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    "## Gradient boosting\n",
    "\n",
    "This is a minimal but workable implementation of Gradient Boosting Decision Trees with scikit-learn\n",
    "\n",
    "Read more in this [blog post](http://nicolas-hug.com/blog/gradient_boosting_descent)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.special import expit as sigmoid\n",
    "from sklearn.base import BaseEstimator, RegressorMixin, ClassifierMixin\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.datasets import make_regression\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BaseGradientBoosting(BaseEstimator):\n",
    "    def __init__(self, n_iter, learning_rate, loss):\n",
    "        self.loss = loss\n",
    "        self.learning_rate = learning_rate\n",
    "        self.n_iter = n_iter\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        rng = np.random.RandomState(seed=0)\n",
    "\n",
    "        n_samples = X.shape[0]\n",
    "        y_pred_train = rng.normal(size=n_samples)\n",
    "\n",
    "        self.predictors = list()\n",
    "\n",
    "        for m in range(self.n_iter):  # Gradient Descent\n",
    "\n",
    "            negative_gradient = -self.loss.compute_gradients(y, y_pred_train)\n",
    "            new_predictor = DecisionTreeRegressor(max_depth=3)\n",
    "            new_predictor.fit(X, y=self.learning_rate * negative_gradient)\n",
    "            y_pred_train += new_predictor.predict(X)\n",
    "\n",
    "            self.predictors.append(new_predictor)  # save for predict()\n",
    "\n",
    "    def predict(self, X):\n",
    "        return sum(predictor.predict(X) for predictor in self.predictors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r squared on training data: 0.997\n",
      "r squared on test data: 0.937\n"
     ]
    }
   ],
   "source": [
    "# GBDT for regression\n",
    "\n",
    "class LeastSquaresLoss:\n",
    "    def compute_gradients(self, y_true, y_pred):\n",
    "        return -2 * (y_true - y_pred)\n",
    "    \n",
    "\n",
    "class GradientBoostingRegressor(BaseGradientBoosting, RegressorMixin):\n",
    "    \n",
    "    def __init__(self, n_iter=100, learning_rate=.1):\n",
    "        super().__init__(n_iter, learning_rate, loss=LeastSquaresLoss())\n",
    "\n",
    "\n",
    "X, y = make_regression(n_samples=1000, random_state=0)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)\n",
    "gb = GradientBoostingRegressor()\n",
    "gb.fit(X_train, y_train)\n",
    "\n",
    "print('r squared on training data: {:.3f}'.format(gb.score(X_train, y_train)))\n",
    "print('r squared on test data: {:.3f}'.format(gb.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy on training data: 0.981\n",
      "accuracy on test data: 0.956\n"
     ]
    }
   ],
   "source": [
    "# GBDT for classification\n",
    "\n",
    "class BinaryCrossEntropy:\n",
    "    def compute_gradients(self, y_true, y_pred):\n",
    "        return sigmoid(y_pred) - y_true\n",
    "    def raw_predictions_to_proba(self, raw_predictions):\n",
    "        return sigmoid(raw_predictions)\n",
    "\n",
    "\n",
    "class GradientBoostingClassifier(BaseGradientBoosting, ClassifierMixin):\n",
    "\n",
    "    def __init__(self, n_iter=100, learning_rate=.1):\n",
    "        super().__init__(n_iter, learning_rate, loss=BinaryCrossEntropy())\n",
    "\n",
    "    def predict(self, X):\n",
    "        raw_predictions = super().predict(X)\n",
    "        proba_positive_class = self.loss.raw_predictions_to_proba(raw_predictions)\n",
    "        return proba_positive_class > .5\n",
    "\n",
    "X, y = make_classification(n_samples=1000, random_state=0)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)\n",
    "gb = GradientBoostingClassifier()\n",
    "gb.fit(X_train, y_train)\n",
    "\n",
    "print('accuracy on training data: {:.3f}'.format(gb.score(X_train, y_train)))\n",
    "print('accuracy on test data: {:.3f}'.format(gb.score(X_test, y_test)))"
   ]
  }
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