3.6-predicting-house-prices.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'2.2.2'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import keras\n",
    "keras.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 주택 가격 예측: 회귀 문제\n",
    "\n",
    "이 노트북은 [케라스 창시자에게 배우는 딥러닝](https://tensorflow.blog/%EC%BC%80%EB%9D%BC%EC%8A%A4-%EB%94%A5%EB%9F%AC%EB%8B%9D/) 책의 3장 6절의 코드 예제입니다. 책에는 더 많은 내용과 그림이 있습니다. 이 노트북에는 소스 코드에 관련된 설명만 포함합니다.\n",
    "\n",
    "----\n",
    "\n",
    "앞의 두 예제는 분류 문제입니다. 입력 데이터 포인트의 개별적인 레이블 하나를 예측하는 것이 목적입니다. 또 다른 종류의 머신 러닝 문제는 개별적인 레이블 대신에 연속적인 값을 예측하는 회귀(regression)입니다. 예를 들어 기상 데이터가 주어졌을 때 내일 기온을 예측하거나 소프트웨어 명세가 주어졌을 때 소프트웨어 프로젝트가 완료될 시간을 예측하는 것입니다.\n",
    "\n",
    "회귀와 로지스틱 회귀 알고리즘을 혼돈하지 마세요. 로지스틱 회귀는 회귀 알고리즘이 아니라 분류 알고리즘입니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 보스턴 주택 가격 데이터셋\n",
    "\n",
    "1970년 중반 보스턴 외곽 지역의 범죄율, 지방세율 등의 데이터가 주어졌을 때 주택 가격의 중간 값을 예측해 보겠습니다.\n",
    "\n",
    "여기서 사용할 데이터셋은 이전 두 개의 예제와 다릅니다. 데이터 포인트가 506개로 비교적 개수가 적고 404개는 훈련 샘플로 102개는 테스트 샘플로 나누어져 있습니다. 입력 데이터에 있는 각 특성(예를 들어 범죄율)은 스케일이 서로 다릅니다. 어떤 값은 0과 1 사이의 비율을 나타내고 어떤 것은 1과 12 사이의 값을 가지거나 1과 100 사이의 값을 가집니다.\n",
    "\n",
    "데이터를 살펴보겠습니다:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.datasets import boston_housing\n",
    "\n",
    "(train_data, train_targets), (test_data, test_targets) =  boston_housing.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(404, 13)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(102, 13)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "여기서 볼 수 있듯이 404개의 훈련 샘플과 102개의 테스트 샘플이 있고 모두 13개의 수치 특성을 가지고 있습니다. 13개의 특성은 다음과 같습니다:\n",
    "\n",
    "1. Per capita crime rate.\n",
    "2. Proportion of residential land zoned for lots over 25,000 square feet.\n",
    "3. Proportion of non-retail business acres per town.\n",
    "4. Charles River dummy variable (= 1 if tract bounds river; 0 otherwise).\n",
    "5. Nitric oxides concentration (parts per 10 million).\n",
    "6. Average number of rooms per dwelling.\n",
    "7. Proportion of owner-occupied units built prior to 1940.\n",
    "8. Weighted distances to five Boston employment centres.\n",
    "9. Index of accessibility to radial highways.\n",
    "10. Full-value property-tax rate per $10,000.\n",
    "11. Pupil-teacher ratio by town.\n",
    "12. 1000 * (Bk - 0.63) ** 2 where Bk is the proportion of Black people by town.\n",
    "13. % lower status of the population.\n",
    "\n",
    "타깃은 주택의 중간 가격으로 천달러 단위입니다:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15.2, 42.3, 50. , 21.1, 17.7, 18.5, 11.3, 15.6, 15.6, 14.4, 12.1,\n",
       "       17.9, 23.1, 19.9, 15.7,  8.8, 50. , 22.5, 24.1, 27.5, 10.9, 30.8,\n",
       "       32.9, 24. , 18.5, 13.3, 22.9, 34.7, 16.6, 17.5, 22.3, 16.1, 14.9,\n",
       "       23.1, 34.9, 25. , 13.9, 13.1, 20.4, 20. , 15.2, 24.7, 22.2, 16.7,\n",
       "       12.7, 15.6, 18.4, 21. , 30.1, 15.1, 18.7,  9.6, 31.5, 24.8, 19.1,\n",
       "       22. , 14.5, 11. , 32. , 29.4, 20.3, 24.4, 14.6, 19.5, 14.1, 14.3,\n",
       "       15.6, 10.5,  6.3, 19.3, 19.3, 13.4, 36.4, 17.8, 13.5, 16.5,  8.3,\n",
       "       14.3, 16. , 13.4, 28.6, 43.5, 20.2, 22. , 23. , 20.7, 12.5, 48.5,\n",
       "       14.6, 13.4, 23.7, 50. , 21.7, 39.8, 38.7, 22.2, 34.9, 22.5, 31.1,\n",
       "       28.7, 46. , 41.7, 21. , 26.6, 15. , 24.4, 13.3, 21.2, 11.7, 21.7,\n",
       "       19.4, 50. , 22.8, 19.7, 24.7, 36.2, 14.2, 18.9, 18.3, 20.6, 24.6,\n",
       "       18.2,  8.7, 44. , 10.4, 13.2, 21.2, 37. , 30.7, 22.9, 20. , 19.3,\n",
       "       31.7, 32. , 23.1, 18.8, 10.9, 50. , 19.6,  5. , 14.4, 19.8, 13.8,\n",
       "       19.6, 23.9, 24.5, 25. , 19.9, 17.2, 24.6, 13.5, 26.6, 21.4, 11.9,\n",
       "       22.6, 19.6,  8.5, 23.7, 23.1, 22.4, 20.5, 23.6, 18.4, 35.2, 23.1,\n",
       "       27.9, 20.6, 23.7, 28. , 13.6, 27.1, 23.6, 20.6, 18.2, 21.7, 17.1,\n",
       "        8.4, 25.3, 13.8, 22.2, 18.4, 20.7, 31.6, 30.5, 20.3,  8.8, 19.2,\n",
       "       19.4, 23.1, 23. , 14.8, 48.8, 22.6, 33.4, 21.1, 13.6, 32.2, 13.1,\n",
       "       23.4, 18.9, 23.9, 11.8, 23.3, 22.8, 19.6, 16.7, 13.4, 22.2, 20.4,\n",
       "       21.8, 26.4, 14.9, 24.1, 23.8, 12.3, 29.1, 21. , 19.5, 23.3, 23.8,\n",
       "       17.8, 11.5, 21.7, 19.9, 25. , 33.4, 28.5, 21.4, 24.3, 27.5, 33.1,\n",
       "       16.2, 23.3, 48.3, 22.9, 22.8, 13.1, 12.7, 22.6, 15. , 15.3, 10.5,\n",
       "       24. , 18.5, 21.7, 19.5, 33.2, 23.2,  5. , 19.1, 12.7, 22.3, 10.2,\n",
       "       13.9, 16.3, 17. , 20.1, 29.9, 17.2, 37.3, 45.4, 17.8, 23.2, 29. ,\n",
       "       22. , 18. , 17.4, 34.6, 20.1, 25. , 15.6, 24.8, 28.2, 21.2, 21.4,\n",
       "       23.8, 31. , 26.2, 17.4, 37.9, 17.5, 20. ,  8.3, 23.9,  8.4, 13.8,\n",
       "        7.2, 11.7, 17.1, 21.6, 50. , 16.1, 20.4, 20.6, 21.4, 20.6, 36.5,\n",
       "        8.5, 24.8, 10.8, 21.9, 17.3, 18.9, 36.2, 14.9, 18.2, 33.3, 21.8,\n",
       "       19.7, 31.6, 24.8, 19.4, 22.8,  7.5, 44.8, 16.8, 18.7, 50. , 50. ,\n",
       "       19.5, 20.1, 50. , 17.2, 20.8, 19.3, 41.3, 20.4, 20.5, 13.8, 16.5,\n",
       "       23.9, 20.6, 31.5, 23.3, 16.8, 14. , 33.8, 36.1, 12.8, 18.3, 18.7,\n",
       "       19.1, 29. , 30.1, 50. , 50. , 22. , 11.9, 37.6, 50. , 22.7, 20.8,\n",
       "       23.5, 27.9, 50. , 19.3, 23.9, 22.6, 15.2, 21.7, 19.2, 43.8, 20.3,\n",
       "       33.2, 19.9, 22.5, 32.7, 22. , 17.1, 19. , 15. , 16.1, 25.1, 23.7,\n",
       "       28.7, 37.2, 22.6, 16.4, 25. , 29.8, 22.1, 17.4, 18.1, 30.3, 17.5,\n",
       "       24.7, 12.6, 26.5, 28.7, 13.3, 10.4, 24.4, 23. , 20. , 17.8,  7. ,\n",
       "       11.8, 24.4, 13.8, 19.4, 25.2, 19.4, 19.4, 29.1])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_targets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이 가격은 일반적으로 10,000달러에서 50,000달러 사이입니다. 저렴하게 느껴질텐데 1970년대 중반이라는 걸 기억하세요. 아직 인플레이션에 영향을 받지 않은 가격입니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 데이터 준비\n",
    "\n",
    "상이한 스케일을 가진 값을 신경망에 주입하면 문제가 됩니다. 네트워크가 이런 다양한 데이터에 자동으로 맞추려고 할 수 있지만 이는 확실히 학습을 더 어렵게 만듭니다. 이런 데이터를 다룰 때 대표적인 방법은 특성별로 정규화를 하는 것입니다. 입력 데이터에 있는 각 특성(입력 데이터 행렬의 열)에 대해서 특성의 평균을 빼고 표준 편차로 나눕니다. 특성의 중앙이 0 근처에 맞춰지고 표준 편차가 1이 됩니다. 넘파이를 사용하면 간단하게 할 수 있습니다:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = train_data.mean(axis=0)\n",
    "train_data -= mean\n",
    "std = train_data.std(axis=0)\n",
    "train_data /= std\n",
    "\n",
    "test_data -= mean\n",
    "test_data /= std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "테스트 데이터를 정규화할 때 사용한 값이 훈련 데이터에서 계산한 값임을 주목하세요. 머신 러닝 작업 과정에서 절대로 테스트 데이터에서 계산한 어떤 값도 사용해서는 안 됩니다. 데이터 정규화처럼 간단한 작업조차도 그렇습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 모델 구성\n",
    "\n",
    "샘플의 개수가 적기 때문에 64개의 유닛을 가진 두 개의 은닉층으로 작은 네트워크를 구성하여 사용하겠습니다. 일반적으로 훈련 데이터의 개수가 적을수록 과대적합이 더 쉽게 일어나므로 작은 모델을 사용하는 것이 과대적합을 피하는 한 방법입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras import models\n",
    "from keras import layers\n",
    "\n",
    "def build_model():\n",
    "    # 동일한 모델을 여러 번 생성할 것이므로 함수를 만들어 사용합니다\n",
    "    model = models.Sequential()\n",
    "    model.add(layers.Dense(64, activation='relu',\n",
    "                           input_shape=(train_data.shape[1],)))\n",
    "    model.add(layers.Dense(64, activation='relu'))\n",
    "    model.add(layers.Dense(1))\n",
    "    model.compile(optimizer='rmsprop', loss='mse', metrics=['mae'])\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이 네트워크의 마지막 층은 하나의 유닛을 가지고 있고 활성화 함수가 없습니다(선형 층이라고 합니다). 이것이 전형적인 스칼라 회귀(하나의 연속적인 값을 예측하는 회귀)를 위한 구성입니다. 활성화 함수를 적용하면 출력 값의 범위를 제한하게 됩니다. 예를 들어 마지막 층에 `sigmoid` 활성화 함수를 적용하면 네트워크가 0과 1 사이의 값을 예측하도록 학습될 것입니다. 여기서는 마지막 층이 순수한 선형이므로 네트워크가 어떤 범위의 값이라도 예측하도록 자유롭게 학습됩니다.\n",
    "\n",
    "이 모델은 `mse` 손실 함수를 사용하여 컴파일합니다. 이 함수는 평균 제곱 오차(mean squared error)의 약자로 예측과 타깃 사이 거리의 제곱입니다. 회귀 문제에서 널리 사용되는 손실 함수입니다.\n",
    "\n",
    "훈련하는 동안 모니터링을 위해 새로운 지표인 평균 절대 오차를 측정합니다. 이는 예측과 타깃 사이 거리의 절댓값입니다. 예를 들어 이 예제에서 MAE가 0.5이면 예측이 평균적으로 $500 정도 차이가 난다는 뜻입니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-겹 검증을 사용한 훈련 검증\n",
    "\n",
    "(훈련에 사용할 에포크의 수 같은) 매개변수들을 조정하면서 모델을 평가하기 위해 이전 예제에서 했던 것처럼 데이터를 훈련 세트와 검증 세트로 나눕니다. 데이터 포인트가 많지 않기 때문에 검증 세트도 매우 작아집니다(약 100개의 샘플). 결국 검증 세트와 훈련 세트로 어떤 데이터 포인트가 선택됐는지에 따라 검증 점수가 크게 달라집니다. 검증 세트의 분할에 대한 검증 점수의 분산이 높습니다. 이렇게 되면 신뢰있는 모델 평가를 신뢰있게 할 수 없습니다.\n",
    "\n",
    "이런 상황에서 가장 좋은 방법은 K-겹 교차 검증을 사용하는 것입니다. 데이터를 K개의 분할(즉, 폴드)로 나누고(일반적으로 K = 4 또는 5), K개의 모델을 각각 만들어 K - 1개의 분할에서 훈련하고 나머지 분할에서 평가하는 방법입니다. 모델의 검증 점수는 K 개의 검증 점수의 평균이 됩니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "코드로 보면 이해하기 쉽습니다:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "처리중인 폴드 # 0\n",
      "처리중인 폴드 # 1\n",
      "처리중인 폴드 # 2\n",
      "처리중인 폴드 # 3\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "k = 4\n",
    "num_val_samples = len(train_data) // k\n",
    "num_epochs = 100\n",
    "all_scores = []\n",
    "for i in range(k):\n",
    "    print('처리중인 폴드 #', i)\n",
    "    # 검증 데이터 준비: k번째 분할\n",
    "    val_data = train_data[i * num_val_samples: (i + 1) * num_val_samples]\n",
    "    val_targets = train_targets[i * num_val_samples: (i + 1) * num_val_samples]\n",
    "\n",
    "    # 훈련 데이터 준비: 다른 분할 전체\n",
    "    partial_train_data = np.concatenate(\n",
    "        [train_data[:i * num_val_samples],\n",
    "         train_data[(i + 1) * num_val_samples:]],\n",
    "        axis=0)\n",
    "    partial_train_targets = np.concatenate(\n",
    "        [train_targets[:i * num_val_samples],\n",
    "         train_targets[(i + 1) * num_val_samples:]],\n",
    "        axis=0)\n",
    "\n",
    "    # 케라스 모델 구성(컴파일 포함)\n",
    "    model = build_model()\n",
    "    # 모델 훈련(verbose=0 이므로 훈련 과정이 출력되지 않습니다)\n",
    "    model.fit(partial_train_data, partial_train_targets,\n",
    "              epochs=num_epochs, batch_size=1, verbose=0)\n",
    "    # 검증 세트로 모델 평가\n",
    "    val_mse, val_mae = model.evaluate(val_data, val_targets, verbose=0)\n",
    "    all_scores.append(val_mae)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.0956787838794217, 2.220593797098292, 2.859968412040484, 2.40535704039111]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3953995083523267"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(all_scores)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "검증 세트가 다르므로 확실히 검증 점수가 2.0에서 2.8까지 변화가 큽니다. 평균값(2.4)이 각각의 점수보다 훨씬 신뢰할 만한 점수입니다. 이것이 K-겹 교차 검증의 핵심입니다. 이 예에서는 평균적으로 3,000달러 정도 차이가 납니다. 주택 가격의 범위가 10,000달러에서 50,000달러 사이인 것을 감안하면 비교적 큰 값입니다.\n",
    "\n",
    "신경망을 조금 더 오래 500 에포크 동안 훈련해 보죠. 각 에포크마다 모델이 얼마나 개선되는지 기록하기 위해 훈련 루프를 조금 수정해서 에포크의 검증 점수를 로그에 저장하겠습니다:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras import backend as K\n",
    "\n",
    "# 메모리 해제\n",
    "K.clear_session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "처리중인 폴드 # 0\n",
      "처리중인 폴드 # 1\n",
      "처리중인 폴드 # 2\n",
      "처리중인 폴드 # 3\n"
     ]
    }
   ],
   "source": [
    "num_epochs = 500\n",
    "all_mae_histories = []\n",
    "for i in range(k):\n",
    "    print('처리중인 폴드 #', i)\n",
    "    # 검증 데이터 준비: k번째 분할\n",
    "    val_data = train_data[i * num_val_samples: (i + 1) * num_val_samples]\n",
    "    val_targets = train_targets[i * num_val_samples: (i + 1) * num_val_samples]\n",
    "\n",
    "    # 훈련 데이터 준비: 다른 분할 전체\n",
    "    partial_train_data = np.concatenate(\n",
    "        [train_data[:i * num_val_samples],\n",
    "         train_data[(i + 1) * num_val_samples:]],\n",
    "        axis=0)\n",
    "    partial_train_targets = np.concatenate(\n",
    "        [train_targets[:i * num_val_samples],\n",
    "         train_targets[(i + 1) * num_val_samples:]],\n",
    "        axis=0)\n",
    "\n",
    "    # 케라스 모델 구성(컴파일 포함)\n",
    "    model = build_model()\n",
    "    # 모델 훈련(verbose=0 이므로 훈련 과정이 출력되지 않습니다)\n",
    "    history = model.fit(partial_train_data, partial_train_targets,\n",
    "                        validation_data=(val_data, val_targets),\n",
    "                        epochs=num_epochs, batch_size=1, verbose=0)\n",
    "    mae_history = history.history['val_mean_absolute_error']\n",
    "    all_mae_histories.append(mae_history)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "그다음 모든 폴드에 대해 에포크의 MAE 점수의 평균을 계산합니다:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_mae_history = [\n",
    "    np.mean([x[i] for x in all_mae_histories]) for i in range(num_epochs)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "그래프로 그려 보겠습니다:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1, len(average_mae_history) + 1), average_mae_history)\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Validation MAE')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이 그래프는 범위가 크고 변동이 심하기 때문에 보기가 좀 어렵습니다. 다음처럼 해 보죠:\n",
    "\n",
    "* 곡선의 다른 부분과 스케일이 많이 다른 첫 10개 데이터 포인트를 제외시킵니다.\n",
    "* 부드러운 곡선을 얻기 위해 각 포인트를 이전 포인트의 지수 이동 평균으로 대체합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def smooth_curve(points, factor=0.9):\n",
    "  smoothed_points = []\n",
    "  for point in points:\n",
    "    if smoothed_points:\n",
    "      previous = smoothed_points[-1]\n",
    "      smoothed_points.append(previous * factor + point * (1 - factor))\n",
    "    else:\n",
    "      smoothed_points.append(point)\n",
    "  return smoothed_points\n",
    "\n",
    "smooth_mae_history = smooth_curve(average_mae_history[10:])\n",
    "\n",
    "plt.plot(range(1, len(smooth_mae_history) + 1), smooth_mae_history)\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Validation MAE')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이 그래프를 보면 검증 MAE가 80번째 에포크 이후에 줄어드는 것이 멈추었습니다. 이 지점 이후로는 과대적합이 시작됩니다.\n",
    "\n",
    "모델의 다른 매개변수에 대한 튜닝이 끝나면(에포크 수뿐만 아니라 은닉층의 크기도 조절할 수 있습니다) 모든 훈련 데이터를 사용하고 최상의 매개변수로 최종 실전에 투입될 모델을 훈련시킵니다. 그다음 테스트 데이터로 성능을 확인합니다:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "102/102 [==============================] - 0s 377us/step\n"
     ]
    }
   ],
   "source": [
    "# 새롭게 컴파인된 모델을 얻습니다\n",
    "model = build_model()\n",
    "# 전체 데이터로 훈련시킵니다\n",
    "model.fit(train_data, train_targets,\n",
    "          epochs=80, batch_size=16, verbose=0)\n",
    "test_mse_score, test_mae_score = model.evaluate(test_data, test_targets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.675027286305147"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_mae_score"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "아직 2,675달러 정도 차이가 나네요."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 정리\n",
    "\n",
    "다음은 이 예제에서 배운 것들입니다.\n",
    "\n",
    "* 회귀는 분류에서 사용했던 것과는 다른 손실 함수를 사용합니다. 평균 제곱 오차(MSE)는 회귀에서 자주 사용되는 손실 함수입니다.\n",
    "* 비슷하게 회귀에서 사용되는 평가 지표는 분류와 다릅니다. 당연히 정확도 개념은 회귀에 적용되지 않습니다. 일반적인 회귀 지표는 평균 절대 오차(MAE)입니다.\n",
    "* 입력 데이터의 특성이 서로 다른 범위를 가지면 전처리 단계에서 각 특성을 개별적으로 스케일 조정해야 합니다.\n",
    "* 가용한 데이터가 적다면 K-겹 검증을 사용하는 것이 신뢰할 수 있는 모델 신뢰있게 평가 방법입니다.\n",
    "* 가용한 훈련 데이터가 적다면 과대적합을 피하기 위해 은닉층의 수를 줄인 모델이 좋습니다(일반적으로 하나 또는 두 개).\n",
    "\n",
    "세 개의 예제 시리즈를 마칩니다. 이제 벡터 데이터 입력을 받는 일반적인 문제를 다룰 수 있습니다:\n",
    "\n",
    "* 이진 분류\n",
    "* 단일 레이블 다중 분류\n",
    "* 스칼라 회귀\n",
    "\n",
    "다음 장에서 이 예제들에서 보았던 데이터 전처리, 모델 평가, 과대접과 같은 개념에 대해 조금 더 이론적인 설명을 보완하겠습니다."
   ]
  }
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