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6,7장 수식 번역

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Haesun Park
2018-04-25 22:56:08 +09:00
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book_equations.ipynb
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@@ -531,43 +531,43 @@
},
"cell_type": "markdown",
"source": [
"# Chapter 6\n",
"**Equation 6-1: Gini impurity**\n",
"# 6장\n",
"**식 6-1: 지니 불순도**\n",
"\n",
"$\n",
"G_i = 1 - \\sum\\limits_{k=1}^{n}{{p_{i,k}}^2}\n",
"$\n",
"\n",
"\n",
"**Equation 6-2: CART cost function for classification**\n",
"**식 6-2: 분류에 대한 CART 비용 함수**\n",
"\n",
"$\n",
"\\begin{split}\n",
"&J(k, t_k) = \\dfrac{m_{\\text{left}}}{m}G_\\text{left} + \\dfrac{m_{\\text{right}}}{m}G_{\\text{right}}\\\\\n",
"&\\text{where }\\begin{cases}\n",
"G_\\text{left/right} \\text{ measures the impurity of the left/right subset,}\\\\\n",
"m_\\text{left/right} \\text{ is the number of instances in the left/right subset.}\n",
"&\\text{여기서 }\\begin{cases}\n",
"G_\\text{left/right} \\text{ 는 왼쪽/오른쪽 서브셋의 불순도}\\\\\n",
"m_\\text{left/right} \\text{ 는 왼쪽/오른쪽 서브셋의 불순도}\n",
"\\end{cases}\n",
"\\end{split}\n",
"$\n",
"\n",
"**Entropy computation example (page 173):**\n",
"**엔트로피 계산 예 (232 페이지):**\n",
"\n",
"$ -\\frac{49}{54}\\log(\\frac{49}{54}) - \\frac{5}{54}\\log(\\frac{5}{54}) $\n",
"$ -\\frac{49}{54}\\log_2(\\frac{49}{54}) - \\frac{5}{54}\\log_2(\\frac{5}{54}) $\n",
"\n",
"\n",
"**Equation 6-3: Entropy**\n",
"**식 6-3: 엔트로피**\n",
"\n",
"$\n",
"H_i = -\\sum\\limits_{k=1 \\atop p_{i,k} \\ne 0}^{n}{{p_{i,k}}\\log(p_{i,k})}\n",
"H_i = -\\sum\\limits_{k=1 \\atop p_{i,k} \\ne 0}^{n}{{p_{i,k}}\\log_2(p_{i,k})}\n",
"$\n",
"\n",
"\n",
"**Equation 6-4: CART cost function for regression**\n",
"**식 6-4: 회귀를 위한 CART 비용 함수**\n",
"\n",
"$\n",
"J(k, t_k) = \\dfrac{m_{\\text{left}}}{m}\\text{MSE}_\\text{left} + \\dfrac{m_{\\text{right}}}{m}\\text{MSE}_{\\text{right}} \\quad\n",
"\\text{where }\n",
"\\text{여기서 }\n",
"\\begin{cases}\n",
"\\text{MSE}_{\\text{node}} = \\sum\\limits_{\\scriptstyle i \\in \\text{node}}(\\hat{y}_{\\text{node}} - y^{(i)})^2\\\\\n",
"\\hat{y}_\\text{node} = \\dfrac{1}{m_{\\text{node}}}\\sum\\limits_{\\scriptstyle i \\in \\text{node}}y^{(i)}\n",
@@ -582,16 +582,16 @@
},
"cell_type": "markdown",
"source": [
"# Chapter 7\n",
"# 7장\n",
"\n",
"**Equation 7-1: Weighted error rate of the j^th^ predictor**\n",
"**식 7-1: j번째 예측기의 가중치가 적용된 에러율**\n",
"\n",
"$\n",
"r_j = \\dfrac{\\displaystyle \\sum\\limits_{\\textstyle {i=1 \\atop \\hat{y}_j^{(i)} \\ne y^{(i)}}}^{m}{w^{(i)}}}{\\displaystyle \\sum\\limits_{i=1}^{m}{w^{(i)}}} \\quad\n",
"\\text{where }\\hat{y}_j^{(i)}\\text{ is the }j^{\\text{th}}\\text{ predictor's prediction for the }i^{\\text{th}}\\text{ instance.}\n",
"$\n",
"\n",
"**Equation 7-2: Predictor weight**\n",
"**식 7-2: 예측기 가중치**\n",
"\n",
"$\n",
"\\begin{split}\n",
@@ -600,28 +600,28 @@
"$\n",
"\n",
"\n",
"**Equation 7-3: Weight update rule**\n",
"**식 7-3: 가중치 업데이트 규칙**\n",
"\n",
"$\n",
"\\begin{split}\n",
"& \\text{ for } i = 1, 2, \\dots, m \\\\\n",
"& w^{(i)} \\leftarrow\n",
"\\begin{cases}\n",
"w^{(i)} & \\text{if }\\hat{y_j}^{(i)} = y^{(i)}\\\\\n",
"w^{(i)} \\exp(\\alpha_j) & \\text{if }\\hat{y_j}^{(i)} \\ne y^{(i)}\n",
"\\end{cases}\n",
"w^{(i)} & \\hat{y_j}^{(i)} = y^{(i)} \\text{ 일 때}\\\\\n",
"w^{(i)} \\exp(\\alpha_j) & \\hat{y_j}^{(i)} \\ne y^{(i)} \\text{ 일 때}\n",
"\\end{cases} \\\\\n",
"& \\text{여기서 } i = 1, 2, \\dots, m \\\\\n",
"\\end{split}\n",
"$\n",
"\n",
"**In the text page 194:**\n",
"**256 페이지 본문 중에서:**\n",
"\n",
"Then all the instance weights are normalized (i.e., divided by $ \\sum_{i=1}^{m}{w^{(i)}} $).\n",
"그런 다음 모든 샘플의 가중치를 정규화합니다(즉, $ \\sum_{i=1}^{m}{w^{(i)}} $으로 나눕니다).\n",
"\n",
"\n",
"**Equation 7-4: AdaBoost predictions**\n",
"**식 7-4: AdaBoost 예측**\n",
"\n",
"$\n",
"\\hat{y}(\\mathbf{x}) = \\underset{k}{\\operatorname{argmax}}{\\sum\\limits_{\\scriptstyle j=1 \\atop \\scriptstyle \\hat{y}_j(\\mathbf{x}) = k}^{N}{\\alpha_j}} \\quad \\text{where }N\\text{ is the number of predictors.}\n",
"\\hat{y}(\\mathbf{x}) = \\underset{k}{\\operatorname{argmax}}{\\sum\\limits_{\\scriptstyle j=1 \\atop \\scriptstyle \\hat{y}_j(\\mathbf{x}) = k}^{N}{\\alpha_j}} \\quad \\text{여기서 }N\\text{은 예측기 수}\n",
"$\n",
"\n",
"\n"