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ML-Kurs-SS2023/notebooks/simple_neural_network_exercise_solution.ipynb

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added notebook with simple neural network example
2023-03-20 10:50:41 +01:00
{
"cells": [
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"# A simple neural network with one hidden layer in pure Python"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## A simple neural network class with ReLU activation function"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [],
"source": [
"# A simple feed-forward neutral network with on hidden layer\n",
"# see also https://towardsdatascience.com/how-to-build-your-own-neural-network-from-scratch-in-python-68998a08e4f6\n",
"\n",
"import numpy as np\n",
"\n",
"class NeuralNetwork:\n",
" def __init__(self, x, y):\n",
" n1 = 4 # number of neurons in the hidden layer\n",
" self.input = x\n",
" self.weights1 = np.random.rand(self.input.shape[1],n1)\n",
" self.bias1 = np.random.rand(n1)\n",
" self.weights2 = np.random.rand(n1,1)\n",
" self.bias2 = np.random.rand(1) \n",
" self.y = y\n",
" self.output = np.zeros(y.shape)\n",
" self.learning_rate = 0.00001\n",
" self.n_train = 0\n",
" self.loss_history = []\n",
"\n",
" def relu(self, x):\n",
" return np.where(x>0, x, 0)\n",
" \n",
" def relu_derivative(self, x):\n",
" return np.where(x>0, 1, 0)\n",
"\n",
" def feedforward(self):\n",
" self.layer1 = self.relu(self.input @ self.weights1 + self.bias1)\n",
" self.output = self.relu(self.layer1 @ self.weights2 + self.bias2)\n",
"\n",
" def backprop(self):\n",
"\n",
" # delta1: [m, 1], m = number of training data\n",
" delta1 = 2 * (self.y - self.output) * self.relu_derivative(self.output)\n",
"\n",
" # Gradient w.r.t. weights from hidden to output layer: [n1, 1] matrix, n1 = # neurons in hidden layer\n",
" d_weights2 = self.layer1.T @ delta1\n",
" d_bias2 = np.sum(delta1) \n",
" \n",
" # shape of delta2: [m, n1], m = number of training data, n1 = # neurons in hidden layer\n",
" delta2 = (delta1 @ self.weights2.T) * self.relu_derivative(self.layer1)\n",
" d_weights1 = self.input.T @ delta2\n",
" d_bias1 = np.ones(delta2.shape[0]) @ delta2 \n",
" \n",
" # update weights and biases\n",
" self.weights1 += self.learning_rate * d_weights1\n",
" self.weights2 += self.learning_rate * d_weights2\n",
"\n",
" self.bias1 += self.learning_rate * d_bias1\n",
" self.bias2 += self.learning_rate * d_bias2\n",
"\n",
" def train(self, X, y):\n",
" self.output = np.zeros(y.shape)\n",
" self.input = X\n",
" self.y = y\n",
" self.feedforward()\n",
" self.backprop()\n",
" self.n_train += 1\n",
" if (self.n_train %1000 == 0):\n",
" loss = np.sum((self.y - self.output)**2)\n",
" print(\"loss: \", loss)\n",
" self.loss_history.append(loss)\n",
" \n",
" def predict(self, X):\n",
" self.output = np.zeros(y.shape)\n",
" self.input = X\n",
" self.feedforward()\n",
" return self.output\n",
" \n",
" def loss_history(self):\n",
" return self.loss_history\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create toy data\n",
"We create three toy data sets\n",
"1. two moon-like distributions\n",
"2. circles\n",
"3. linearly separable data sets"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [],
"source": [
"# https://scikit-learn.org/stable/auto_examples/classification/plot_classifier_comparison.html#sphx-glr-auto-examples-classification-plot-classifier-comparison-py\n",
"import numpy as np\n",
"from sklearn.datasets import make_moons, make_circles, make_classification\n",
"from sklearn.model_selection import train_test_split\n",
"\n",
"X, y = make_classification(\n",
" n_features=2, n_redundant=0, n_informative=2, random_state=1, n_clusters_per_class=1\n",
")\n",
"rng = np.random.RandomState(2)\n",
"X += 2 * rng.uniform(size=X.shape)\n",
"linearly_separable = (X, y)\n",
"\n",
"datasets = [\n",
" make_moons(n_samples=200, noise=0.1, random_state=0),\n",
" make_circles(n_samples=200, noise=0.1, factor=0.5, random_state=1),\n",
" linearly_separable,\n",
"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create training and test data set"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [],
"source": [
"# datasets: 0 = moons, 1 = circles, 2 = linearly separable\n",
"X, y = datasets[1]\n",
"X_train, X_test, y_train, y_test = train_test_split(\n",
" X, y, test_size=0.4, random_state=42\n",
")\n",
"\n",
"x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5\n",
"y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Train the model"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
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"loss: 2.387205713503783\n",
"loss: 2.387205938855604\n",
"loss: 2.3872061633253967\n",
"loss: 2.3872063880939898\n",
"loss: 2.387206613272621\n",
"loss: 2.3872063644496766\n",
"loss: 2.387205417523893\n",
"loss: 2.387205642655334\n",
"loss: 2.3872058668390554\n",
"loss: 2.3872060910716635\n",
"loss: 2.3872063157741197\n",
"loss: 2.387206542322383\n",
"loss: 2.387206692745429\n",
"loss: 2.3872056660868344\n",
"loss: 2.3872055706534514\n",
"loss: 2.3872057946635303\n",
"loss: 2.387206019070375\n",
"loss: 2.387206245277133\n",
"loss: 2.387206470316894\n",
"loss: 2.3872066957452835\n",
"loss: 2.3872059933352743\n",
"loss: 2.3872054990132523\n",
"loss: 2.387205722878048\n",
"loss: 2.387205948575221\n",
"loss: 2.387206173353647\n",
"loss: 2.3872063984591825\n",
"loss: 2.3872066226559827\n",
"loss: 2.3872063207497023\n",
"loss: 2.3872054272954717\n",
"loss: 2.3872056526531233\n",
"loss: 2.3872058770925495\n",
"loss: 2.3872061007027394\n",
"loss: 2.387206325498709\n",
"loss: 2.387206552189155\n",
"loss: 2.3872066470668103\n",
"loss: 2.387205618564661\n",
"loss: 2.387205580450609\n",
"loss: 2.3872058044940334\n",
"loss: 2.3872060289891905\n",
"loss: 2.387206255311463\n",
"loss: 2.387206480708284\n",
"loss: 2.387206705586487\n",
"loss: 2.3872059484852777\n",
"loss: 2.387205508896236\n",
"loss: 2.387205733053314\n",
"loss: 2.3872059590012453\n",
"loss: 2.38720618326989\n",
"loss: 2.387206408350126\n",
"loss: 2.3872066339450995\n",
"loss: 2.3872062743922324\n",
"loss: 2.3872054376631935\n",
"loss: 2.3872056632364425\n",
"loss: 2.3872058871467248\n",
"loss: 2.387206111855699\n",
"loss: 2.387206337069455\n",
"loss: 2.3872065625907197\n",
"loss: 2.387206598875525\n",
"loss: 2.3872055726406853\n",
"loss: 2.3872055914219663\n",
"loss: 2.3872058158103724\n",
"loss: 2.3872060406633677\n",
"loss: 2.3872062658126643\n",
"loss: 2.3872064913732993\n",
"loss: 2.3872067166127193\n",
"loss: 2.38720589721323\n",
"loss: 2.3872055203865594\n",
"loss: 2.3872057448636044\n",
"loss: 2.387205969632241\n",
"loss: 2.3872061948051737\n",
"loss: 2.387206419656803\n",
"loss: 2.3872066454234093\n",
"loss: 2.38720622109226\n",
"loss: 2.3872054496058155\n",
"loss: 2.387205673994574\n",
"loss: 2.387205898781459\n",
"loss: 2.3872061232475654\n",
"loss: 2.3872063486162522\n",
"loss: 2.3872065743640327\n",
"loss: 2.38720654403819\n",
"loss: 2.3872055202172575\n",
"loss: 2.3872056032796642\n",
"loss: 2.3872058273645207\n",
"loss: 2.387206052339985\n",
"loss: 2.3872062776900504\n",
"loss: 2.3872065035141774\n",
"loss: 2.3872067282141374\n",
"loss: 2.3872058427484215\n",
"loss: 2.387205531994678\n",
"loss: 2.387205756582158\n",
"loss: 2.387205981539894\n",
"loss: 2.3872062069646356\n",
"loss: 2.387206431282743\n",
"loss: 2.387206657412996\n",
"loss: 2.3872061679858723\n",
"loss: 2.3872054613328837\n",
"loss: 2.3872056859037873\n",
"loss: 2.3872059109348127\n",
"loss: 2.387206134876376\n",
"loss: 2.387206360603658\n",
"loss: 2.3872065860311924\n",
"loss: 2.3872064904558536\n",
"loss: 2.3872054658487727\n",
"loss: 2.3872056154159624\n",
"loss: 2.387205838986268\n",
"loss: 2.3872060643164303\n",
"loss: 2.38720629000679\n",
"loss: 2.387206515465516\n",
"loss: 2.3872067402918593\n",
"loss: 2.3872057868542456\n",
"loss: 2.3872055436974926\n",
"loss: 2.387205768622451\n",
"loss: 2.3872059939050634\n",
"loss: 2.3872062189566643\n",
"loss: 2.387206443389059\n",
"loss: 2.387206669729105\n",
"loss: 2.387206114421231\n",
"loss: 2.3872054733876444\n",
"loss: 2.3872056982757286\n",
"loss: 2.3872059236497964\n",
"loss: 2.3872061471739836\n",
"loss: 2.38720637304622\n",
"loss: 2.387206597910911\n",
"loss: 2.3872064349529696\n",
"loss: 2.3872054090077848\n",
"loss: 2.3872056281842866\n",
"loss: 2.387205851329026\n",
"loss: 2.387206076790427\n",
"loss: 2.387206301261524\n",
"loss: 2.387206527494985\n",
"loss: 2.3872067526753113\n",
"loss: 2.387205728959938\n"
]
}
],
"source": [
"y_train = y_train.reshape(-1, 1)\n",
"\n",
"nn = NeuralNetwork(X_train, y_train)\n",
"\n",
"for i in range(1000000):\n",
" nn.train(X_train, y_train)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot the loss vs. the number of epochs"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'loss')"
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"plt.plot(nn.loss_history)\n",
"plt.xlabel(\"# epochs / 1000\")\n",
"plt.ylabel(\"loss\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.colorbar.Colorbar at 0x147ecf700>"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 900x700 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"from matplotlib.colors import ListedColormap\n",
"\n",
"cm = plt.cm.RdBu\n",
"cm_bright = ListedColormap([\"#FF0000\", \"#0000FF\"])\n",
"\n",
"xv = np.linspace(x_min, x_max, 10)\n",
"yv = np.linspace(y_min, y_max, 10)\n",
"Xv, Yv = np.meshgrid(xv, yv)\n",
"XYpairs = np.vstack([ Xv.reshape(-1), Yv.reshape(-1)])\n",
"zv = nn.predict(XYpairs.T)\n",
"Zv = zv.reshape(Xv.shape)\n",
"\n",
"fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(9, 7))\n",
"ax.set_aspect(1)\n",
"cn = ax.contourf(Xv, Yv, Zv, cmap=\"coolwarm_r\", alpha=0.4)\n",
"\n",
"ax.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap=cm_bright, edgecolors=\"k\")\n",
"\n",
"# Plot the testing points\n",
"ax.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap=cm_bright, alpha=0.4, edgecolors=\"k\")\n",
"\n",
"ax.set_xlim(x_min, x_max)\n",
"ax.set_ylim(y_min, y_max)\n",
"# ax.set_xticks(())\n",
"# ax.set_yticks(())\n",
"\n",
"fig.colorbar(cn)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
},
"vscode": {
"interpreter": {
"hash": "b0fa6594d8f4cbf19f97940f81e996739fb7646882a419484c72d19e05852a7e"
}
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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