MachineLearning/hands-on
1
0
Fork 0
Code Issues Pull Requests Releases Activity

2,3,4장 식 업데이트

Browse Source
This commit is contained in:
Haesun Park
2018-04-24 21:50:25 +09:00
parent e8115ede0b
commit f90d5a85b7
1 changed files with 23 additions and 34 deletions
Download Patch File Download Diff File Expand all files Collapse all files

57
book_equations.ipynb
View File

@@ -14,16 +14,6 @@
} }
}, },
"cells": [ "cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"[View in Colaboratory](https://colab.research.google.com/github/rickiepark/handson-ml/blob/master/book_equations.ipynb)"
]
},
{ {
"metadata": { "metadata": {
"id": "ZICa1cn5n1Yv", "id": "ZICa1cn5n1Yv",
@@ -45,13 +35,12 @@
}, },
"cell_type": "markdown", "cell_type": "markdown",
"source": [ "source": [
"# Chapter 1\n", "# 1장\n",
"**Equation 1-1: A simple linear model**\n", "**식 1-1: 간단한 선형 모델**\n",
"\n", "\n",
"$\n", "$\n",
"\\text{life_satisfaction} = \\theta_0 + \\theta_1 \\times \\text{GDP_per_capita}\n", "\\text{삶의_만족도} = \\theta_0 + \\theta_1 \\times \\text{1인당_GDP}\n",
"$\n", "$"
"\n"
] ]
}, },
{ {
@@ -61,15 +50,15 @@
}, },
"cell_type": "markdown", "cell_type": "markdown",
"source": [ "source": [
"# Chapter 2\n", "# 2장\n",
"**Equation 2-1: Root Mean Square Error (RMSE)**\n", "**식 2-1: 평균 제곱근 오차 (RMSE)**\n",
"\n", "\n",
"$\n", "$\n",
"\\text{RMSE}(\\mathbf{X}, h) = \\sqrt{\\frac{1}{m}\\sum\\limits_{i=1}^{m}\\left(h(\\mathbf{x}^{(i)}) - y^{(i)}\\right)^2}\n", "\\text{RMSE}(\\mathbf{X}, h) = \\sqrt{\\frac{1}{m}\\sum\\limits_{i=1}^{m}\\left(h(\\mathbf{x}^{(i)}) - y^{(i)}\\right)^2}\n",
"$\n", "$\n",
"\n", "\n",
"\n", "\n",
"**Notations (page 38):**\n", "**표기법 (72 페이지):**\n",
"\n", "\n",
"$\n", "$\n",
" \\mathbf{x}^{(1)} = \\begin{pmatrix}\n", " \\mathbf{x}^{(1)} = \\begin{pmatrix}\n",
@@ -100,13 +89,13 @@
"$\n", "$\n",
"\n", "\n",
"\n", "\n",
"**Equation 2-2: Mean Absolute Error**\n", "**식 2-2: 평균 절대 오차**\n",
"\n", "\n",
"$\n", "$\n",
"\\text{MAE}(\\mathbf{X}, h) = \\frac{1}{m}\\sum\\limits_{i=1}^{m}\\left| h(\\mathbf{x}^{(i)}) - y^{(i)} \\right|\n", "\\text{MAE}(\\mathbf{X}, h) = \\frac{1}{m}\\sum\\limits_{i=1}^{m}\\left| h(\\mathbf{x}^{(i)}) - y^{(i)} \\right|\n",
"$\n", "$\n",
"\n", "\n",
"**$\\ell_k$ norms (page 39):**\n", "**$\\ell_k$ 노름 (74 페이지):**\n",
"\n", "\n",
"$ \\left\\| \\mathbf{v} \\right\\| _k = (\\left| v_0 \\right|^k + \\left| v_1 \\right|^k + \\dots + \\left| v_n \\right|^k)^{\\frac{1}{k}} $\n" "$ \\left\\| \\mathbf{v} \\right\\| _k = (\\left| v_0 \\right|^k + \\left| v_1 \\right|^k + \\dots + \\left| v_n \\right|^k)^{\\frac{1}{k}} $\n"
] ]
@@ -118,25 +107,25 @@
}, },
"cell_type": "markdown", "cell_type": "markdown",
"source": [ "source": [
"# Chapter 3\n", "# 3장\n",
"**Equation 3-1: Precision**\n", "**식 3-1: 정밀도**\n",
"\n", "\n",
"$\n", "$\n",
"\\text{precision} = \\cfrac{TP}{TP + FP}\n", "\\text{정밀도} = \\cfrac{TP}{TP + FP}\n",
"$\n", "$\n",
"\n", "\n",
"\n", "\n",
"**Equation 3-2: Recall**\n", "**식 3-2: 재현율**\n",
"\n", "\n",
"$\n", "$\n",
"\\text{recall} = \\cfrac{TP}{TP + FN}\n", "\\text{재현율} = \\cfrac{TP}{TP + FN}\n",
"$\n", "$\n",
"\n", "\n",
"\n", "\n",
"**Equation 3-3: $F_1$ score**\n", "**식 3-3: $F_1$ 점수**\n",
"\n", "\n",
"$\n", "$\n",
"F_1 = \\cfrac{2}{\\cfrac{1}{\\text{precision}} + \\cfrac{1}{\\text{recall}}} = 2 \\times \\cfrac{\\text{precision}\\, \\times \\, \\text{recall}}{\\text{precision}\\, + \\, \\text{recall}} = \\cfrac{TP}{TP + \\cfrac{FN + FP}{2}}\n", "F_1 = \\cfrac{2}{\\cfrac{1}{\\text{정밀도}} + \\cfrac{1}{\\text{재현율}}} = 2 \\times \\cfrac{\\text{정밀도}\\, \\times \\, \\text{재현율}}{\\text{정밀도}\\, + \\, \\text{재현율}} = \\cfrac{TP}{TP + \\cfrac{FN + FP}{2}}\n",
"$\n", "$\n",
"\n" "\n"
] ]
@@ -148,41 +137,41 @@
}, },
"cell_type": "markdown", "cell_type": "markdown",
"source": [ "source": [
"# Chapter 4\n", "# 4장\n",
"**Equation 4-1: Linear Regression model prediction**\n", "**식 4-1: 선형 회귀 모델의 예측**\n",
"\n", "\n",
"$\n", "$\n",
"\\hat{y} = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\dots + \\theta_n x_n\n", "\\hat{y} = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\dots + \\theta_n x_n\n",
"$\n", "$\n",
"\n", "\n",
"\n", "\n",
"**Equation 4-2: Linear Regression model prediction (vectorized form)**\n", "**식 4-2: 선형 회귀 모델의 예측 (벡터 형태)**\n",
"\n", "\n",
"$\n", "$\n",
"\\hat{y} = h_{\\mathbf{\\theta}}(\\mathbf{x}) = \\mathbf{\\theta}^T \\cdot \\mathbf{x}\n", "\\hat{y} = h_{\\mathbf{\\theta}}(\\mathbf{x}) = \\mathbf{\\theta}^T \\cdot \\mathbf{x}\n",
"$\n", "$\n",
"\n", "\n",
"\n", "\n",
"**Equation 4-3: MSE cost function for a Linear Regression model**\n", "**식 4-3: 선형 회귀 모델의 MSE 비용 함수**\n",
"\n", "\n",
"$\n", "$\n",
"\\text{MSE}(\\mathbf{X}, h_{\\mathbf{\\theta}}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{(\\mathbf{\\theta}^T \\cdot \\mathbf{x}^{(i)} - y^{(i)})^2}\n", "\\text{MSE}(\\mathbf{X}, h_{\\mathbf{\\theta}}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{(\\mathbf{\\theta}^T \\cdot \\mathbf{x}^{(i)} - y^{(i)})^2}\n",
"$\n", "$\n",
"\n", "\n",
"\n", "\n",
"**Equation 4-4: Normal Equation**\n", "**식 4-4: 정규 방정식**\n",
"\n", "\n",
"$\n", "$\n",
"\\hat{\\mathbf{\\theta}} = (\\mathbf{X}^T \\cdot \\mathbf{X})^{-1} \\cdot \\mathbf{X}^T \\cdot \\mathbf{y}\n", "\\hat{\\mathbf{\\theta}} = (\\mathbf{X}^T \\cdot \\mathbf{X})^{-1} \\cdot \\mathbf{X}^T \\cdot \\mathbf{y}\n",
"$\n", "$\n",
"\n", "\n",
"\n", "\n",
"** Partial derivatives notation (page 114):**\n", "** 편도함수 기호 (165 페이지):**\n",
"\n", "\n",
"$\\frac{\\partial}{\\partial \\theta_j} \\text{MSE}(\\mathbf{\\theta})$\n", "$\\frac{\\partial}{\\partial \\theta_j} \\text{MSE}(\\mathbf{\\theta})$\n",
"\n", "\n",
"\n", "\n",
"**Equation 4-5: Partial derivatives of the cost function**\n", "**식 4-5: 비용 함수의 편도함수**\n",
"\n", "\n",
"$\n", "$\n",
"\\dfrac{\\partial}{\\partial \\theta_j} \\text{MSE}(\\mathbf{\\theta}) = \\dfrac{2}{m}\\sum\\limits_{i=1}^{m}(\\mathbf{\\theta}^T \\cdot \\mathbf{x}^{(i)} - y^{(i)})\\, x_j^{(i)}\n", "\\dfrac{\\partial}{\\partial \\theta_j} \\text{MSE}(\\mathbf{\\theta}) = \\dfrac{2}{m}\\sum\\limits_{i=1}^{m}(\\mathbf{\\theta}^T \\cdot \\mathbf{x}^{(i)} - y^{(i)})\\, x_j^{(i)}\n",