{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Polynomial Regression, Overfitting, and Regularization"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {
"id": "-SinsrSt1_NL"
},
"source": [
"## Polynomial Regression\n",
"\n",
"\n",
"\n",
"[Slides: Polynomial Regression, Overfitting and Regularization 1](https://github.com/ichatnun/brainCodeCamp2023_lectures/blob/main/IntroToModeling/modeling_part2a_polynomial1.pdf)\n",
"\n",
"
\n",
"\n",
"ข้อมูลจำนวนมากที่พบเจอในการทำงานจริง มักมีความสัมพันธ์ที่ซับซ้อน ซึ่งเมื่อนำมา plot ดูแล้วอาจจะมีหน้าตาที่ไม่สอดคล้องกับโมเดลเชิงเส้น ดังตัวอย่างด้านล่าง ที่ $y$ ถูกสร้างมาจากสมการ $y=x^2$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"id": "CIY2cgN32BpM"
},
"outputs": [],
"source": [
"import sys\n",
"import numpy as np\n",
"from numpy.linalg import norm\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.linear_model import LinearRegression\n",
"from sklearn.preprocessing import PolynomialFeatures\n",
"\n",
"import ipywidgets as widgets # ใช้สำหรับการทำ interactive display\n",
"\n",
"np.random.seed(777) # ตั้งค่า random seed เอาไว้ เพื่อให้การรันโค้ดนี้ได้ผลเหมือนเดิม"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 449
},
"id": "iOh-ADt2jiEr",
"outputId": "1c314274-c7d7-46e1-f6d4-6c4aa7070c19"
},
"outputs": [
{
"data": {
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",
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