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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Algorytm najszybszego spadku dla regresji wielomianowej. \n",
"Zakładamy, że dysponujemy zbiorem składającym się z dwóch cech (x i y). Modelujemy zależność y od x za pomocą funkcji wielomianowej. Celem projektu jest implementacja metody najszybszego spadku dla tego problemu. Zakładamy kwadratową funkcję straty. Implementacja powinna umożliwiać podanie stopnia wielomianu, który ma być użyty do modelowania. Implementacja powinna zwracać wektor oszacowanych parametrów oraz pokazywać wizualnie zmiany wartości funkcji straty wraz z postępem uczenia."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Zbiór danych: https://www.kaggle.com/varpit94/apple-stock-data-updated-till-22jun2021?select=AAPL.csv\n",
"This dataset provides historical data of APPLE INC. stock (AAPL). The data is available at a daily level. Currency is USD."
]
},
{
"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
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"import matplotlib.pyplot as plt\n",
"import numpy as np"
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]
},
{
"cell_type": "code",
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"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"degree = 6\n",
"X_plot = np.linspace(0, 150, 1000)\n",
"initial_theta = [0] * (degree + 1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
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"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Open</th>\n",
" <th>High</th>\n",
" <th>Low</th>\n",
" <th>Close</th>\n",
" <th>Adj Close</th>\n",
" <th>Volume</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1980-12-12</td>\n",
" <td>0.128348</td>\n",
" <td>0.128906</td>\n",
" <td>0.128348</td>\n",
" <td>0.128348</td>\n",
" <td>0.100751</td>\n",
" <td>469033600</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1980-12-15</td>\n",
" <td>0.122210</td>\n",
" <td>0.122210</td>\n",
" <td>0.121652</td>\n",
" <td>0.121652</td>\n",
" <td>0.095495</td>\n",
" <td>175884800</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1980-12-16</td>\n",
" <td>0.113281</td>\n",
" <td>0.113281</td>\n",
" <td>0.112723</td>\n",
" <td>0.112723</td>\n",
" <td>0.088485</td>\n",
" <td>105728000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1980-12-17</td>\n",
" <td>0.115513</td>\n",
" <td>0.116071</td>\n",
" <td>0.115513</td>\n",
" <td>0.115513</td>\n",
" <td>0.090676</td>\n",
" <td>86441600</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1980-12-18</td>\n",
" <td>0.118862</td>\n",
" <td>0.119420</td>\n",
" <td>0.118862</td>\n",
" <td>0.118862</td>\n",
" <td>0.093304</td>\n",
" <td>73449600</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Open High Low Close Adj Close Volume\n",
"0 1980-12-12 0.128348 0.128906 0.128348 0.128348 0.100751 469033600\n",
"1 1980-12-15 0.122210 0.122210 0.121652 0.121652 0.095495 175884800\n",
"2 1980-12-16 0.113281 0.113281 0.112723 0.112723 0.088485 105728000\n",
"3 1980-12-17 0.115513 0.116071 0.115513 0.115513 0.090676 86441600\n",
"4 1980-12-18 0.118862 0.119420 0.118862 0.118862 0.093304 73449600"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df = pd.read_csv('AAPL.csv')\n",
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"X = df[['Low']]\n",
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"Y = df['Volume']\n",
"display(df.head(5))"
]
},
{
"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
"outputs": [
{
"data": {
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"image/png": "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"text/plain": [
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"<Figure size 720x360 with 1 Axes>"
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
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"fig = plt.figure(figsize=(10,5))\n",
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"chart = fig.add_subplot()\n",
"chart.plot(X,Y ,\"go\")\n",
"plt.show()"
]
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},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Metody do regresji wielomianowej"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"11\n",
"441.0\n"
]
}
],
"source": [
"def polynomial_regression(theta, x):\n",
" value = 0\n",
" for i in range(len(theta)):\n",
" value += theta[i] * x**i\n",
" return value \n",
"\n",
"def mean_squared_error(Y_predicted, Y):\n",
" result = 0\n",
" for i in range(len(Y)):\n",
" result += (Y_predicted[i] - Y[i]) ** 2\n",
" return result/len(Y)\n",
"\n",
"def gradient(theta, X, Y):\n",
" return 1.0 / len(y) * (X.T * (X * theta - Y)) \n",
"\n",
"def gradient_descent(X, Y, theta, cost_function = mean_squared_error, alpha=0.1, eps=0.001, max_steps = 1000000):\n",
" cost = cost_function([polynomial_regression(theta, x) for x in X], Y)\n",
" logs = [[cost, theta]]\n",
" \n",
" for i in range(max_steps):\n",
" theta = theta - alpha * gradient(theta, X, Y)\n",
" next_cost = cost_function([polynomial_regression(theta, x) for x in X], Y)\n",
" logs.append([next_cost, theta])\n",
" if abs(cost - next_cost) <= eps:\n",
" break\n",
" return theta, logs\n",
" \n",
" \n",
"print(polynomial_regression([1,1,0,1], 2))\n",
"print(mean_squared_error([1,2,1,1],[1,2,43,1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Metody do wykresów"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def plot_polynomial_regression(theta):\n",
" fig = plt.figure(figsize=(10,5))\n",
" Y_plot = [polynomial_regression(theta, x) for x in X_plot]\n",
" chart = fig.add_subplot()\n",
" chart.plot(X_plot, Y_plot, color=\"red\", lw=2, label=f\"degree {len(theta)}\")\n",
" chart.plot(X,Y ,\"go\")\n",
" plt.show()\n",
" \n",
"plot_polynomial_regression([1,100,0,1000]) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Wyniki za pomocą gotowej biblioteki"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
"from sklearn.pipeline import make_pipeline\n",
"from sklearn.linear_model import Ridge, LinearRegression"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Pipeline(steps=[('polynomialfeatures', PolynomialFeatures(degree=6)),\n",
" ('linearregression', LinearRegression())])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model = make_pipeline(PolynomialFeatures(degree=degree, include_bias=True), \n",
" LinearRegression())\n",
"model.fit(X,Y)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"6"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Y_plot = model.predict([[x] for x in X_plot])\n",
"\n",
"fig = plt.figure(figsize=(10,5))\n",
"chart = fig.add_subplot()\n",
"chart.plot(X,Y ,\"go\")\n",
"chart.plot(X_plot, Y_plot, color=\"red\", lw=2, label=f\"degree {degree}\")\n",
"degree"
]
2021-06-24 11:07:41 +02:00
}
],
"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": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
