225 lines
239 KiB
Plaintext
225 lines
239 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# Regresja wielomianowa"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 81,
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"metadata": {
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"slideshow": {
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"slide_type": "notes"
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}
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},
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"outputs": [],
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"source": [
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"import ipywidgets as widgets\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"import pandas\n",
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"\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 82,
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"metadata": {
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"slideshow": {
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"slide_type": "notes"
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}
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},
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"outputs": [],
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"source": [
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"# Przydatne funkcje\n",
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"\n",
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"def cost(theta, X, y):\n",
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" \"\"\"Wersja macierzowa funkcji kosztu\"\"\"\n",
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" m = len(y)\n",
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" J = 1.0 / (2.0 * m) * ((X * theta - y).T * (X * theta - y))\n",
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" return J.item()\n",
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"\n",
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"def gradient(theta, X, y):\n",
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" \"\"\"Wersja macierzowa gradientu funkcji kosztu\"\"\"\n",
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" return 1.0 / len(y) * (X.T * (X * theta - y)) \n",
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"\n",
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"def gradient_descent(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-7):\n",
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" \"\"\"Algorytm gradientu prostego (wersja macierzowa)\"\"\"\n",
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" current_cost = fJ(theta, X, y)\n",
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" logs = [[current_cost, theta]]\n",
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" while True:\n",
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" theta = theta - alpha * fdJ(theta, X, y)\n",
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" current_cost, prev_cost = fJ(theta, X, y), current_cost\n",
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" if abs(prev_cost - current_cost) > 10**15:\n",
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" print('Algorithm does not converge!')\n",
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" break\n",
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" if abs(prev_cost - current_cost) <= eps:\n",
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" break\n",
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" logs.append([current_cost, theta]) \n",
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" return theta, logs\n",
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"\n",
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"def plot_data(X, y, xlabel, ylabel):\n",
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" \"\"\"Wykres danych (wersja macierzowa)\"\"\"\n",
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" fig = plt.figure(figsize=(16*.6, 9*.6))\n",
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" ax = fig.add_subplot(111)\n",
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" fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n",
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" ax.scatter([X[:, 1]], [y], c='r', s=50, label='Dane')\n",
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" \n",
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" ax.set_xlabel(xlabel)\n",
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" ax.set_ylabel(ylabel)\n",
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" ax.margins(.05, .05)\n",
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" plt.ylim(y.min() - 1, y.max() + 1)\n",
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" plt.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n",
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" return fig\n",
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"\n",
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"def plot_fun(fig, fun, X):\n",
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" \"\"\"Wykres funkcji `fun`\"\"\"\n",
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" ax = fig.axes[0]\n",
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" x0 = np.min(X[:, 1]) - 1.0\n",
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" x1 = np.max(X[:, 1]) + 1.0\n",
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" Arg = np.arange(x0, x1, 0.1)\n",
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" Val = fun(Arg)\n",
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" return ax.plot(Arg, Val, linewidth='2')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 83,
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"metadata": {
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"slideshow": {
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"slide_type": "notes"
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}
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},
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"outputs": [],
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"source": [
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"# Wczytanie danych (mieszkania) przy pomocy biblioteki pandas\n",
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"\n",
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"alldata = pandas.read_csv('data_flats.tsv', header=0, sep='\\t',\n",
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" usecols=['price', 'rooms', 'sqrMetres'])\n",
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"data = np.matrix(alldata[['sqrMetres', 'price']])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 84,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"# Funkcja regresji wielomianowej\n",
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"\n",
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"def h_poly(Theta, x):\n",
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" \"\"\"Funkcja wielomianowa\"\"\"\n",
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" return sum(theta * np.power(x, i) for i, theta in enumerate(Theta.tolist()))\n",
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"\n",
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"def get_poly_data(data, deg):\n",
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" m, n_plus_1 = data.shape\n",
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" n = n_plus_1 - 1\n",
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"\n",
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" X1 = data[:, 0:n]\n",
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" X1 /= np.amax(X1, axis=0)\n",
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"\n",
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" Xs = [np.ones((m, 1)), X1]\n",
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"\n",
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" for i in range(2, deg+1):\n",
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" Xn = np.power(X1, i)\n",
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" Xn /= np.amax(Xn, axis=0)\n",
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" Xs.append(Xn)\n",
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"\n",
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" X = np.matrix(np.concatenate(Xs, axis=1)).reshape(m, deg * n + 1)\n",
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"\n",
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" y = np.matrix(data[:, -1]).reshape(m, 1)\n",
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"\n",
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" return X, y\n",
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"\n",
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"\n",
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"def polynomial_regression(theta, X, y, n):\n",
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" \"\"\"Funkcja regresji wielomianowej\"\"\"\n",
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" theta_start = np.matrix([0] * (n+1)).reshape(n+1, 1)\n",
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" theta, logs = gradient_descent(cost, gradient, theta_start, X, y)\n",
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" return lambda x: h_poly(theta, x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 85,
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"metadata": {
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"slideshow": {
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"slide_type": "subslide"
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}
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},
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"outputs": [
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{
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"output_type": "execute_result",
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"data": {
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"text/plain": [
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"[<matplotlib.lines.Line2D at 0x23797dfe880>]"
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]
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},
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"metadata": {},
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"execution_count": 85
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},
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{
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"output_type": "display_data",
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"data": {
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"text/plain": "<Figure size 691.2x388.8 with 1 Axes>",
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"image/png": "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
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
}
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"n = 2\n",
|
||
|
|
"x, y = get_poly_data(data, n)\n",
|
||
|
|
"fig = plot_data(x, y, xlabel='x', ylabel='y')\n",
|
||
|
|
"plot_fun(fig, polynomial_regression(theta, x, y, n), x)"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"author": "Paweł Skórzewski",
|
||
|
|
"celltoolbar": "Slideshow",
|
||
|
|
"email": "pawel.skorzewski@amu.edu.pl",
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"lang": "pl",
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.8.8-final"
|
||
|
|
},
|
||
|
|
"livereveal": {
|
||
|
|
"start_slideshow_at": "selected",
|
||
|
|
"theme": "white"
|
||
|
|
},
|
||
|
|
"subtitle": "5.Regresja wielomianowa. Problem nadmiernego dopasowania[wykład]",
|
||
|
|
"title": "Uczenie maszynowe",
|
||
|
|
"year": "2021"
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 4
|
||
|
|
}
|