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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Model Evaluation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Review of last class\n",
      "\n",
      "- Goal was to predict the species of an **unknown iris**\n",
      "- Made predictions using KNN models with **different values of K**\n",
      "- Need a way to choose the **\"best\" model**: the one that \"generalizes\" to \"out-of-sample\" data\n",
      "\n",
      "**Solution:** Create a procedure that **estimates** how well a model is likely to perform on out-of-sample data and use that to choose between models."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Evaluation procedure #1: Train and test on the entire dataset"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. Train the model on the **entire dataset**.\n",
      "2. Test the model on the **same dataset**, and evaluate how well we did by comparing the **predicted** response values with the **true** response values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# read the iris data into a DataFrame\n",
      "import pandas as pd\n",
      "url = 'http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data'\n",
      "col_names = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width', 'species']\n",
      "iris = pd.read_csv(url, header=None, names=col_names)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# map each iris species to a number\n",
      "iris['species_num'] = iris.species.map({'Iris-setosa':0, 'Iris-versicolor':1, 'Iris-virginica':2})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# store feature matrix in \"X\"\n",
      "feature_cols = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width']\n",
      "X = iris[feature_cols]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# store response vector in \"y\"\n",
      "y = iris.species_num"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### KNN (K=50)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# import the class\n",
      "from sklearn.neighbors import KNeighborsClassifier\n",
      "\n",
      "# instantiate the model\n",
      "knn = KNeighborsClassifier(n_neighbors=50)\n",
      "\n",
      "# train the model on the entire dataset\n",
      "knn.fit(X, y)\n",
      "\n",
      "# predict the response values for the observations in X (\"test the model\")\n",
      "knn.predict(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
        "       1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
        "       1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2,\n",
        "       2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2,\n",
        "       1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], dtype=int64)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# store the predicted response values\n",
      "y_pred = knn.predict(X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To evaluate a model, we also need an **evaluation metric:**\n",
      "\n",
      "- Numeric calculation used to **quantify** the performance of a model\n",
      "- Appropriate metric depends on the **goals** of your problem\n",
      "\n",
      "Most common choices for classification problems:\n",
      "\n",
      "- **Classification accuracy**: percentage of correct predictions (reward function)\n",
      "- **Classification error**: percentage of incorrect predictions (loss function)\n",
      "\n",
      "In this case, we'll use classification accuracy."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute classification accuracy\n",
      "from sklearn import metrics\n",
      "print metrics.accuracy_score(y, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.94\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is known as **training accuracy** because we are testing the model on the same data we used to train the model."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![50NN classification map](images/iris_50nn_map.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### KNN (K=1)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "knn = KNeighborsClassifier(n_neighbors=1)\n",
      "knn.fit(X, y)\n",
      "y_pred = knn.predict(X)\n",
      "print metrics.accuracy_score(y, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.0\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Does that mean that K=1 is the best value for K?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![1NN classification map](images/iris_01nn_map.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problems with training and testing on the same data\n",
      "\n",
      "- Goal is to estimate likely performance of a model on **out-of-sample data**\n",
      "- But, maximizing training accuracy rewards **overly complex models** that won't necessarily generalize\n",
      "- Unnecessarily complex models **overfit** the training data:\n",
      "    - Will do well when tested using the in-sample data\n",
      "    - May do poorly on out-of-sample data\n",
      "    - Learns the \"noise\" in the data rather than the \"signal\"\n",
      "    - From Quora: [What is an intuitive explanation of overfitting?](http://www.quora.com/What-is-an-intuitive-explanation-of-overfitting/answer/Jessica-Su)\n",
      "\n",
      "**Thus, training accuracy is not a good estimate of out-of-sample accuracy.**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Evaluation procedure #2: Train/test split"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. Split the dataset into two pieces: a **training set** and a **testing set**.\n",
      "2. Train the model on the **training set**.\n",
      "3. Test the model on the **testing set**, and evaluate how well we did.\n",
      "\n",
      "What does this accomplish?\n",
      "\n",
      "- Model can be trained and tested on **different data** (we treat testing data like out-of-sample data).\n",
      "- Response values are **known** for the testing set, and thus **predictions can be evaluated**.\n",
      "- **Testing accuracy** is a better estimate than training accuracy of out-of-sample performance."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Side note on \"unpacking\""
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def min_max(nums):\n",
      "    smallest = min(nums)\n",
      "    largest = max(nums)\n",
      "    return [smallest, largest]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "min_and_max = min_max([1, 2, 3])\n",
      "print min_and_max\n",
      "print type(min_and_max)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1, 3]\n",
        "<type 'list'>\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "the_min, the_max = min_max([1, 2, 3])\n",
      "print the_min\n",
      "print type(the_min)\n",
      "print the_max\n",
      "print type(the_max)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n",
        "<type 'int'>\n",
        "3\n",
        "<type 'int'>\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Understanding the `train_test_split` function"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.cross_validation import train_test_split\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# before splitting\n",
      "print X.shape\n",
      "\n",
      "# after splitting\n",
      "print X_train.shape\n",
      "print X_test.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(150, 4)\n",
        "(90L, 4L)\n",
        "(60L, 4L)\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# before splitting\n",
      "print y.shape\n",
      "\n",
      "# after splitting\n",
      "print y_train.shape\n",
      "print y_test.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(150L,)\n",
        "(90L,)\n",
        "(60L,)\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![train_test_split](images/train_test_split.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Understanding the `random_state` parameter"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WITHOUT a random_state parameter\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4)\n",
      "\n",
      "# print the first element of each object\n",
      "print X_train[0]\n",
      "print X_test[0]\n",
      "print y_train[0]\n",
      "print y_test[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 6.1  3.   4.6  1.4]\n",
        "[ 6.2  2.9  4.3  1.3]\n",
        "1\n",
        "1\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WITH a random_state parameter\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=4)\n",
      "\n",
      "# print the first element of each object\n",
      "print X_train[0]\n",
      "print X_test[0]\n",
      "print y_train[0]\n",
      "print y_test[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 4.6  3.4  1.4  0.3]\n",
        "[ 6.4  2.8  5.6  2.1]\n",
        "0\n",
        "2\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Using the train/test split procedure (K=1)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# STEP 1: split X and y into training and testing sets (using random_state for reproducibility)\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# STEP 2: train the model on the training set (using K=1)\n",
      "knn = KNeighborsClassifier(n_neighbors=1)\n",
      "knn.fit(X_train, y_train)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
        "           metric_params=None, n_neighbors=1, p=2, weights='uniform')"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# STEP 3: test the model on the testing set, and check the accuracy\n",
      "y_pred = knn.predict(X_test)\n",
      "print metrics.accuracy_score(y_test, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.95\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Repeat for K=50"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "knn = KNeighborsClassifier(n_neighbors=50)\n",
      "knn.fit(X_train, y_train)\n",
      "y_pred = knn.predict(X_test)\n",
      "print metrics.accuracy_score(y_test, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.933333333333\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Bias-variance tradeoff](images/bias_variance.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Search for the \"best\" value of K"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# calculate TRAINING ERROR and TESTING ERROR for K=1 through 50\n",
      "k_range = range(1, 51)\n",
      "training_error = []\n",
      "testing_error = []\n",
      "for k in k_range:\n",
      "    knn = KNeighborsClassifier(n_neighbors=k)\n",
      "    # training error\n",
      "    knn.fit(X, y)\n",
      "    y_pred = knn.predict(X)\n",
      "    training_error.append(1 - metrics.accuracy_score(y, y_pred))\n",
      "    # testing error\n",
      "    knn.fit(X_train, y_train)\n",
      "    y_pred = knn.predict(X_test)\n",
      "    testing_error.append(1 - metrics.accuracy_score(y_test, y_pred))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "plt.style.use('ggplot')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the relationship between K (HIGH TO LOW) and TESTING ERROR\n",
      "plt.plot(k_range, testing_error)\n",
      "plt.gca().invert_xaxis()\n",
      "plt.xlabel('Value of K for KNN')\n",
      "plt.ylabel('Testing Error')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.text.Text at 0x176cb860>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9990n+LxSYuISHAkDZ+Z98tXFIdE+09zkBDB03nNOqihbrey2it/Z9Bc2x3Fu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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x17594b38>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What can we conclude?\n",
      "\n",
      "- A value of K around 11 is likely the **best value for K** when using KNN on the iris dataset.\n",
      "- When given the measurements of an **unknown iris**, we estimate that we would be able to correctly predict its species 98% of the time."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Training error versus testing error"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create a DataFrame of K, training error, and testing error\n",
      "df = pd.DataFrame({'K': k_range, 'train':training_error, 'test':testing_error}).set_index('K').sort_index(ascending=False)\n",
      "df.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>test</th>\n",
        "      <th>train</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>K</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>50</th>\n",
        "      <td>0.066667</td>\n",
        "      <td>0.060000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>49</th>\n",
        "      <td>0.083333</td>\n",
        "      <td>0.040000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>48</th>\n",
        "      <td>0.066667</td>\n",
        "      <td>0.053333</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>47</th>\n",
        "      <td>0.050000</td>\n",
        "      <td>0.046667</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>46</th>\n",
        "      <td>0.050000</td>\n",
        "      <td>0.053333</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "        test     train\n",
        "K                     \n",
        "50  0.066667  0.060000\n",
        "49  0.083333  0.040000\n",
        "48  0.066667  0.053333\n",
        "47  0.050000  0.046667\n",
        "46  0.050000  0.053333"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the relationship between K (HIGH TO LOW) and both TRAINING ERROR and TESTING ERROR\n",
      "df.plot()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<matplotlib.axes._subplots.AxesSubplot at 0x176f04e0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Nc7Sln+1VczNjJHMO6HQw4I7wLKG2FcFxx/vosN9El2zkntLYN3vMRi33lph5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\na1X9E0hELwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x176f2cf8>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Roughly speaking:\n",
      "\n",
      "- **Training error** decreases as model complexity increases (lower value of K)\n",
      "- **Testing error** is minimized at the optimum model complexity"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Bias-variance tradeoff](images/training_testing_error.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Making predictions on out-of-sample data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given the measurements of a (truly) unknown iris, how do we predict its species?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# instantiate the model with the best known parameters\n",
      "knn = KNeighborsClassifier(n_neighbors=11)\n",
      "\n",
      "# re-train the model with X and y (not X_train and y_train) - why?\n",
      "knn.fit(X, y)\n",
      "\n",
      "# make a prediction for an out-of-sample observation\n",
      "knn.predict([3, 5, 4, 2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "array([1], dtype=int64)"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Disadvantages of train/test split?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What would happen if the `train_test_split` function had split the data differently? Would we get the same exact results as before?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# try different values for random_state\n",
      "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=4)\n",
      "knn = KNeighborsClassifier(n_neighbors=50)\n",
      "knn.fit(X_train, y_train)\n",
      "y_pred = knn.predict(X_test)\n",
      "print metrics.accuracy_score(y_test, y_pred)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.933333333333\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- Testing accuracy is a **high-variance estimate** of out-of-sample accuracy\n",
      "- **K-fold cross-validation** overcomes this limitation and provides more reliable estimates\n",
      "- But, train/test split is still useful because of its **flexibility and speed**"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}