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FYS-STK4155/doc/Programs/IsingModel/onedim.ipynb
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2018-07-05 15:43:45 +02:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Predicting the energy in the one-dimensional Ising model\n",
"\n",
"We will in this notebook use linear (ordinary least squares), ridge and LASSO regression to predict the energy in the nearest neighbor one-dimensional Ising model on a ring, i.e., the endpoints wrap around. We will use the linear regression models to fit a value for the coupling constant to achieve this."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
"import seaborn as sns\n",
"import scipy.linalg as scl\n",
"from sklearn.model_selection import train_test_split\n",
"import sklearn.linear_model as skl\n",
"import tqdm\n",
"\n",
"%matplotlib inline\n",
"\n",
"sns.set(color_codes=True)\n",
"cmap_args=dict(vmin=-1., vmax=1., cmap='seismic')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The one-dimensional Ising model\n",
"\n",
"The one-dimensional Ising model with nearest neighbor interaction, no external field and a constant coupling constant $J$ is given by\n",
"\n",
"\\begin{align}\n",
" H = -J \\sum_{k}^L s_k s_{k + 1},\n",
"\\end{align}\n",
"\n",
"where $s_i \\in \\{-1, 1\\}$ and $s_{N + 1} = s_1$. The number of spins in the system is determined by $L$. For the low temperature limit there is no phase transition.\n",
"\n",
"We will look at a system of $L = 40$ spins with a coupling constant of $J = 1$. To get enough training data we will generate 10000 states with their respective energies."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"L = 40\n",
"n = int(1e4)\n",
"\n",
"spins = np.random.choice([-1, 1], size=(n, L))\n",
"J = 1.0\n",
"\n",
"energies = np.zeros(n)\n",
"\n",
"for i in range(n):\n",
" energies[i] = - J * np.dot(spins[i], np.roll(spins[i], 1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Reformulating the problem to suit regression\n",
"\n",
"A more general form for the one-dimensional Ising model is\n",
"\n",
"\\begin{align}\n",
" H = - \\sum_j^L \\sum_k^L s_j s_k J_{jk}.\n",
"\\end{align}\n",
"\n",
"Here we allow for interactions beyond the nearest neighbors and a more adaptive coupling matrix. This latter expression can be formulated as a matrix-product on the form\n",
"\n",
"\\begin{align}\n",
" H = X J,\n",
"\\end{align}\n",
"\n",
"where $X_{jk} = s_j s_k$ and $J$ is the matrix consisting of the elements $-J_{jk}$. This form of writing the energy fits perfectly with the form utilized in linear regression, viz.\n",
"\n",
"\\begin{align}\n",
" y = X\\omega + \\epsilon,\n",
"\\end{align}\n",
"\n",
"where $\\omega$ are the weights we wish to fit and $\\epsilon$ is noise with zero-mean. In the case of the Ising model we have $\\sigma = 0$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"X = np.zeros((n, L ** 2))\n",
"for i in range(n):\n",
" X[i] = np.outer(spins[i], spins[i]).ravel()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"y = energies\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.96)\n",
"\n",
"X_train_own = np.concatenate(\n",
" (np.ones(len(X_train))[:, np.newaxis], X_train),\n",
" axis=1\n",
")\n",
"\n",
"X_test_own = np.concatenate(\n",
" (np.ones(len(X_test))[:, np.newaxis], X_test),\n",
" axis=1\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Linear regression\n",
"\n",
"The problem at hand is to try to fit the equation\n",
"\n",
"\\begin{align}\n",
" y = f(x) + \\epsilon,\n",
"\\end{align}\n",
"\n",
"where $f(x)$ is some unknown function of the data $x$ and $\\epsilon$ is normally distributed with mean zero noise with standard deviation $\\sigma_{\\epsilon}$. Our job is to try to find a predictor which estimates the function $f(x)$. In linear regression we assume that we can formulate the problem as\n",
"\n",
"\\begin{align}\n",
" y = X\\omega + \\epsilon,\n",
"\\end{align}\n",
"\n",
"where $X$ and $\\omega$ are now matrices. Our job at hand is now to find a _cost function_ $C$, which we wish to minimize in order to find the best estimate of $\\omega$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Ordinary least squares\n",
"\n",
"In the ordinary least squares method we choose the cost function\n",
"\n",
"\\begin{align}\n",
" C(X, \\omega) = ||X\\omega - y||^2\n",
" = (X\\omega - y)^T(X\\omega - y)\n",
"\\end{align}\n",
"\n",
"We then find the extremal point of $C$ by taking the derivative with respect to $\\omega$ and setting it to zero, i.e.,\n",
"\n",
"\\begin{align}\n",
" \\dfrac{\\mathrm{d}C}{\\mathrm{d}\\omega}\n",
" = 0.\n",
"\\end{align}\n",
"\n",
"This yields the expression for $\\omega$ to be\n",
"\n",
"\\begin{align}\n",
" \\omega = \\frac{X^T y}{X^T X},\n",
"\\end{align}\n",
"\n",
"which immediately imposes some requirements on $X$ as there must exist an inverse of $X^T X$. If the expression we are modelling contains an intercept, i.e., a constant expression we must make sure that the first column of $X$ consists of $1$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def get_ols_weights_naive(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
" return scl.inv(x.T @ x) @ (x.T @ y)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"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<ipython-input-6-a21f2381e9a7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0momega\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_ols_weights_naive\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[0m\n\u001b[0m",
"\u001b[0;32m<ipython-input-5-92b155609649>\u001b[0m in \u001b[0;36mget_ols_weights_naive\u001b[0;34m(x, y)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mget_ols_weights_naive\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[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[0m\n\u001b[0m",
"\u001b[0;32m/Users/Schoyen/anaconda3/lib/python3.6/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 817\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[0m\n\u001b[1;32m 818\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[0m\n\u001b[0;32m--> 819\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[0m\n\u001b[0m\u001b[1;32m 820\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[0m\n\u001b[1;32m 821\u001b[0m raise ValueError('illegal value in %d-th argument of internal '\n",
"\u001b[0;31mLinAlgError\u001b[0m: singular matrix"
]
}
],
"source": [
"omega = get_ols_weights_naive(X_train_own, y_train)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Hmmm, doing the inversion directly turns out to be a bad idea as the matrix $X^TX$ is singular. An alternative approach is to use the _singular value decomposition_. Using the definition of the Moore-Penrose pseudoinverse we can write the equation for $\\omega$ as\n",
"\n",
"\\begin{align}\n",
" \\omega = X^{+}y,\n",
"\\end{align}\n",
"\n",
"where the pseudoinverse of $X$ is given by\n",
"\n",
"\\begin{align}\n",
" X^{+} = \\frac{X^T}{X^T X}.\n",
"\\end{align}\n",
"\n",
"Using singular value decomposition we have that $X = U\\Sigma V^T$, where $X^{+} = V\\Sigma^{+} U^T$. This reduces the equation for $\\omega$ to\n",
"\n",
"\\begin{align}\n",
" \\omega = V\\Sigma^{+} U^T y.\n",
"\\end{align}\n",
"\n",
"Note that solving this equation by actually doing the pseudoinverse (which is what we will do) is not a good idea as this operation scales as $\\mathcal{O}(n^3)$, where $n$ is the number of elements in a general matrix. Instead, doing $QR$-factorization and solving the linear system as an equation would reduce this down to $\\mathcal{O}(n^2)$ operations."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def get_ols_weights(x: np.ndarray, y: np.ndarray) -> np.ndarray:\n",
" u, s, v = scl.svd(x)\n",
" return v.T @ scl.pinv(scl.diagsvd(s, u.shape[0], v.shape[0])) @ u.T @ y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before passing in the data to the function we append a column with ones to the training data."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"omega = get_ols_weights(X_train_own,y_train)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we fit a `LinearRegression`-model from Scikit-learn for comparison."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"clf = skl.LinearRegression().fit(X_train, y_train)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Extracting the $J$-matrix from both our own method and the Scikit-learn model where we make sure to remove the intercept."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"J_own = omega[1:].reshape(L, L)\n",
"J_sk = clf.coef_.reshape(L, L)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A way of looking at the coefficients in $J$ is to plot the matrices as images."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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I3HnnnVq/fr2mTZumGTNmqL6+XgUFBcrJyVF+fr6k5hm427Zt07Bh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\nevRQVVWVkpKSWlzfeNmpU6fazNi3b58k6f3339fs2bOVmZmp7du3a82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dHg6HdfDgQfXv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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1301bb710>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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nMeQYAAAAADxA76D3cQwAAAAAAD6JBi0AAAAAwCcx5BgAAAAAPEDvoPdxDAAA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\nWoOfw6Lzt7sPikxR5H8txO3b1/qC6g0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A4EtMaAEAAAAAvkTLMQAAAADEgJbj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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x12f23cdd8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(20, 14))\n",
"im = plt.imshow(J_own, **cmap_args)\n",
"plt.title(\"Home-made OLS\", fontsize=18)\n",
"plt.xticks(fontsize=18)\n",
"plt.yticks(fontsize=18)\n",
"cb = fig.colorbar(im)\n",
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
"\n",
"fig = plt.figure(figsize=(20, 14))\n",
"im = plt.imshow(J_sk, **cmap_args)\n",
"plt.title(\"LinearRegression from Scikit-learn\", fontsize=18)\n",
"plt.xticks(fontsize=18)\n",
"plt.yticks(fontsize=18)\n",
"cb = fig.colorbar(im)\n",
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that our model for the least squares method performes close to the benchmark from Scikit-learn. It is interesting to note that OLS considers both $J_{j, j + 1} = -0.5$ and $J_{j, j - 1} = -0.5$ as valid matrix elements for $J$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Ridge regression\n",
"\n",
"Having explored the ordinary least squares we move on to ridge regression. In ridge regression we include a _regularizer_. This involves a new cost function which leads to a new estimate for the weights $\\omega$. This results in a penalized regression problem. The cost function is given by\n",
"\n",
"\\begin{align}\n",
" C(X, \\omega; \\lambda) = ||X\\omega - y||^2 + \\lambda ||\\omega||^2\n",
" = (X\\omega - y)^T(X\\omega - y) + \\lambda \\omega^T\\omega.\n",
"\\end{align}\n",
"\n",
"Finding the extremum of this function yields the weights\n",
"\n",
"\\begin{align}\n",
" \\omega(\\lambda) = \\frac{X^Ty}{X^TX + \\lambda} \\to \\frac{\\omega_{\\text{LS}}}{1 + \\lambda},\n",
"\\end{align}\n",
"\n",
"where $\\omega_{\\text{LS}}$ is the weights from ordinary least squares. The last assumption assumes that $X$ is orthogonal, which it is not. We will therefore resort to solving the equation as it stands on left hand side."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def get_ridge_weights(x: np.ndarray, y: np.ndarray, _lambda: float) -> np.ndarray:\n",
" return x.T @ y @ scl.inv(\n",
" x.T @ x + np.eye(x.shape[1], x.shape[1]) * _lambda\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"_lambda = 0.1"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"omega_ridge = get_ridge_weights(X_train_own, y_train, np.array([_lambda]))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"J_ridge_own = omega_ridge[1:].reshape(L, L)\n",
"J_ridge_sk = clf_ridge.coef_.reshape(L, L)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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yMT7I7lMfWHy0/Q06paDe3PMVGWkslQoLzeWycxydTqmkxHOcneNolyOkzlyy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\ntBwDAAAAQBRoOY6/hEgkEon3ICRJVVVudWlp3rW1tbGP55T0dLusRMO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ah/e1UEiB2hrP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no8zlxwTm+5l5gHToiJidHo0aO71XRpaamOHTumjIwM6t4hdnIvUfehcPHiRe3du1cbN26Uz+fT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\nqdUpBdlZT0YAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x12f321668>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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yV2FZrFmuhLhqs1x7C1xmubolObmGRSpSgeP21XRqeYNOCPAyaxZXTYVZrtxc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\nBQAAAAD4EhNaAAAAAIAvcVguAAAAAIgGRzmOO1Z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N57LS7XbNVdV222taqt3z2K+xyuUe\n1a+7d93+irTYB3TSt/P3mGX94OFcs6zFi5rMsn7wsHdz1uLF0k9/6p21eMhagxE1q5tyl1lWTqPd\n86iBA+2iHF/aLncZVF1sgzlTZaVdluFjpnfescsa+2WzqLp6uybHoOGHlJo8u7+xrMwsSoP72mUB\nZ6LlGAAAAADgS11mhRYAAAAA/ISW4/hjhRYAAAAA4EtMaAEAAAAAvkTLMQAAAABEgZbj+GOFFgAA\nAADgS0xoAQAAAAC+RMsxAAAAAESBluP4Y4UWAAAAAOBLTGgBAAAAAL5EyzEAAAAARIGW4/hjhRYA\nAAAA4EtMaAEAAAAAZ7Vu3TpNmDBBw4YN06RJk7Rx40an29XW1mrRokX68pe/rKFDh2rcuHFatmyZ\nGhoaWtW9/vrruuKKK9r9t2fPng7vg5ZjAAAAAIjChdBy/Oyzz2rp0qWaMGGCCgoKtGnTJs2bN08J\nCQmaOHHiWW8XiUT04IMPauvWrZo6dapyc3O1Y8cOPf300youLtbKlStbavfu3auEhAQtWbJEgUDr\nNdf+/ft3OD4mtAAAAACANmpqarRixQrdfPPN+tnPfiZJuuOOO3T33Xdr6dKluvHGG9WtW7d2b/vH\nP/5RW7Zs0SOPPKK77rpLkjRt2jRlZGToqaee0rZt2/QP//APkpontOFwWFOmTOn0GGk5BgAAAAC0\nsXnzZtXV1WnatGktlwUCAd155536+OOP9e677571tlu3bpWkNpPUr371q5LU6rZ79+5VTk5OVGNk\nhRYAAAAAovD33nK8c+dOSdKQIUNaXT548OCW66+++up2b/vtb39bU6ZMUTAYbHX54cOHJUmJic1T\n0Ugkov3792v06NGSpBMnTqhbt24t13thhRYAAAAA0MahQ4fUu3dv9ezZs9Xlffr0kSSVl5ef9bap\nqam68sor21z+m9/8RpI0YsQISdKBAwd0/PhxlZaWatKkSRo+fLjy8vI0d+5cVVVVeY6xy6zQZmba\n1VZXxzaW09U1JpllpaSYRenL1zR4FzkqrbD7GzVokFlUZaVZlLIa99uFGT6RTXkjneoCDrWBslKD\nEZ1m6FC7rHfescs6y7eA0ago8a7JyZEqKhzqMrrM7rSV5GTDsETLMEcOr7ecyo6Pftgp6elmUd/7\nnlmUfvCw3ffPixc1OVQFnOoKF90V+4BOmu7wOnOVmp5rF2b4mcL1s45TXW3XXRbaVRL0LnI0OCPD\nLCtQeci7qG9fp7qg5Yc6w6xGw+11cGaNXZhChlmw8Mknn3R4fTAYVK9evXTs2DElt/Nh4tRlx48f\n79T9vvTSS3rllVc0ZswYDR8+XFJzu7Ekvffee5o1a5YyMzO1bds2rV69WsXFxXrxxRfbHcMpXfMT\nGAAAAAB0cX5tOR47dmyH1z/wwAOaO3euIpGIEhISzlrX0XVn+uMf/6iHH35Yffr00WOPPdZy+aWX\nXqo5c+Zo0qRJGjBggCQpPz9fl112mRYuXKj169dr+vTpZ81lQgsAAAAAF5BFixZ1eP2pVuFgMKj6\n+vo215+6rFevXk7392//9m9asGCBevXqpWeeeUbhcLjlutzcXOXmtu2sue222/TjH/9Yb731ls2E\n9o033tAvfvELffDBBwoEAho+fLi++93vKi8vr6Xm61//uv73f/+3zW1vvPFGPfnkk653BQAAAAA4\nR26//Xanuv79++vIkSNqaGhQUtLnP1M8dKi5Nb9fv36eGb/97W/1T//0T+rdu7eee+45DXL8iWL3\n7t0VCoVUV1fXYZ3ThHbr1q2aNWuWvvCFL2ju3LlqbGzUunXrNH36dK1bt07Dhg1TJBLRvn37lJ+f\nr/Hjx7e6/SWXXOI0aAAAAADwC7+2HLsaMmSIIpGIdu/e3fKbV0navXu3JOmqq67q8PYvvfSSFi5c\nqL59++q5557T5Zdf3qZm+fLlevnll7VhwwalnPab8urqalVVVXnOJZ0mtIsXL1b//v31wgsvtBzh\n6tZbb9XEiRO1bNky/epXv1JZWZnq6up0ww03aPLkyS6xAAAAAIAu6rrrrlOPHj20Zs2algltU1OT\n1q1bp0suuaRVt+6ZiouL9cMf/lBpaWlas2aNsrOz260Lh8MqKyvT+vXrVVBQ0HL5ypUrJUmTJk3q\ncIyeE9ojR46oqKhI99xzT6vDNaenp2vUqFH685//3DJgSe3OugEAAAAA/nLxxRdr9uzZ+vnPf65I\nJKJrrrlGr7zyirZt26Zly5apW7duLbWvvfaapOYDOknSihUr1NDQoC996Ut677339N5777XKvuKK\nKzRo0CBNmTJFL7zwgh5//HGVlJQoNzdXW7Zs0auvvqqpU6dq1KhRHY7Rc0KbkpKiP/zhD23OPSQ1\nnxT31B9x6nDLpya0dXV1bU6iCwAAAAB/L/7eW44lac6cOerZs6fWrl2rTZs2KTs7W8uXL9eECRNa\n1S1evFjS5xPat99+W5K0YcMGbdiwoU3ugw8+qEGDBql79+5atWqVnnjiCW3atEnr16/XpZdeqoce\nekgzZszwHJ/nhLZbt27tLg8XFRVp+/btLYd83rt3r3r16qUlS5bo3//931VXV6dLL71Uc+fO1U03\n3eQ5EAAAAABA15KQkKCZM2dq5syZHdZt3ry51f9PdfK6SE1NVWFhoQoLCzs9vqhO23Ps2DF9//vf\nlyTNnj1bUnPL8bFjx3T06FEtXbpUNTU1Wr16tebNm6e//e1vuvXWW6O5KwAAAAAA2pUQiUQinbnB\n8ePHdf/99+utt97S/fffr3nz5kmSfvOb36ipqUl33XVXS219fb1uvvlmHT9+XH/6059a9VifKRKR\nOnFeXgAAAABdXU2NFArFexTnzMmpUJfzxBPxHsH506kV2pqaGt1///3avn27brvtNs2dO7flumnT\nprWpT05O1uTJk7VixQoVFxfriiuuOGt2JNL8z0sgIDU1dVxTXe2d4yo52S6rnXMSRy0tpcEsq7Qi\nybtIUlaWVFrqUVO/x2BEzUqT255gOVpZjfvNsnTa4cRj1ZTe16nOZbsPlHk8OZ2VmWmX9c47dllX\nX20Wtb8k4FmTkyPtd9h8cjI6PkdavNTJ7lgGwUS7/Y6TpCSpweE+S0rs7jM93SyqSmlmWT/9qVmU\nFi/y2JlIbjsdSYWLvF9DrqZPN4tSaqpdliWXcTk+9ArU1sQ+oNMZfnjaVZtlljU40e5zhdMT0Lev\ndPL8mh0y/Cxg+WGzqtruNZmWaLyNAeeI81b/6aefasaMGdq+fbumTp2qRx99VAkOS6ppac1v6F4n\nxAUAAAAAoDOcVmhra2s1c+ZM7d69WwUFBXrooYdaXX/w4EHde++9+upXv6oHH3yw1XUffvihJCnT\ncrUHAAAAAOLsQjjKcVfntEJbWFio3bt3a8aMGW0ms5LUr18/1dTU6MUXX1RtbW3L5eXl5frd736n\nMWPGqE+fPnajBgAAAABc8DxXaPft26cNGzYoFArpyiuvbPccQpMnT9bChQs1Z84cfeMb39Dtt9+u\nY8eOae3atUpMTNTChQvPyeABAAAAABcuzwnt1q1bJTUfEKq91VmpeUKbn5+vlStX6umnn9ZPf/pT\nJScna/To0Zo3b54uv/xy21EDAAAAQJzRchx/nhPaadOmtXsE4/bk5+crPz8/5kEBAAAAAODFoHAY\njQAAIABJREFU7tjeAAAAAACcR506D+255Hw+tVDIszYt2fDP+p//MYtqvHqcWVZ5pdu5Y11kVWx1\nLBztXZuXF/uATkq3bOEorvWucZWRYRZV6zisUMi7trLR7rx/kpRTb3eqrTcbR5tlXW24XeRkupxX\nNcmprinR7nyvrtuFi+PH7bKCfQz3rS7nvExLc3owttfanbN6ZLXj/tBBSp7ddr94yFqzrMJFd3nW\nPPKI2zlmH3nY4YSpju69z+479h/9yCzK9HSjr73mXTN+vFvd2LGh2Ad0mqM97PIGp9u9fzQZnpPe\n5ZTVOX2l/bXe54jPqTc897thz2qa4QZb6vA4uMqy3Vy7FFqO448VWgAAAACALzGhBQAAAAD4Updp\nOQYAAAAAP6HlOP5YoQUAAAAA+BITWgAAAACAL9FyDAAAAABRoOU4/lihBQAAAAD4EhNaAAAAAIAv\n0XIMAAAAAFGg5Tj+WKEFAAAAAPgSE1oAAAAAgC/RcgwAAAAAUaDlOP5YoQUAAAAA+BITWgAAAACA\nL9FyDAAAAABRoOU4/lihBQAAAAD4EhNaAAAAAIAv0XIMAAAAAFGg5Tj+EiKRSCTeg5AkVVW51aWl\nedfW1sY+nlPS0+2yEg2/PzDMqqt3W6gPBqW6Oo+aesfn0UFDSppZVlmZWZQqKuyyrh1a41YYCkk1\nHrUpKbEP6DT7S+waOLKzzaIUaGywC6uu9q7p21c6dMi7rrIy9vGc1DRosFmW5Rvt4cN2Wf0udnge\nk5KkBu+60ookgxE1y6rdZZaljAyzqLpku/2hyz4sJ0fav9+7btGi2Mdzyv+3qsksa/FjdvuvBQvM\nohTY+b530bBh0vsOdampsQ/odIafK5oywmZZlvuwpFqHzygunzNl+xmlvt4sSqEUu9dRVbXd6yjN\n7uHqcm65Jd4jaN/vfx/vEZw/tBwDAAAAAHyJlmMAAAAAiAItx/HHCi0AAAAAwJeY0AIAAAAAfImW\nYwAAAACIAi3H8ccKLQAAAADAl5jQAgAAAAB8iZZjAAAAAIgCLcfxxwotAAAAAMCXWKEFAAAAgCiw\nQht/rNACAAAAAHyJCS0AAAAAwJdoOQYAAACAKNByHH+s0AIAAAAAfIkJLQAAAADAl2g5BgAAAIAo\n0HIcf6zQAgAAAAB8iQktAAAAAMCXEiKRSCTeg5Ckhga3uqQk79qkxrrYB3TSwaNBs6x+n5WbZVl6\nsyTsVHfttdKbb3rUpO8xGFGzg71zzbK6qn7H9rsV5uRI+zuurUnPMRjR55KT7bLeeccu69o8u9d3\nebX36zsclsodXrrhyvcNRnRSRoZZVFN6X7OsQFmpWVZ5YpZnjetjX1FhMKCTRg51fDNysL8sySwr\np9Fu31qV7r1vTUuTqqq8s2prDQZ00vPP22X9YEGTWdbsB+y++//lUw7jCgSkJu+6/SW2axK9etll\n9Ttotz+syR5mlpXo8EO7YFCqc3ibsdzv5KQ6vNgc7a9OM8tKTzeLUihkl9XVjBwZ7xG0b/v2eI/g\n/GGFFgAAAADgS0xoAQAAAAC+xFGOAQAAACAKHOU4/lihBQAAAAD4EhNaAAAAAIAv0XIMAAAAAFGg\n5Tj+WKEFAAAAAPgSE1oAAAAAgC/RcgwAAAAAUaDlOP5YoQUAAAAA+BITWgAAAACAL9FyDAAAAABR\noOU4/lihBQAAAAD4EhNaAAAAAIAv0XIMAAAAAFGg5Tj+WKEFAAAAAPgSE1oAAAAAgC/RcgwAAAAA\nUaDlOP66zIQ2qbHOsTDoXVtfH/uATup3pMwsS5mZZlG/fy1olnVLXqljZZauzfSoTbf7G/s11phl\nqbLSLsvwedRnye61yR3XFhfHOJYz5OXZZWVk2GXVyW7b79bNrm5X4rDYBnOaQelmUQrU2r2OSpVl\nlpWV0eRQFVDYoS4jw67Z6K23k8yyxvTZb5algQPtsqrtolJS7LIWLLDLmv2A3Tbxy6dctlU3X73J\ne1z/8R9udStXWozoc/0ucvwc5uIiu+211nB7Dae47A9DCjp8/khNDcU+oFPeeccsqj5zvFlWba1Z\nlEKGDxdwJlqOAQAAAAC+1GVWaAEAAADAT2g5jj9WaAEAAAAAvsSEFgAAAADgS7QcAwAAAEAUaDmO\nP1ZoAQAAAAC+xIQWAAAAAOBLtBwDAAAAQBRoOY4/VmgBAAAAAL7EhBYAAAAA4Eu0HAMAAABAFGg5\njj9WaAEAAAAAvsSEFgAAAABwVuvWrdOECRM0bNgwTZo0SRs3bnS63euvv64rrrii3X979uwxuQ9a\njgEAAAAgChdCy/Gzzz6rpUuXasKECSooKNCmTZs0b948JSQkaOLEiR3edu/evUpISNCSJUsUCLRe\nS+3fv7/JfTChBQAAAAC0UVNToxUrVujmm2/Wz372M0nSHXfcobvvvltLly7VjTfeqG7dup319nv3\n7lU4HNaUKVPO2X3QcgwAAAAAaGPz5s2qq6vTtGnTWi4LBAK688479fHHH+vdd9/t8PZ79+5VTk7O\nOb0PJrQAAAAAEIXGxq75z8rOnTslSUOGDGl1+eDBg1td355IJKL9+/dr4MCBkqQTJ06osZ3BxXIf\nEhNaAAAAAEA7Dh06pN69e6tnz56tLu/Tp48kqby8/Ky3PXDggI4fP67S0lJNmjRJw4cPV15enubO\nnauqqiqT+5C60m9oO/NVgkdtU2pajIP5XKCiwixrV0nQLGvCBLMoNSVmOdUFJDVldlxr+Y1QUnXH\nG2+nZGaaRTUlJpllBQy3+5HJu2IcTWt7igebZfXubRal+nq7rI8+8q7p18+tbqS2xz6gU3ba7Zp3\nJQ4zyxqcWWOWpR3F3jUjR0o7dnjX5Y2MfTwnjRlwyCxr886OW6w6Y6Dhu7Xr7jA11bvmtddiG8vp\nxme8b5b1y6eGmmV99Sa77/7/Y2OTQ1XAqe7JFbZrEmPG2H1GsXwdZWTYjUsVtd41oZBU612XmBIy\nGNBJgwaZRWU6vG5dVVfbZaHr+eSTTzq8PhgMqlevXjp27JiSk5PbXH/qsuPHj581Y+/evZKk9957\nT7NmzVJmZqa2bdum1atXq7i4WC+++KKSk5Njug+pK01oAQAAAMBHIhGXL6rioeMvvcaOHdvh9Q88\n8IDmzp2rSCSihISEs9Z1dN2ll16qOXPmaNKkSRowYIAkKT8/X5dddpkWLlyo9evXa/r06THdh8SE\nFgAAAAAuKIsWLerw+iuvvFJS80ptfTvtcacu69Wr11kzcnNzlZub2+by2267TT/+8Y/11ltvafr0\n6THdh9SJCe2WLVv05JNPqqioSCkpKZowYYK++93vtrqDAwcO6Cc/+Ym2bt0qSbr++uu1YMECpaXZ\ntQADAAAAAKJ3++23O9X1799fR44cUUNDg5KSPv/Z3aFDzT8t6NevX6fvu3v37gqFQqqrqzO5D6cf\nYGzZskX33nuv/va3v+l73/ueJk+erH/+53/Wfffdp6am5mX2w4cP65vf/KZ27Nih++67T/fcc482\nb96se+65Rw0NDZ3+QwEAAACga/usi/6zMWTIEEUiEe3evbvV5af+f9VVV531tsuXL9cNN9yg2jN+\nl15dXa2qqipdcsklMd+H5LhC+/jjj6t///56/vnnW36c279/fxUWFuqNN97Qddddp+eee04VFRV6\n+eWXdfnll0uShg8frnvuuUcvvfSS7rjjDpe7AgAAAAB0Adddd5169OihNWvWaPjw4ZKkpqYmrVu3\nTpdccony8vLOettwOKyysjKtX79eBQUFLZevXLlSkjRp0qSY70NymNCeOHFCF198scaPH9/q6FOj\nR4+WJP3lL3/Rddddp40bN2r06NEtk1lJuvbaazVgwABt3LiRCS0AAAAA+MjFF1+s2bNn6+c//7ki\nkYiuueYavfLKK9q2bZuWLVumbt26tdS+dvLQ9/n5+ZKkKVOm6IUXXtDjjz+ukpIS5ebmasuWLXr1\n1Vc1depUjRo1qtP30R7PCW2PHj307LPPtrn81BJwOBzWkSNHdODAAd14441t6oYMGaLXX3/d624A\nAAAAwGfs2nttdTdLmjNnjnr27Km1a9dq06ZNys7O1vLlyzXhjPOILl68WNLnE9ru3btr1apVeuKJ\nJ7Rp0yatX79el156qR566CHNmDEjqvtoT6ePcvzRRx/prbfe0k9+8hPl5ubqK1/5iv76179Kav8H\nu3369NHRo0d19OhRXXTRRZ29OwAAAABAnCQkJGjmzJmaOXNmh3WbN29uc1lqaqoKCwtVWFhoch/t\n6dSEtrq6WuPGjZMk9ezZUw8//LB69OihY8eOtVx2ph49ekiS6urqmNACAAAAAMwkRCKRiGvxkSNH\n9Oc//1kNDQ1as2aNdu/erWXLlqlPnz6aNm2aFi1a1OYQ0MuWLdNTTz2lN954Q3379j17+GefSR79\n0QAAAAD8o7RUysqK9yjOnYSEY/EeQrsikY7P3fr3pFMrtL1799bEiRMlSRMmTNDNN9+sJUuW6Kmn\nnpLUfACpM526LCUlpePwY44bQygk1dR0WNKUEnLLchAo2mWWtUuDzbIGDjSLUqLjVhAISCfP0nRW\njY2xj+eUpMpyu7D0dLOopsQk7yJHgbJSt8KsrOZ3hI6ccUj0WO1JtNtee/c2i1J3u5+EqKTEu2bk\nSGn7doc6ORS5cn1ROtiVOMwsa3Bmx/veTiku9q5xfPCb8kYaDKhZoPKQWdbmnR18idtJlvv8zEzv\nGpf9vSSdPP6HifEZ79uFDR1qFvXVm5zOcOjkPzY6PKiOD/6TK+zGJUljxhhmDbB7HTWl272OAhUO\nnyvCYancu64mJWwwomahasfPAg5qUu1mjtXVZlHAORX13jA5OVnXX3+9Pv7445aV108++aRN3aFD\nhxQKhRQMBqMfJQAAAAAAZ/Cc0O7bt0/jxo3T2rVr21x37NgxJSQkKCkpSZmZmfrggw/a1OzatUtD\nDb8pBQAAAICuoamL/rtweE5oL7vsMh09elS//e1v1dDQ0HL5Rx99pFdeeUWjRo1SSkqKxo8fry1b\ntmjfvn0tNW+++aY+/PDDljZlAAAAAACseP5QKzExUQ8//LDmz5+vu+++W7fccosOHz6stWvXKhAI\n6Ic//KEkadasWdqwYYMKCgp077336sSJE1q1apWGDBmiyZMnn/M/BAAAAABwYXE68sjkyZNbToy7\nZMkSBYNBXXPNNZo7d64GDBggSUpLS9Pzzz+vJUuW6Mknn1RycrLy8/M1f/58JSXZHUQHAAAAALqG\nz+I9gAue86E0J06c6Nk6nJOTo2eeeSbmQQEAAAAA4MX2mO8AAAAAAJwndic7BAAAAIALCi3H8dZl\nJrS7ykJOdYMHe9cOTtxjMaRmjY1mUYNT9ptllVbkmGVlVTuezH7YMAV2dlyblGi4SWVkmEU1Jdr9\njjvwzlazLMu/0TRLUmayXVZwp91jVjd0tFmWqcpKu6z8fLOoxp1mUdpf6bafdtGYMtKzJlfSHoe6\nzHqDAZ1UUdvXLOuaa8yiFFSdXVitw/taKKRAbY1n2dixdtuEKlPNovaX2DWgrVxpFqUnV3iP6zvf\ncax70Pa0HIsfs3vMxixIN8vy+tzRKS776XBYKiryLAtlVBsM6KTMTLOo3bvNojTmSu99gDvDfQVw\nBlqOAQAAAAC+1GVWaAEAAADAX2g5jjdWaAEAAAAAvsSEFgAAAADgS7QcAwAAAEBUaDmON1ZoAQAA\nAAC+xIQWAAAAAOBLtBwDAAAAQFRszwmNzmOFFgAAAADgS0xoAQAAAAC+RMsxAAAAAESFoxzHGyu0\nAAAAAABfYkILAAAAAPAlWo4BAAAAICq0HMcbK7QAAAAAAF9iQgsAAAAA8CVajgEAAAAgKrQcxxsr\ntAAAAAAAX+oyK7SD0w85Vvb1rq01/LNSUsyi3q/NMcsapvfNskpThznVZTnUZmU2GYyoWV293fct\nwYpys6ymq0ebZTU2utUlSWrIyOq4prEu9gGdJlix3y4sO9ssqqzMLErJyXZ1VVePj20wp0kr3mOW\nNXRorlmW6/bqIinRZV8RUO5AhzrDgeUkVphl1anj12ynVFbaZbkIhaTqas+yoz1CZncZTLR77+7V\nwyxK/S6y27eOGRN0rPOuWfyY7ZrEDxbYvX/PKLAb24oVbp9RXIQSd7kVZmR41wwcGNtgTvN+UZJZ\n1pgRDWZZKiqxyxpm9zwCZ+oyE1oAAAAA8BdajuONlmMAAAAAgC8xoQUAAAAA+BItxwAAAAAQFbvf\nnyM6rNACAAAAAHyJCS0AAAAAwJdoOQYAAACAqHCU43hjhRYAAAAA4EtMaAEAAAAAvkTLMQAAAABE\nhZbjeGOFFgAAAADgS0xoAQAAAAC+RMsxAAAAAESFluN4Y4UWAAAAAOBLTGgBAAAAAL5EyzEAAAAA\nRIWW43hjhRYAAAAA4EtMaAEAAAAAvtR1Wo7r681qD/bKiXEwnyspMYvSmP6lZll16cPMsrKqyx0r\nw8pK7Li2qjoc+4BOSk01izINC1RXmWVV1KY51WVlSRUVHjWJ1QYj+pzl6+iI4dCys+2yXA0c6F2T\nVF9zfu/QUaCxwSyrtjbJLKuoyPv71Guvld78H4e69BKDETWry8w1ywoWv2+WZblN7CoJetYMlrSr\nNsu7Lr3OYETNmpLt3j/67TR87C+ye+zHDDjkUNXXqW7MgvTYB3SaGQV2axyrn2syyypcZDeuBx8c\n7FmTJqkqw7su1fATdKLlp3HLsM58Nr+g2W3viA4rtAAAAAAAX+o6K7QAAAAA4CscFCreWKEFAAAA\nAPgSE1oAAAAAgC/RcgwAAAAAUaHlON5YoQUAAAAA+BITWgAAAACAL9FyDAAAAABRoeU43lihBQAA\nAAD4EhNaAAAAAIAv0XIMAAAAAFGh5TjeWKEFAAAAAPgSE1oAAAAAgC/RcgwAAAAAUWmK9wAueKzQ\nAgAAAAB8iQktAAAAAMCXaDkGAAAAgKhwlON4Y4UWAAAAAOBLCZFIJBLvQUiS6urc6oJB79pEu4Xn\n0ooks6ys+j1mWbsac82y/s//cavr1086eNCjpntV7AM6pb7eLKomJWyWVVtrFqXUVLc6l80+OTn2\n8ZyuosIuK5xst128X5ZmljUs02FcaWlSlUOd5YZh+WQa7g9rEu0e+5BqHIpCUo1DnaG6xJBZVrDR\ncOw7dthlZWR41+TmSnu837OaBtq9FzU2mkVZvn2YvrRdHvpAQGpyOMZMYOf7sQ/oNDXZw8yyli83\ni9IjD9sdcKdwkfc6ziOPSIWF3ll5eQYDOmnCBLssS0mNjp/NXQSDdlldTELCH+I9hHZFIl10wzoH\naDkGAAAAgKjQchxvtBwDAAAAAHyJCS0AAAAAwJdoOQYAAACAqNByHG+s0AIAAAAAfIkJLQAAAADA\nl2g5BgAAAICo2J1aCtFhhRYAAAAA4EtMaAEAAAAAvkTLMQAAAABEhaMcxxsrtAAAAAAAX2KFFgAA\nAABwVuvWrdPq1atVXl6uyy67TA888IBuuummDm+zYMEC/eu//utZrx89erTWrFkjSXr99dc1e/bs\ndutefvll5ebmnjWHCS0AAAAAROXvv+X42Wef1dKlSzVhwgQVFBRo06ZNmjdvnhISEjRx4sSz3m7q\n1Kn64he/2ObyV199Va+99pr+8R//seWyvXv3KiEhQUuWLFEg0LqJuH///h2OjwktAAAAAKCNmpoa\nrVixQjfffLN+9rOfSZLuuOMO3X333Vq6dKluvPFGdevWrd3bjhgxQiNGjGh1WXl5uQoLCzV27Fjd\nc889LZfv3btX4XBYU6ZM6fQY+Q0tAAAAAKCNzZs3q66uTtOmTWu5LBAI6M4779THH3+sd999t1N5\njz32mE6cOKGFCxcqISGh5fK9e/cqJycnqjEyoQUAAACAqHzWRf/Z2LlzpyRpyJAhrS4fPHhwq+td\nfPDBB3r11Vc1ffp0ZWVltVweiUS0f/9+DRw4UJJ04sQJNTY2OucyoQUAAAAAtHHo0CH17t1bPXv2\nbHV5nz59JDW3ELv6xS9+oaSkpDYHfzpw4ICOHz+u0tJSTZo0ScOHD1deXp7mzp2rqqoqz1x+QwsA\nAAAAF5BPPvmkw+uDwaB69eqlY8eOKTk5uc31py47fvy40/0dPHhQ//mf/6kpU6YoLS2t1XV79+6V\nJL333nuaNWuWMjMztW3bNq1evVrFxcV68cUX2x3DKV1mQlteHXSqCwe9a8PFf7IYkiQpa+hQsyzp\n7E9EZw1WqVmWuqc4FqapX3ePb0kSDTep9HSzqFCl+7dHXhJTw2ZZwWrHcQXDnrUHu9mNS5LCZVvN\nshryRptlDRpkFqWa+jTPmpCkmkSHusqS2Ad0Umn6SLOsLMN9RUi1ZlkqLvauGTdOeucd77rrr495\nOKcEd2w3y2rKs3seNfbLZlGBykNuhampniUlJbGN5XQ5qd7fwrtqTPZ+zboKp9SYZanC4TUUDitQ\n4fDeUFkZ+3hOE0rcZZb14IODzbIKF9k1Ez7ycJNDVcCpbv4Cu3Hdkmf4mS7F9TOdt9Jau9fRad2l\nf4f8eZTjsWPHdnj9Aw88oLlz5yoSibT6reuZOrrudP/yL/+ixsZGTZ8+vc11l156qebMmaNJkyZp\nwIABkqT8/HxddtllWrhwodavX9/u7U7pMhNaAAAAAMC5t2jRog6vv/LKKyU1r9TW19e3uf7UZb16\n9XK6v82bNys7O1uD2lmZyM3Nbfc8s7fddpt+/OMf66233mJCCwAAAABodvvttzvV9e/fX0eOHFFD\nQ4OSkpJaLj90qLnbp1+/fp4Zn376qXbu3KlZs2Z1aozdu3dXKBRSXV1dh3XO/RJbtmzRtGnTNGLE\nCH3pS1/So48+qmPHjrWq+frXv64rrriizb/vfOc7nRo8AAAAAHR9TV30n40hQ4YoEolo9+7drS4/\n9f+rrrrKM+Pdd99VJBLRF7/4xXavX758uW644QbV1rb+WUZ1dbWqqqp0ySWXdJjvtEK7ZcsW3Xvv\nvRoyZIi+973v6eOPP9bq1au1c+dOrV27VoFAQJFIRPv27VN+fr7Gjx/f6vZegwAAAAAAdC3XXXed\nevTooTVr1mj48OGSpKamJq1bt06XXHKJ8vLyPDOKiookqd12Y0kKh8MqKyvT+vXrVVBQ0HL5ypUr\nJUmTJk3qMN9pQvv444+rf//+ev7551uOMNW/f38VFhbqjTfe0HXXXaeysjLV1dXphhtu0OTJk11i\nAQAAAABd1MUXX6zZs2fr5z//uSKRiK655hq98sor2rZtm5YtW6Zu3bq11L722muSmg/odLq//vWv\n6tmzZ5ujG58yZcoUvfDCC3r88cdVUlKi3NxcbdmyRa+++qqmTp2qUaNGdThGzwntiRMndPHFF2v8\n+PGtDpc8enTzUUv/8pe/6LrrrlPxySNWXn755V6RAAAAAPB3wJ9HOe6MOXPmqGfPnlq7dq02bdqk\n7OxsLV++XBMmTGhVt3jxYkltJ7TV1dVK6eAI3N27d9eqVav0xBNPaNOmTVq/fr0uvfRSPfTQQ5ox\nY4bn+DwntD169NCzzz7b5vJTfdPhcPOpQk6dP+jUhLaurk7BoNupeAAAAAAAXU9CQoJmzpypmTNn\ndli3efPmdi9/5plnPO8jNTVVhYWFKiws7PT4On0SrY8++ki/+93v9Oijjyo3N1df+cpXJDVPaHv1\n6qUlS5ZoxIgRGjFihPLz87Vx48ZODwoAAAAAAC8JkUgk4lpcXV2tMWPGSJJ69uypp59+uuX/U6ZM\n0a5du3TjjTdq0qRJqqmp0erVq1VUVKSf/OQnuvXWWzvM/tvfpO7dY/hLAAAAAHQppaVSVla8R3Hu\nJCSsivcQ2hWJ3BfvIZw3nZrQHjlyRH/+85/V0NCgNWvWaPfu3Vq2bJluvPFG/eY3v1FTU5Puuuuu\nlvr6+nrdfPPNOn78uP70pz+1+tHwmcrL3cYQDnvXhov/5BbmYuhQu6wzDkXdZXTQ095KWppUVdVx\nTaLhqY1P+812zCorzaLqUsNmWcFquw3/YDe7cUlSv79uNctqyBttlmWpnfOEtxEKSTU1DnXF22Mf\n0Eml6SPNsrJUapZl6uRxFzo0bpx0lvalVq6/PubhtNixwyyqKc/uebQUqDzkXdS3r3TIu25/bV+D\nETXLSfV4f+mEuuT2DzwSjWCjww7AlcvnAJcPOpJ08qihZjIyzKKqMgabZa1YYRalRx52OJVJICA1\nedfNX9DpJsezWvqg4X7a9TOdg9Jau9cRE9rz70Ka0Hbq1di7d29NnDhRt956q9auXatwOKwlS5ZI\nkqZNm9ZqMitJycnJmjx5siorK1sOGgUAAAAAgIWov15KTk7W9ddfr48//lhVHazanTo8c11dXbR3\nBQAAAABd0Gdd9N+Fw3NCu2/fPo0bN05r165tc92xY8eUkJCg48eP66abbtKKdvpCPvzwQ0lSZmam\nwXABAAAAAGjmOaG97LLLdPToUf32t79VQ0NDy+UfffSRXnnlFY0aNUqXXHKJampq9OKLL6r2tN+H\nlJeX63e/+53GjBmjPn36nJu/AAAAAABwQfI8gk9iYqIefvhhzZ8/X3fffbduueUWHT58WGvXrlUg\nENAPf/hDSdLChQs1Z84cfeMb39Dtt9+uY8eOae3atUpMTNTChQvP+R8CAAAAAOfXhdXe2xU5HZJ2\n8uTJ6t69u1atWqUlS5YoGAzqmmuu0dy5czVgwABJUn5+vlauXKmnn35aP/3pT5WcnKzRo0dr3rx5\nuvzyy8/pHwEAAAAAuPA4n2Nl4sSJmjhxYoc1+fn5ys/Pj3lQAAAAAAB4MTxpKAAAAABcSBzOb4xz\nqstMaMPpDd5FkqQkz9qmjC/HPqCTAmWGJ7s2PGm508nZHf1pp9uJs7/8Ze/aoUMtRtQsrWSPWdZb\nh3PNskakm0VJ6Z0I86g9URHjWM5UUmIWVTtwtFlWWsUus6zG7MFOdYkue8rOPJcestKa92r3AAAR\nLElEQVTtTnNWVW93Nvu0svfNspSdbVe3c2csI2mlPGOkWVbY8ENOXX3UZ9lrI5iS4lboUJdTb/ce\n2ZBit61WlJlFKTU1ZJaVmOKdFZJUkxL2rsuoNhjRaQYONItKNfx0mZdnlzV/gffraOlSx7rH7F7f\nm//Lbtsfl3f2U2l2luuuAog3u3dIAAAAAADOoy6zQgsAAAAA/sJRjuONFVoAAAAAgC8xoQUAAAAA\n+BItxwAAAAAQFVqO440VWgAAAACALzGhBQAAAAD4Ei3HAAAAABAVWo7jjRVaAAAAAIAvMaEFAAAA\nAPgSLccAAAAAEBVajuONFVoAAAAAgC8xoQUAAAAA+BItxwAAAAAQFVqO440VWgAAAACALzGhBQAA\nAAD4Ei3HAAAAABCVpngP4ILHCi0AAAAAwJcSIpFIJN6DkKSaGre6UMi7NlRbHvuATikpMYsqz77W\nLCtcvcssSykpbnVZWVJpaYclVSlZBgNqlpZcZ5al5GSzqKpqu++B0mo7fjxbODz2TZl2j70kBaqr\n7MLKyuyyBg2yyyoq8q4ZNkx6/33PsoZBwwwGZK+21i4r0bCnx2Vc4bBU7rA7D6ca7iss/8jqarss\nw32Y0z4/EJCaHFYdDN8ja9JzzLJCjYb7r3fescty2X857O8lSampsY/nNO+XhMyyLF9GAwfaZSVV\nODyujo//5mK799xx19ut8P1yld1nlNnX7zHLUm6uXVYXk5Dw43gPoV2RyA/jPYTzhpZjAAAAAIgK\nRzmON1qOAQAAAAC+xIQWAAAAAOBLtBwDAAAAQFRoOY43VmgBAAAAAL7EhBYAAAAA4Eu0HAMAAABA\nVGg5jjdWaAEAAAAAvsSEFgAAAADgS7QcAwAAAEBUmuI9gAseK7QAAAAAAF9iQgsAAAAA8CVajgEA\nAAAgKhzlON5YoQUAAAAA+BITWgAAAACAL9FyDAAAAABRoeU43lihBQAAAAD4EhNaAAAAAIAvJUQi\nkUi8ByFJ2rXLrW7wYO/aQYNiH89Ju4rs5vwDB5pF6fBhu6x+F9W5FQaDUp1HbXJy7AM6qbTM7rHP\nKnvTLKs8+1qzrHDiIbfCvn2lQx61tbWxD+h0mZl2WfX1dlmNjXZZLtury3YvqSk5aDCgZoGKcrOs\nmpSwWVaoutQsy0lWllR6nu8zPd0u6513zKJq8r5sluXyEkpLk6qqHOoaHfdhLgwf+/0ldu8flrsv\nl91qKCTV1HjX7d4d+3hON2ZEg11Yot0v2hoa7Z7LpFqXjdpx4zf0y/VpZlmz72syy5q/wO6xX7rU\nLKrLSUj4f+I9hHZFIv833kM4b1ihBQAAAAD4EhNaAAAAAIAvcZRjAAAAAIgKRzmON1ZoAQAAAAC+\nxIQWAAAAAOBLtBwDAAAAQFTsjiyN6LBCCwAAAADwJSa0AAAAAABfouUYAAAAAKLCUY7jjRVaAAAA\nAIAvMaEFAAAAAPgSLccAAAAAEBVajv//9u4/psq6/+P4C2hwwBPeOtE7cKZ383grRtKEnGuTGCkD\nDF2pWc6Mymr8I6yZtmrlMr7RFiVurSX/SKDFna1vw2WxVmvFdIV/pHFQyKYpX6Hk5wEP/ri+f3Rz\n7pvgyAVc1/khz8fmH36u9/nw8c37c833ua5zrmDjCi0AAAAAICzR0AIAAAAAwhK3HAMAAADAuHDL\ncbBxhRYAAAAAEJa4QgsAAAAA48IV2mDjCi0AAAAAICyFzBXaXf9aZCru5ZdHj92xw4oV/elvf7Nu\nrujeS5bNNcvba9lc6rpsLs7lkn777cYxf//7xNfzb7/9Fm/ZXHPmzrVsrsRb2iybq88501RcnInY\nuF4La0LSgKItmyv6xA+WzaVlyyyb6sL/jf6eXmKcdKEzbtQ4t9uKFf1p6dJEy+aKv6XPsrk0Y4Z1\nc129ai7OzEnY4ZjYWv5bc7N1c/3zn5ZNNdqpdywWze42ERWv6beMHne219w5zAxnp2VTWVqqVp5a\nO038G+PjzcXds9DM73EM3L9aN9dlk/+vMCF68WLL5jrbO33UmDnTzcU5nVas6E9bM05ZNtf2HS7L\n5ir9n+uWzcU1NNgpZBpaAAAAAAgv3HIcbLxdAgAAAAAISzS0AAAAAICwxC3HAAAAADAuVn7WGOPB\nFVoAAAAAQFiioQUAAAAAhCVuOQYAAACAceFbjoONK7QAAAAAgLBEQwsAAAAACEvccgwAAAAA48It\nx8HGFVoAAAAAQFiioQUAAAAAjOrs2bNKSUnR0aNHTb+murpa2dnZSklJ0erVq1VbWzuhuL+ioQUA\nAACAcbkWon+s193drcLCQnm9XtOvqaio0KuvvqoFCxbohRde0MyZM1VcXKzDhw+PK24kNLQAAAAA\nAL9aWlq0YcMGnTp1yvRruru7tXfvXuXl5emdd97Rww8/rPfff19Lly5VaWmprl27NqY4f2hoAQAA\nAAAj+uSTT5Sfn6/Ozk6tW7fO9Ou++uor9fX1aePGjb6xyMhIPfLII2ptbdXx48fHFOcPDS0AAAAA\njMv1EP1jnaamJuXm5uqzzz7T3Xffbfp1J06ckCQlJycPGV+0aNGQ42bj/OGxPQAAAACAERUXFys6\nOnrMr2tra9PUqVMVGxs7ZDwhIUGSdOHChTHF+UNDCwAAAACTSHt7+w2Px8XFacqUKZI0rmZWkjwe\njxwOx7DxwbH+/v4xxfkTMg3tyy/bEztRiYlWzjbdwqksnGssXK6A/ajly62czdJfpGXixhI7WvA/\n/jGRpQwzvlOXH9b+Mi1jdn+bibP2XGGlsVRZCIqPD+zP+/ftTaFm0UwrZzOZUxO5nxPgX08wBLoE\nJWnOHDNRFi8sJcXa+UKQubyaj7PMdOv+b1VaatlU4pOJ5hjG/wZ7CeNy77333vD4M888o6Kiogn9\nDMMwFBER4ff44DGzcf6ETEMLAAAAALDfa6+9dsPjCxcunPDPiIuL0+XLl4eND44NXgE2G+cPDS0A\nAAAATCJj+bbi8brtttvU1dWlgYGBIbctt7W1SZJmzZo1pjh/uJcAAAAAAGCp5ORkGYahxsbGIeOD\nf7/zzjvHFOcPDS0AAAAAwFIrVqxQTEyMKisrfWPXr19XdXW1kpKStGTJkjHF+cMtxwAAAACACamr\nq5MkZWVlSZKmTZumrVu3qry8XIZhaNmyZTpy5Ih+/PFHlZWVKSoqakxx/tDQAgAAAAAm5PXXX5f0\nn4ZWkgoLCxUbG6uqqip9+eWXmjt3rt5++21lZ2cPea3ZuJFEGIZhWPtPsd65c+f0xhtv6NixY5Kk\njIwM7dixQ9OD9eiaSeahhx7STz/9NGx81apV2rNnTxBWdPN76aWX9Ouvvw659UJiLwSCv9yzD+zx\n7bff6t1339XJkycVGRmpu+66S9u2bRtyexF1bw8zuafu7VFfX689e/bI7XbL6XQqOztb27ZtG/JN\nntS9PczknroHwkvIX6Ht6OjQY489poGBAT355JO6du2aKioq1NTUpJqamnE/6BfmGIahlpYWZWVl\naeXKlUOOJSUlBWlVN7eamhp99NFHSk9PHzLOXrCfv9yzD+xx7NgxPfXUU5o/f76Kiop09epVVVdX\na9OmTaqurlZKSgp1bxMzuafu7VFfX6+CggIlJyfrueeeU2trq/bv368TJ06oqqpKkZGR1L1NzOSe\nugfCkBHi3nrrLWPhwoVGc3Ozb+y7774zXC6X8eGHHwZxZZPD2bNnDZfLZXz88cfBXspN7+rVq0Z5\nebmxYMECw+VyGZs2bRpynL1gn9Fyzz6wR35+vpGRkWH09fX5xtrb2420tDRjy5YthmFQ93Yxk3vq\n3h5r16417rvvPqO/v9839sEHHxgul8v4+uuvDcOg7u1iJvfUPRB+Qv5bjmtra5Wenq477rjDN7Z8\n+XLNmzdPtbW1QVzZ5NDc3CxJQ/IP63m9Xq1du1bl5eXKz88f8Xlb7AV7mMk9+8B6XV1dcrvdys7O\nVmxsrG98xowZSktL0/HjxyVR93Ywm3vq3nper1fTpk3T+vXr5XA4fOODd4U0NTVJou7tYDb31D0Q\nfkL6luOuri6dO3dOq1atGnYsOTlZ33zzTRBWNbmcPn1a0n9O7H19fYqLiwvmkm5KXq9Xvb29Kisr\nU05OjjIzM4ccZy/YZ7TcS+wDOzidTn3++edDGqpBHR0dioqKou5tYib3EnVvh5iYGFVUVAwbH3zW\nYmJiInVvEzO5l6h7IByF9BXaixcvStKIV0wSEhLU09Ojnp6eQC9rUjl9+rSmTJmikpISpaamKjU1\nVVlZWbxDbDGn06kvvvhCOTk5Ix5nL9hntNxL7AM7REVFae7cucNq2u12q6GhQampqdS9TczkXqLu\nA+H8+fM6dOiQdu/eLZfLpfvvv5+6D5CRci9R90A4CukrtB6PR5JGfBc5JiZG0p/vnN16660BXddk\n0tzcLI/Ho56eHpWWlqq7u1v79+9XcXGxrly5ojVr1gR7iTeFyMhIRUb6f3+JvWCf0XIvsQ8CxePx\n6Pnnn5ckbd26lboPoL/mXqLu7dbZ2em7IyQ2NlYvvviiYmJiqPsA8Jd7iboHwlFIN7SGiScKRURE\nBGAlk9f69et1/fp1Pfroo76x3Nxc5eXl6c0339Tq1atHfdgxJo69EFzsA/v19/fr2Wefldvt1tNP\nP6309HQ1NDSM+jrqfuJGyr1E3dstIiJCZWVlGhgYUGVlpR5//HGVlZUpISHB1Gsxfv5yv2rVKuoe\nCEMhfcvx4GcWvF7vsGODY06nM6Brmmw2btw45KQuSQ6HQ/n5+fr99999X54Ae7EXgot9YK/u7m4V\nFBTo6NGjevDBB1VUVCSJug8Ef7mXqHu7TZ06VTk5OVqzZo2qqqqUmJiokpIS6j4A/OVeou6BcBTS\nDe3gB/Tb29uHHWtra1N8fDwf1A+SwQe79/X1BXklkwN7ITSxDybujz/+0ObNm9XQ0KANGzZo9+7d\nvqtP1L29bpT7G6HuredwOJSRkaHW1lbNnDlTEnUfKP+d+0uXLvmNo+6B0BXSDW18fLxmz56tkydP\nDjv2888/a/HixUFY1eRx8eJF5ebmau/evcOOnTlzRpI0e/bsQC9rUmIvBA/7wD69vb164okn1NjY\nqC1btmjXrl1DGirq3j6j5Z66t0dLS4syMzNVVVU17JjH41FERISio6OpexuYyX1/fz91D4ShkG5o\nJWnlypWqr69XS0uLb+z777/XmTNnbvitpJi4WbNmqbu7WzU1Nert7fWNX7hwQYcOHdI999xj6rM+\nsAZ7ITjYB/bZtWuXGhsbtXnzZu3cuXPEGOreHqPlnrq3x+23366enh4dPHhQAwMDvvHz58/ryJEj\nSktLk9PppO5tYCb3SUlJ1D0QhiIMM982E0SXLl1SXl6eoqKiVFBQIK/Xq3379mnOnDk6ePCgoqOj\ng73Em1pdXZ0KCws1f/58rVu3Th6PR1VVVbpy5YoOHDjAg8dtkpmZqaSkJFVWVvrG2AuBMVLu2QfW\na2lpUU5OjuLj47Vz584Rv2QlPz+fureB2dxT9/b49NNPtX37di1ZskQPPPCAOjo6fHmtrq6Wy+Wi\n7m1iJvfUPRB+Qr6hlaRffvlFJSUl+uGHH+RwOLRixQpt377d93kG2Kuurk7vvfee3G63HA6H0tPT\nVVxczEndRiM1VRJ7IRD85Z59YK0DBw7olVdeuWFMU1OTJOreamPJPXVvj8OHD2vfvn06deqU4uLi\ntGzZMhUVFWnevHm+GOreHmZyT90D4SUsGloAAAAAAP4q5D9DCwAAAADASGhoAQAAAABhiYYWAAAA\nABCWaGgBAAAAAGGJhhYAAAAAEJZoaAEAAAAAYYmGFgAAAAAQlmhoAQAAAABhiYYWAAAAABCWaGgB\nAAAAAGHp/wGxE7KVpqRV5gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10484f7f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(20, 14))\n",
"im = plt.imshow(J_ridge_own, **cmap_args)\n",
"plt.title(\"Home-made ridge regression\", fontsize=18)\n",
"plt.xticks(fontsize=18)\n",
"plt.yticks(fontsize=18)\n",
"cb = fig.colorbar(im)\n",
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
"\n",
"fig = plt.figure(figsize=(20, 14))\n",
"im = plt.imshow(J_ridge_sk, **cmap_args)\n",
"plt.title(\"Ridge from Scikit-learn\", fontsize=18)\n",
"plt.xticks(fontsize=18)\n",
"plt.yticks(fontsize=18)\n",
"cb = fig.colorbar(im)\n",
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In other words, our implementation of ridge regression seems to match well with the benchmark from Scikit-learn. We can also see the same symmetry pattern as for OLS."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### LASSO regression\n",
"\n",
"In the _Least Absolute Shrinkage and Selection Operator_ (LASSO)-method we get a third cost function.\n",
"\n",
"\\begin{align}\n",
" C(X, \\omega; \\lambda) =\n",
" ||X\\omega - y||^2 + \\lambda ||\\omega||\n",
" = (X\\omega - y)^T(X\\omega - y) + \\lambda \\sqrt{\\omega^T\\omega}.\n",
"\\end{align}\n",
"\n",
"Finding the extremal point of this cost function is not so straight-forward as in least squares and ridge. We will therefore rely solely on the function ``Lasso`` from Scikit-learn."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n",
"J_lasso_sk = clf_lasso.coef_.reshape(L, L)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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V7aR/5ejXr19mz56dYcOGZcaMGbnjjjvS3NycmTNnprGxMUny5JNPZsqUKXny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\nMZJxxic7AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1109acf60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(20, 14))\n",
"im = plt.imshow(J_lasso_sk, **cmap_args)\n",
"plt.title(\"Lasso from Scikit-learn\", fontsize=18)\n",
"plt.xticks(fontsize=18)\n",
"plt.yticks(fontsize=18)\n",
"cb = fig.colorbar(im)\n",
"cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is quite striking how LASSO breaks the symmetry of the coupling constant as opposed to ridge and OLS. We get a sparse solution with $J_{j, j + 1} = -1$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Performance of the different models\n",
"\n",
"In order to judge which model performs best at varying values of $\\lambda$ (for ridge and LASSO) we compute $R^2$ which is given by\n",
"\n",
"\\begin{align}\n",
" R^2 = 1 - \\frac{(y - \\hat{y})^2}{(y - \\bar{y})^2},\n",
"\\end{align}\n",
"\n",
"where $y$ is a vector with the true values of the energy, $\\hat{y}$ is the predicted values of $y$ from the models and $\\bar{y}$ is the mean of $\\hat{y}$."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def r_squared(y, y_hat):\n",
" return 1 - np.sum((y - y_hat) ** 2) / np.sum((y - np.mean(y_hat)) ** 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is the same metric used by Scikit-learn for their regression models when scoring."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"y_hat = clf.predict(X_test)\n",
"r_test = r_squared(y_test, y_hat)\n",
"sk_r_test = clf.score(X_test, y_test)\n",
"\n",
"assert abs(r_test - sk_r_test) < 1e-2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Performance as function of the regularization parameter\n",
"\n",
"We see how the different models perform for a different set of values for $\\lambda$."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
" 0%| | 0/10 [00:00<?, ?it/s]/Users/Schoyen/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
" ConvergenceWarning)\n",
"100%|██████████| 10/10 [00:19<00:00, 1.91s/it]\n"
]
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x12f59bb38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lambdas = np.logspace(-4, 5, 10)\n",
"\n",
"train_errors = {\n",
" \"ols_own\": np.zeros(lambdas.size),\n",
" \"ols_sk\": np.zeros(lambdas.size),\n",
" \"ridge_own\": np.zeros(lambdas.size),\n",
" \"ridge_sk\": np.zeros(lambdas.size),\n",
" \"lasso_sk\": np.zeros(lambdas.size)\n",
"}\n",
"\n",
"test_errors = {\n",
" \"ols_own\": np.zeros(lambdas.size),\n",
" \"ols_sk\": np.zeros(lambdas.size),\n",
" \"ridge_own\": np.zeros(lambdas.size),\n",
" \"ridge_sk\": np.zeros(lambdas.size),\n",
" \"lasso_sk\": np.zeros(lambdas.size)\n",
"}\n",
"\n",
"plot_counter = 1\n",
"\n",
"fig = plt.figure(figsize=(32, 54))\n",
"\n",
"for i, _lambda in enumerate(tqdm.tqdm(lambdas)):\n",
" omega = get_ols_weights(X_train_own, y_train)\n",
" y_hat_train = X_train_own @ omega\n",
" y_hat_test = X_test_own @ omega\n",
"\n",
" train_errors[\"ols_own\"][i] = r_squared(y_train, y_hat_train)\n",
" test_errors[\"ols_own\"][i] = r_squared(y_test, y_hat_test)\n",
"\n",
" plt.subplot(10, 5, plot_counter)\n",
" plt.imshow(omega[1:].reshape(L, L), **cmap_args)\n",
" plt.title(\"Home made OLS\")\n",
" plot_counter += 1\n",
"\n",
" omega = get_ridge_weights(X_train_own, y_train, _lambda)\n",
" y_hat_train = X_train_own @ omega\n",
" y_hat_test = X_test_own @ omega\n",
"\n",
" train_errors[\"ridge_own\"][i] = r_squared(y_train, y_hat_train)\n",
" test_errors[\"ridge_own\"][i] = r_squared(y_test, y_hat_test)\n",
"\n",
" plt.subplot(10, 5, plot_counter)\n",
" plt.imshow(omega[1:].reshape(L, L), **cmap_args)\n",
" plt.title(r\"Home made ridge, $\\lambda = %.4f$\" % _lambda)\n",
" plot_counter += 1\n",
"\n",
" for key, method in zip(\n",
" [\"ols_sk\", \"ridge_sk\", \"lasso_sk\"],\n",
" [skl.LinearRegression(), skl.Ridge(alpha=_lambda), skl.Lasso(alpha=_lambda)]\n",
" ):\n",
" method = method.fit(X_train, y_train)\n",
"\n",
" train_errors[key][i] = method.score(X_train, y_train)\n",
" test_errors[key][i] = method.score(X_test, y_test)\n",
"\n",
" omega = method.coef_.reshape(L, L)\n",
"\n",
" plt.subplot(10, 5, plot_counter)\n",
" plt.imshow(omega, **cmap_args)\n",
" plt.title(r\"%s, $\\lambda = %.4f$\" % (key, _lambda))\n",
" plot_counter += 1\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that LASSO quite fast reaches a good solution for low values of $\\lambda$, but will \"wither\" when we increase $\\lambda$ too much. Ridge is more stable over a larger range of values for $\\lambda$, but eventually also fades away."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Finding the optimal value of $\\lambda$\n",
"\n",
"To determine which value of $\\lambda$ is best we plot the accuracy of the models when predicting the training and the testing set. We expect the accuracy of the training set to be quite good, but if the accuracy of the testing set is much lower this tells us that we might be subject to an overfit model. The ideal scenario is an accuracy on the testing set that is close to the accuracy of the training set."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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MDSS92/PoEwUA2FghM6z9N39Ghc6fVsGz8rbFlIoj39bLx56Ww6pcAAFBEAWs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\nAAAAlIUiCgAAAICy+D+dy/kL0wEutgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x13491a978>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(20, 14))\n",
"\n",
"colors = {\n",
" \"ols_own\": \"b\",\n",
" \"ridge_own\": \"g\",\n",
" \"ols_sk\": \"r\",\n",
" \"ridge_sk\": \"y\",\n",
" \"lasso_sk\": \"c\"\n",
"}\n",
"\n",
"for key in train_errors:\n",
" plt.semilogx(\n",
" lambdas,\n",
" train_errors[key],\n",
" colors[key],\n",
" label=\"Train {0}\".format(key),\n",
" linewidth=4.0\n",
" )\n",
"\n",
"for key in test_errors:\n",
" plt.semilogx(\n",
" lambdas,\n",
" test_errors[key],\n",
" colors[key] + \"--\",\n",
" label=\"Test {0}\".format(key),\n",
" linewidth=4.0\n",
" )\n",
"#plt.semilogx(lambdas, train_errors[\"ols_own\"], label=\"Train (OLS own)\")\n",
"#plt.semilogx(lambdas, test_errors[\"ols_own\"], label=\"Test (OLS own)\")\n",
"\n",
"plt.legend(loc=\"best\", fontsize=18)\n",
"plt.xlabel(r\"$\\lambda$\", fontsize=18)\n",
"plt.ylabel(r\"$R^2$\", fontsize=18)\n",
"plt.tick_params(labelsize=18)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the above figure we can see that LASSO with $\\lambda = 10^{-2}$ achieve a very good accuracy on the test set. This by far surpases the other models for all values of $\\lambda$."
]
}
],
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