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    "# 01 - Introduction To Causality\n",
    "\n",
    "## Why Bother?\n",
    "\n",
    "인과관계(Causality)는 왜 공부해야 할까요?\n",
    "\n",
    "## Data Science is Not What it Used to Be (or it Finally Is)\n",
    "\n",
    "하버드 비즈니스 리뷰는 데이터과학자를 [21세기 가장 섹시한 직업](https://hbr.org/2012/10/data-scientist-the-sexiest-job-of-the-21st-century)으로 선정했습니다. 정말로 지난 몇 년 동안 데이터과학자는 많은 주목을 받았습니다. 인공지능 전문가의 연봉은 [스포츠 슈퍼스타들과 견줄 정도입니다.](https://www.economist.com/business/2016/04/02/million-dollar-babies) 많은 사람은 빠르게 전문적인 데이터과학자가 되기 위해 엄청난 노력을 합니다. 새로운 데이터 과학 교육 과정도 많이 생기고 있습니다. 어떤 사람은 기적적인 방법으로 어떠한 수학 공식 없이도 데이터과학자가 될 수 있다고 주장합니다. 컨설턴트는 데이터의 잠재력을 깨우기만 한다면 당신의 회사가 수백만 달러를 더 벌어들일 수 있다고 주장합니다. 과연 인공지능과 기계학습은 새로운 황금향일까요?\n",
    "\n",
    "반면 인과관계를 고민하던 사람들도 있습니다. 경제학자들은 교육이 소득에 미치는 진짜 원인을 밝히고자 노력해 왔습니다. 생물 통계학자들은 포화 지방이 심장마비의 진짜 원인인지 밝히고자 했으며, 심리학자들은 긍정의 단어가 더 행복한 결혼 생활을 만들지 이해하려 해 왔습니다. 우리는 이러한 \"옛날의\" 데이터 과학을 등한시하는 경향이 있습니다. 사실 데이터 과학은 새로운 분야가 아닙니다. 단지 언론에 의해 엄청나게 과장되어 있을 뿐입니다.\n",
    "\n",
    "데이터 과학을 맥주를 컵에 따르는 것으로 비유해 보겠습니다. 컵은 대부분 맥주로 채워지겠지만, 컵의 꼭대기에는 손가락 하나 두께의 거품이 생기게 됩니다.\n",
    "\n",
    "1. 맥주는 기초 통계학, 과학적 호기심, 복잡한 문제에 대한 열정입니다. 수백 년 동안 가치 있는 것으로 증명되었습니다.\n",
    "2. 거품은 결국 사라질 기대입니다.\n",
    "\n",
    "경제학자에 따르면 거품은 생각보다 빠르게 꺼질 수 있습니다.\n",
    "\n",
    "> 최근 현장에서 인공지능 구현이 어렵고 열정이 식어가고 있다고 보고되었습니다. 가트너의 Svetlana Sicular는 2020년이 AI 거품이 빠지는 해가 될 수 있다고 말합니다. 투자자들은 밴드왜건(다른 사람들을 따라 하는 현상)에서 벗어나고 있습니다. 벤처 캐피털 펀드인 MMC는 유럽 AI 스타트업 중 40%가 AI를 전혀 사용하지 않고 있다고 보고합니다.\n",
    "\n",
    "인공지능의 폭풍 속에서 데이터과학자 혹은 \"그냥\" 과학자는 무엇을 해야 할까요? 우리는 거품을 무시하는 방법을 배워야 합니다. 맥주에만 집중해야 합니다. 수학과 통계는 영원할 것입니다. 쓸데없는 최첨단 도구보다는 당신을 가치 있게 하는 것을 배우세요.\n",
    "\n",
    "여기에 지름길은 없습니다. 수학과 통계 지식은 어렵기 때문에 가치 있습니다. 경제이론에 따르면 모두 익힐 수 있는 내용은 과잉 공급으로 가치가 없어집니다. **힘내세요**! 가능한 한 열심히 배우세요. 당신은 할 수 있습니다. **용감하고 진실한** 사람의 길을 즐겁게 따르기를 바랍니다.\n",
    "\n",
    "![img](./data/img/intro/tougher-up-cupcake1.jpg)\n",
    "\n",
    "## Answering a Different Kind of Question\n",
    "\n",
    "`Machine Learning`(기계학습)은 예측 문제를 잘 해결합니다. Ajay Agrawal, Joshua Gans, Avi Goldfarb의 책 \"Prediction Machines\"에 따르면 \"인공지능의 새로운 물결은 지능 자체보다는 지능의 구성요소를 제공합니다.\" `Machine Learning`으로 아름다운 작업을 할 수 있습니다. 우리가 해야 할 일은 문제를 예측 문제로 바꾸는 것뿐입니다. 영어를 포르투갈어로 번역하고 싶나요? 영어 문장을 넣고 포르투갈어 문장을 예측하는 ML 모델을 만듭니다. 얼굴인식 프로그램을 만들고 싶나요? 사진에서 얼굴 위치를 예측하는 ML 모델을 만듭니다. 자율주행 자동차를 만들고 싶나요? ML 모델로 차량 주변의 이미지와 센서값을 받아 휠의 방향, 브레이크, 가속기의 압력을 예측하세요.\n",
    "\n",
    "하지만 `ML`이 만병통치약은 아닙니다. ML은 학습된 데이터 내에서 예측하는 것을 잘합니다. \"Prediction Machines\"에 소개된 예를 들면, \"많은 산업에서 낮은 가격은 낮은 판매와 관련됩니다. 호텔 가격은 비수기에 낮지만, 성수기에 높아집니다. 따라서 가격을 올리면 더 많은 방이 팔릴 것이라고 단순한 예측을 할 수 있습니다.\"\n",
    "\n",
    "`ML`은 인과문제를 해결하지 못하기로 악명 높습니다. 인과문제는 경제학자들이 `counterfactual`(반사실)이라 부르는, \"만약\"이라는 질문에 대답하는 것입니다. 상품가격을 바꾸면 더 많이 팔릴까요? 만약 저지방 다이어트 대신 저설탕 다이어트를 하면 어떨까요? 만약 고객의 신용한도를 바꾸면 은행의 수익이 늘어날까요? 만약 학교에서 모든 학생에게 태블릿을 제공하면 성적이 향상될까요? \n",
    "\n",
    "질문의 핵심은 인과관계입니다. 인과관계는 매출을 올리는 방법과 같은 일상적인 문제에 스며들어 있습니다. 인생에서 성공하기 위해 비싼 학교에 들어가야 할까요? (학위는 높은 연봉을 보장할까요?) 이민은 실업률을 높일까요? 저소득층을 보조하면 범죄율은 낮아질까요? 분야와 상관없이 인과 문제는 산재해 있습니다. 우리는 인과문제를 해결해야 하지만 상관관계에 기반을 둔 `ML`로는 해결할 수 없습니다.\n",
    "\n",
    "인과관계에 대한 대답은 생각보다 어렵습니다. 아마도 여러분은 \"상관은 인과가 아니다.\"라는 말을 들어봤을 겁니다. 사실은 `association`(상관)이 왜 `causation`(인과)과 다른지 설명하는 것이 더 중요합니다. 도입은 이것으로 마칩니다. 이제부터는 **상관관계를 인과관계로 만드는 방법**을 찾는 데 집중해 봅시다.\n",
    "\n",
    "## When Association IS Causation\n",
    "\n",
    "직관적으로는 왜 상관관계가 인과관계가 아닌지 알고 있을 겁니다. 만약 전교생에 태블릿을 제공하는 학교가 그렇지 않은 학교보다 평균 성적이 높다면, 태블릿이 성적 향상의 원인이라기보다는 태블릿을 제공하는 학교들이 더 부유했기 때문이라고 평균 성적이 높을 것으로 생각할 수 있습니다. 이 경우 태블릿과 관계없이 사교육 등으로 성적이 더 좋을 수도 있습니다. 따라서 태블릿이 성적 향상의 원인이라 부를 수는 없습니다. 단지 태블릿을 제공하는 것과 높은 성적이 상관관계가 있다고 할 수 있을 뿐입니다."
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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.special import expit\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import style\n",
    "\n",
    "style.use(\"fivethirtyeight\")\n",
    "\n",
    "np.random.seed(123)\n",
    "n = 100\n",
    "tuition = np.random.normal(1000, 300, n).round()\n",
    "tablet = np.random.binomial(1, expit((tuition - tuition.mean()) / tuition.std())).astype(bool)\n",
    "enem_score = np.random.normal(200 - 50 * tablet + 0.7 * tuition, 200)\n",
    "enem_score = (enem_score - enem_score.min()) / enem_score.max()\n",
    "enem_score *= 1000\n",
    "\n",
    "data = pd.DataFrame(dict(enem_score=enem_score, Tuition=tuition, Tablet=tablet))"
   ]
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    {
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",
      "text/plain": [
       "<Figure size 600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,8))\n",
    "sns.boxplot(y=\"enem_score\", x=\"Tablet\", data=data).set_title('ENEM score by Tablet in Class')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "몇 가지 용어를 만들어 봅시다. 이 용어들은 앞으로 우리의 일상적인 언어가 될 것입니다. 다른 용감하고 진정한 \"인과 전사\"를 식별하는 데 사용할 공용어라 생각하세요. 다가올 많은 전투에서 우리의 함성이 될 것입니다.\n",
    "\n",
    "$T_i$는 `unit`(단위 데이터, table의 경우 1개 row에 해당) $i$에 대한 `treatment`(처치)입니다.\n",
    "\n",
    "$\n",
    "T_i=\\begin{cases}\n",
    "1 \\ \\text{if unit i received the treatment}\\\\\n",
    "0 \\ \\text{otherwise}\\\\\n",
    "\\end{cases}\n",
    "$\n",
    "\n",
    "처치는 약이나 의료 분야에서 주로 쓰이는 용어이기는 하지만, 여기서는 어떠한 개입을 나타내기 위해 사용합니다. 태블릿 예시에서 처치는 태블릿 제공 여부입니다. 참고로 처치는 시간(주로 $T$로 표기)과 구분하기 위해 $D$로 표기하기도 합니다.\n",
    "\n",
    "$Y_i$는 `unit` $i$에 대한 관측 결과입니다.\n",
    "\n",
    "`outcome`(결과)은 우리가 관심이 있는 결과입니다. 우리는 처치가 결과에 어떤 영향을 주는지 알고 싶습니다. 태블릿 예시에서 결과는 성적입니다.\n",
    "\n",
    "이제 재미있는 부분입니다. **인과추론의 근본적인 어려움**은 같은 단위 데이터에서 모든 처치에 대한 결과를 알 수 없는 것에서 나옵니다. 로버트 프로스트의 시처럼 우리가 알 수 있는 것은 갈라진 두 개의 길 중 선택한 하나의 길 끝에 있는 무엇입니다. \n",
    "```\n",
    "노란 숲속에 길이 두 갈래로 났었습니다.  \n",
    "나는 두 길을 다 가지 못하는 것을 안타깝게 생각하면서,  \n",
    "오랫동안 서서 한 길이 굽어 꺾여 내려간 데까지,  \n",
    "바라다볼 수 있는 데까지 멀리 바라다보았습니다.  \n",
    "```\n",
    "\n",
    "이러한 문제를 다루기 위해 `potential outcome`(잠재결과)을 다뤄야 합니다. 실제로 나타나지 않은 결과는 잠재해 있습니다. 잠재 결과는 만약 처치가 적용되었다면 **어떻게 되었을까**에 대한 결과입니다. 발생한 결과는 `factual`(사실), 발생하지 않은 결과는 `counterfactual`(반사실)이라 부릅니다.\n",
    "\n",
    "표기는 다음과 같이 아래첨자를 사용합니다.\n",
    "\n",
    "$Y_{0i}$는 처치되지 않은 데이터 $i$의 잠재결과입니다.\n",
    "\n",
    "$Y_{1i}$는 처치가 적용된 **동일한** 데이터 $i$의 잠재결과입니다.\n",
    "\n",
    "잠재결과는 $Y_i(t)$로 표기하기도 합니다. $Y_{0i} = Y_i(0)$, $Y_{1i} = Y_i(1)$입니다. 이 책에서는 아래첨자 표기법을 사용하겠습니다.\n",
    "\n",
    "![img](./data/img/intro/potential_outcomes.png)\n",
    "\n",
    "$Y_{1i}$는 태블릿을 지급한 학생 $i$의 성적입니다. 사실이든 반사실이든 $Y_{1i}$는 동일합니다. 학생 $i$가 태블릿을 받았다면 $Y_{1i}$를 알 수 있습니다. 받지 않았다면 $Y_{0i}$를 알 수 있습니다. $Y_{0i}$을 알고 있다면 $Y_{1i}$는 알 수 없습니다. 이 경우 $Y_{1i}$는 반사실적 잠재결과가 됩니다.\n",
    "\n",
    "잠재결과로 `individual treatment effect`(개별 처치 효과)를 정의할 수 있습니다.\n",
    "\n",
    " $Y_{1i} - Y_{0i}$\n",
    " \n",
    "물론 잠재결과 중 하나만 알 수 있으므로 근본적으로 개별 처치 효과를 알 수 없습니다. 당분간은 개별 처치 효과보다 더 쉬운 것에 초점을 맞추겠습니다. 아래처럼 정의된 **average treatment effect**(ATE, 평균 처치 효과)를 살펴봅시다.\n",
    "\n",
    "$ATE = E[Y_1 - Y_0]$\n",
    "\n",
    "`E[...]`는 기댓값입니다. 생각하기 쉬운 다른 것은 **average treatment effect on the treated**(ATT, 처치된 평균 처치 효과)입니다:\n",
    "\n",
    "$ATT = E[Y_1 - Y_0 | T=1]$\n",
    "\n",
    "현실적으로 모든 잠재결과는 알지 못합니다. 하지만 가능하다고 가정해 봅시다. 인과추론의 신이 우리를 가엾게 여겨 모든 잠재결과를 알려줬습니다. 아래와 같이 4개 학교에 대한 데이터를 수집했습니다. 당신은 태블릿 지급 여부에 따른 학생의 성적을 모두 알고 있습니다. 태블릿 지급 여부는 처치가 되므로 학생에게 태블릿을 제공했을 때 $T=1$입니다. $Y$는 성적이 됩니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
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       "      <th>i</th>\n",
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       "   i   y0   y1  t    y   te\n",
       "0  1  500  450  0  500  -50\n",
       "1  2  600  600  0  600    0\n",
       "2  3  800  600  1  600 -200\n",
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    "pd.DataFrame(dict(\n",
    "    i= [1,2,3,4],\n",
    "    y0=[500,600,800,700],\n",
    "    y1=[450,600,600,750],\n",
    "    t= [0,0,1,1],\n",
    "    y= [500,600,600,750],\n",
    "    te=[-50,0,-200,50],\n",
    "))"
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   "source": [
    "$ATE$는 마지막 `te`열의 평균, 즉 `treatment effect`(처치 효과)의 평균입니다. \n",
    "\n",
    "$ATE=(-50 + 0 - 200 + 50) / 4 = -50$\n",
    "\n",
    "$ATE$에 따르면 태블릿 지급은 평균적으로 성적을 50점 낮춥니다. \n",
    "\n",
    "$ATT$는 $T=1$인 마지막 `te`열의 평균입니다.\n",
    "\n",
    "$ATT=(-200 + 50) / 2 = -75$\n",
    "\n",
    "처치가 적용된 학교에서는 태블릿이 평균적으로 성적을 75점 낮춥니다. \n",
    "\n",
    "물론 $ATE$와 $ATT$를 직접 계산할 수는 없습니다. 현실적인 데이터는 다음과 같습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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       "      <th>1</th>\n",
       "      <td>2</td>\n",
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       "      <th>2</th>\n",
       "      <td>3</td>\n",
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       "      <td>600.0</td>\n",
       "      <td>1</td>\n",
       "      <td>600</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>750.0</td>\n",
       "      <td>1</td>\n",
       "      <td>750</td>\n",
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       "   i     y0     y1  t    y  te\n",
       "0  1  500.0    NaN  0  500 NaN\n",
       "1  2  600.0    NaN  0  600 NaN\n",
       "2  3    NaN  600.0  1  600 NaN\n",
       "3  4    NaN  750.0  1  750 NaN"
      ]
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   "source": [
    "pd.DataFrame(dict(\n",
    "    i= [1,2,3,4],\n",
    "    y0=[500,600,np.nan,np.nan],\n",
    "    y1=[np.nan,np.nan,600,750],\n",
    "    t= [0,0,1,1],\n",
    "    y= [500,600,600,750],\n",
    "    te=[np.nan,np.nan,np.nan,np.nan],\n",
    "))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "약간 다르지만, 처치된 데이터 평균과 처치되지 않은 데이터 평균과 비교하면 안 될까요? \n",
    "\n",
    "$ATE = (600 + 750) / 2 - (500 + 600)/2 = 125$\n",
    "\n",
    "절대로! 안 됩니다! 결과가 얼마나 다른지 보세요. 당신은 상관관계를 인과관계로 판단한 가장 큰 죄를 지었습니다. 인과추론 분야의 거대한 악당을 소개합니다.\n",
    "\n",
    "## Bias\n",
    "\n",
    "편향은 상관관계가 인과관계가 아니게 만듭니다. 직관적으로 이해해 봅시다. 누군가 태블릿을 제공하는 학교의 성적이 더 높다고 주장하면, 우리는 태블릿은 성적과 상관없다고 반박할 수 있습니다. 원인은 학교의 재정상태일 수 있습니다. 자금이 넉넉한 학교는 많은 돈을 들여 더 나은 교사, 더 나은 교실을 제공할 수 있습니다. 따라서 태블릿 지급 여부로 학교를 비교할 수 없습니다.\n",
    "\n",
    "잠재결과 표기에 따르면 처치된 $Y_0$는 처치되지 않은 $Y_0$와 다릅니다. 처치된 $Y_0$는 **반사실**입니다. 관측할 수 없는 값으로 추론만 가능합니다. 태블릿이 제공된 학교의 $Y_0$은 그렇지 않은 학교의 $Y_0$보다 더 클 수 있습니다. 학교는 성적을 위해 다른 요소(더 좋은 선생님, 더 좋은 교실)를 제공할 수 있기 때문입니다.\n",
    "\n",
    "상관관계가 왜 인과관계가 될 수 없는지 수학적으로 확인해 봅시다. 상관관계는 $E[Y|T=1] - E[Y|T=0]$로 계산합니다. 태블릿을 제공한 학교의 평균 점수에서 태블릿을 제공하지 않은 학교의 평균 점수를 뺀 값입니다. 반면 인과관계는 $E[Y_1 - Y_0]$입니다.\n",
    "\n",
    "상관관계에서 결과(`Y`)를 잠재결과(`Y_0` 또는 `Y_1`)로 대체해 보겠습니다. 처치된 경우 잠재결과는 $Y_1$, 반대는 $Y_0$입니다.\n",
    "\n",
    "$\n",
    "E[Y|T=1] - E[Y|T=0] = E[Y_1|T=1] - E[Y_0|T=0]\n",
    "$\n",
    "\n",
    "이제 $E[Y_0|T=1]$를 더하고 빼겠습니다. $E[Y_0|T=1]$은 반사실 결과입니다. 태블릿이 제공된 학교에서 \"만약\" 태블릿이 제공되지 않았다면 받았을 가상의 성적이 됩니다.\n",
    "\n",
    "$\n",
    "E[Y|T=1] - E[Y|T=0] = E[Y_1|T=1] - E[Y_0|T=0] + E[Y_0|T=1] - E[Y_0|T=1]\n",
    "$\n",
    "\n",
    "수식을 정리하고 몇 가지 기댓값을 합칩니다.\n",
    "\n",
    "$\n",
    "E[Y|T=1] - E[Y|T=0] = \\underbrace{E[Y_1 - Y_0|T=1]}_{ATT} + \\underbrace{\\{ E[Y_0|T=1] - E[Y_0|T=0] \\}}_{BIAS}\n",
    "$\n",
    "\n",
    "이 간단한 방정식은 인과추론에서 마주치는 모든 문제를 다루고 있습니다. 이 수식은 꼭 이해하고 넘어가야 합니다. 만약 문신한다면 좋은 후보가 될 것입니다. 성경 구절과 같이 깊게 이해해야 합니다. 차근차근 살펴보겠습니다. 위 방정식은 상관관계가 인과관계가 아닌 이유를 보여줍니다. 상관관계는 `ATT`에 편향을 더한 것과 같습니다. **편향은 처치가 적용되기 전 실험군과 대조군의 차이와 같습니다.** 이제 태블릿이 성적을 높인다는 주장에 대해 의심스러운 점을 정확히 말할 수 있습니다. $E[Y_0|T=0] < E[Y_0|T=1]$로 태블릿을 지급할 여유 있는 학교는 그렇지 못한 학교보다 **태블릿 지급 여부와 관계없이** 성적이 높습니다.\n",
    "\n",
    "왜 편향이 생길까요? `confounder`(교란변수)에 대해서는 나중에 이야기하겠습니다. 지금은 통제할 수 없는 많은 것들이 처치와 함께 바뀌어 편향이 생긴다고 이해할 수 있습니다. 실험군과 대조군은 처치 여부만 다르지 않습니다. 교사의 수준, 교실의 수준 또한 다릅니다. 태블릿이 성적을 올려준다고 주장하려면 다른 모든 상황이 비슷한 학교를 비교해야 합니다."
   ]
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   "execution_count": 5,
   "metadata": {
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    {
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "sns.scatterplot(x=\"Tuition\", y=\"enem_score\", hue=\"Tablet\", data=data, s=70).set_title('ENEM score by Tuition Cost')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이제 우리는 상관관계를 인과관계로 만드는 방법을 알고 있습니다. **$E[Y_0|T=0] = E[Y_0|T=1]$일 때 상관관계는 인과관계가 됩니다!** $E[Y_0|T=0] = E[Y_0|T=1]$는 처치 전후에 실험군과 대조군이 같다는 의미입니다. 만약 처치가 없을 때 모든 $Y_0$을 알 수 있다면 실험군과 대조군에서 결과가 같을 것입니다. 수학적으로 편향이 사라집니다.\n",
    "\n",
    "$\n",
    "E[Y|T=1] - E[Y|T=0] = E[Y_1 - Y_0|T=1] = ATT\n",
    "$\n",
    "\n",
    "실험군과 대조군에서 처치 여부만 다르다면 $E[Y_0|T=0] = E[Y_0|T=1]$이고, 인과 영향 정도는 (매우 유사하므로) 처치 여부에 상관없이 같습니다.\n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "E[Y_1 - Y_0|T=1] &= E[Y_1|T=1] - E[Y_0|T=1] \\\\\n",
    "&= E[Y_1|T=1] - E[Y_0|T=0] \\\\\n",
    "&= E[Y|T=1] - E[Y|T=0]\n",
    "\\end{align}\n",
    "$\n",
    "\n",
    "따라서 **평균의 차이는 인과관계가 됩니다.**\n",
    "\n",
    "$\n",
    "E[Y|T=1] - E[Y|T=0] = ATT\n",
    "$\n",
    "\n",
    "또한, (실험군과 대조군이 처치 여부만 다를 때) $E[Y_1|T=0] = E[Y_1|T=1]$입니다. 즉, 처치에 대한 반응이 유사합니다. $E[Y_1 - Y_0|T=1] = E[Y_1 - Y_0|T=0]$를 만족하므로,\n",
    " \n",
    "$\n",
    "E[Y|T=1] - E[Y|T=0] = ATT = ATE\n",
    "$\n",
    "\n",
    "이는 너무나 중요하므로 아래 그림으로 다시 살펴보겠습니다. 처치된 그룹(대조군)과 아닌 그룹(실험군)을 단순 평균하여 비교하면 다음과 같습니다. (실험군은 파란색입니다.)\n",
    "\n",
    "![img](./data/img/intro/anatomy1.png)\n",
    "\n",
    "두 그룹 간의 결과 차이의 원인은 두 가지입니다.\n",
    "\n",
    "1. 처치효과입니다. 태블릿 제공이 성적 향상의 원인입니다.\n",
    "2. 교육비가 성적에 영향을 줍니다. 두 그룹 차이는 교육비의 차이이며 태블릿 자체는 원인이 아닙니다.\n",
    "   \n",
    "개별 처치 효과는 같은 학생에 대한 처치에 따른 이론적인 결과의 차이입니다. 실제 처치 효과는 아래 왼쪽 그림과 같이 모든 잠재결과를 알 수 있는 신과 같은 능력이 있을 때만 알 수 있습니다. 반사실을 밝은 색으로 표시했습니다. \n",
    "\n",
    "![img](./data/img/intro/anatomy2.png)\n",
    "\n",
    "위의 오른쪽 그림은 편향을 나타냅니다. 모든 사람에게 처치를 제공하지 않으면 편향을 얻을 수 있습니다. 이 경우 $T_0$인 잠재결과만 남는데, 실험군과 대조군의 차이가 편향이 됩니다. 편향이 있다면 처치가 아닌 요인이 결과를 다르게 하는 원인입니다. 편향은 처치 효과를 왜곡시킵니다.\n",
    "\n",
    "편향이 없는 가상의 상황과 대조해 봅시다. 이제 태블릿이 무작위로 제공됩니다. 학교와 상관없이 태블릿을 받을 가능성은 같습니다. 처치는 학교 전반에 걸쳐 잘 분배됩니다.\n",
    "\n",
    "![img](./data/img/intro/anatomy3.png)\n",
    "\n",
    "이 경우 실험군과 대조군의 결과 차이는 평균적인 인과효과와 같습니다. 처치 외에 결과에 영향을 주는 요인이 없기 때문입니다. 모든 차이는 처치에 의한 것으로 편향이 존재하지 않습니다.\n",
    "\n",
    "![img](./data/img/intro/anatomy4.png)\n",
    "\n",
    "$Y_0$만 알 수 있게 (모든 사람이 처치받지 않게) 설정한다면 두 그룹 간 차이를 찾을 수 없을 것입니다.\n",
    "\n",
    "편향은 인과추론을 대단히 어렵게 합니다. 편향을 제거하여 두 그룹을 비교하는 방법은 평균적인 처치 효과만을 알려줍니다. 궁극적으로 인과추론은 망상과 잘못된 해석을 없애고 세상이 어떻게 돌아가는지 알아내는 것입니다. 앞으로 편향을 없애는 강력한 방법을 터득하여 인과효과를 계산해 보겠습니다.\n",
    "\n",
    "## Key Ideas\n",
    "\n",
    "1장에서는 상관관계와 인과관계가 무엇이 다른지 배웠습니다. 더 중요한 것은 상관관계를 인과관계로 만드는 방법입니다. 인과추론 방법을 수학적으로 표현하기 위해 `potential outcome`(잠재결과)에 대한 표기법을 도입했습니다. 잠재결과는 `outcome`(결과)을 두 가지 가능한 사실로 나눕니다. 하나는 `treatment`(처치)가 제공되는 것, 다른 하나는 처치가 제공되지 않는 것입니다. 실제로는 둘 중 하나만 알 수 있는데, 이는 인과추론의 근본적인 어려움입니다.\n",
    "\n",
    "다음 장에서는 무작위 실험 같은 인과효과를 추정하기 위한 몇 가지 기본 기술을 살펴봅니다. 또한 몇 가지 통계적 개념을 배울 예정입니다. 마지막으로 인과추론 수업에서 자주 사용되는 인용구로 마무리하겠습니다. `Kung Fu` 시리즈에서 가져온 것입니다.\n",
    "\n",
    "Caine: 사람의 앞날은 이미 정해져 있습니다. 운명에 따라야 합니다.  \n",
    "Old Man: 그래, 하지만 원하는 대로 살 수 있어. 반대로 보이지만, 모두 맞단다.\n",
    "\n",
    "## References\n",
    "\n",
    "I like to think of this book as a tribute to Joshua Angrist, Alberto Abadie and Christopher Walters for their amazing Econometrics class. Most of the ideas here are taken from their classes at the American Economic Association. Watching them is what's keeping me sane during this tough year of 2020.\n",
    "* [Cross-Section Econometrics](https://www.aeaweb.org/conference/cont-ed/2017-webcasts)\n",
    "* [Mastering Mostly Harmless Econometrics](https://www.aeaweb.org/conference/cont-ed/2020-webcasts)\n",
    "\n",
    "I'll also like to reference the amazing books from Angrist. They have shown me that Econometrics, or 'Metrics as they call it, is not only extremely useful but also profoundly fun.\n",
    "\n",
    "* [Mostly Harmless Econometrics](https://www.mostlyharmlesseconometrics.com/)\n",
    "* [Mastering 'Metrics](https://www.masteringmetrics.com/)\n",
    "\n",
    "My final reference is Miguel Hernan and Jamie Robins' book. It has been my trustworthy companion in the most thorny causal questions I had to answer.\n",
    "\n",
    "* [Causal Inference Book](https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/)\n",
    "\n",
    "The beer analogy was taken from the awesome [Stock Series](https://jlcollinsnh.com/2012/04/15/stocks-part-1-theres-a-major-market-crash-coming-and-dr-lo-cant-save-you/), by JL Colins. This is an absolute must read for all of those wanting to learn how to productively invest their money.\n",
    "\n",
    "![img](./data/img/poetry.png)\n",
    "\n",
    "## Contribute\n",
    "\n",
    "Causal Inference for the Brave and True is an open-source material on causal inference, the statistics of science. Its goal is to be accessible monetarily and intellectually. It uses only free software based on Python.\n",
    "If you found this book valuable and want to support it, please go to [Patreon](https://www.patreon.com/causal_inference_for_the_brave_and_true). If you are not ready to contribute financially, you can also help by fixing typos, suggesting edits, or giving feedback on passages you didn't understand. Go to the book's repository and [open an issue](https://github.com/matheusfacure/python-causality-handbook/issues). Finally, if you liked this content, please share it with others who might find it helpful and give it a [star on GitHub](https://github.com/matheusfacure/python-causality-handbook/stargazers)."
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