geography.pdf}
- \caption{Some Norwegian geography, complete with a fjord.}\label{fig:geo}
-\end{figure}
-
-To determine the best possible model for the terrain, I have chosen to iterate over different polynomial degrees and compare ordinary least squares with Ridge regression for a selection of \(\lambda\)s for each degree. The best \(\lambda\) is determined for each degree, and the overall best approximation (measured by MSE for test data in bootstrap) is visualised in~\vref{fig:geoapprox}.
-\begin{table}[H]
- \centering
- \caption{Errors for different approximations to~\vref{fig:geo}. Several values of \(\lambda\) for Ridge regression are tried for each degree, and the one resulting in the smallest test MSE during bootstrapping is reported. Ordinary least squares is seen to perform well for polynomials of a small degree, while higher order polynomials lead to severe overfitting. On the other hand, the regularisation of Ridge manages to keep the variance and overfitting in check and give reasonable results also for higher degrees.}\label{tab:geo}
- \small
- \pgfplotstabletypeset[columns/lambda/.style={column name={$\lambda$}},columns/$d$/.style={fixed},sci, sci zerofill,precision=1]{data/geography_mse.dat}
-\end{table}
-
-\begin{figure}[H]
- \centering
- \begin{tikzpicture}
- \begin{axis}[
- thick,
- width=6in,
- height=3in,
- ymode=log,
- xlabel = {\(d\)},
- ylabel = {Error},
- legend cell align=left,
- legend style={draw=none,at={(0.98,0.02)},anchor=south east},
- grid
- ]
- \addplot+ table[skip first n=1, y index=4] {data/geography_mse.dat};
- \addlegendentry{MSE};
- \addplot+ table[skip first n=1,y index=5] {data/geography_mse.dat};
- \addlegendentry{Bias};
- \addplot+ table[skip first n=1,y index=6] {data/geography_mse.dat};
- \addlegendentry{Variance};
- \end{axis}
- \end{tikzpicture}
- \caption{Error, bias and variance as a function of polynomial degree \(d\) for Ridge regression. The parameter \(\lambda\) is estimated for each \(d\) by bootstrapping for different \(\lambda\)s and choosing the one which gives the smallest mean squared error for the test data. Regularisation keeps the variance low even for a high polynomial degree, which is not the case for ordinary least squares according to~\vref{tab:geo}.}
-\end{figure}
-Bias and variance still add up to the mean squared error with approximately the same accuracy as when approximating Franke's function with noise. This was not necessarily expected due to the assumption of identically, independently and normally distributed noise in the derivation, which was added artificially. Geographical data is certainly not independent, and the other assumptions may also not hold.
-
-Ideally, there should be some polynomial degree for which the error is minimised, since overfitting will occur and the variance will increase as the degree of the polynomial grows and the approximation becomes more sensitive to noise. Overfitting requires that the number of basis functions, \(p=(d+1)(d+2)/2\), becomes non-negligible compared to the number of data points. I have here used approximately \(\num{65000}\) data points, meaning that a polynomial must be of a very high degree in order to overfit. Ridge regression scales as \(\mathcal{O}(p^3) = \mathcal{O}(d^6)\) and ordinary least squares possibly even worse, so the runtime increases drastically when the polynomial degree becomes large. The simulation giving the figures and tables in this section took roughly 100 CPU hours.
-
-\begin{figure}[H]
- \centering
- \includegraphics{figs/geography_approx.pdf}
- \caption{Polynomial approximation to the geographical data in\vref{fig:geo} using the best model from~\vref{tab:geo}. The model captures key elements such as the fjord, while missing the finer details of the mountainous landscape. In particular, the steep climb from the fjord is almost step-like, which no polynomial of finite degree can approximate.}\label{fig:geoapprox}
-\end{figure}
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-\section{Summary and conclusion}
-This report started with a lengthy discussion of theory, culminating in three different regression methods, some error analysis and a few implementational tidbits.
-Ordinary least squares is derived from a minimisation of the training error, which has been proven correct.
-The bias-variance decomposition showed that the predicting error can be decomposed into bias, which measures the approximating function's ability to model the data's underlying function, and variance, which measures how much the approximation varies when applied to different parts of the data set, such as in bootstrapping.
-Predicting models obtained from ordinary least squares have been inferior to Ridge and LASSO regression when applied to test data not used in the fitting procedure, as these methods have a regularisation term in their cost function which prevents the regressor from being affected by noise and overfitting to the same extent as ordinary least squares.
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-Application of the regression techniques to Franke's function showed that the regularised methods perform better than ordinary least squares when a data set with few points and much noise is approximated, while a large number of data points reduces overfitting and makes ordinary least squares on par with Ridge and LASSO regression as long as a model with moderate complexity is used.
-Newton's method proved ineffective at minimising the LASSO cost function due to its non-differentiability, while the implementations of ordinary least squares, Ridge regression and bootstrapping performed well in terms of both accuracy and performance, the latter being crucial for large data sets with polynomials of a high degree.
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-Lastly, geographical data from a Norwegian fjord was fitted. Ordinary least squares proved to be utterly useless unless a moderate order of polynomials is used, while Ridge regression performed well for a variety of polynomial degrees when the optimal regularisation parameter was chosen for each polynomial degree. The main geographical features were reproduced, despite difficult features such as a Heaviside-like incline on the side of the fjord.
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-Future work includes using a prediction method which scales better with data and model complexity, such as neural networks. Additionally, a better version of the LASSO technique can be implemented by using a minimisation algorithm such as coordinate descent. A sparse solution with some \(\beta_j\)s exactly equal to zero is then expected due to the use of a soft thresholding operator, and its performance should be evaluated on e.g. Franke's function and geographical data and compared with the other regression methods.
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-\clearpage
-\nocite{*}
-\printbibliography{}
-\addcontentsline{toc}{section}{\bibname}
-\end{document}