Lecture10-Demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "b6a45fa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.pipeline import Pipeline, make_pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from sklearn.linear_model import LinearRegression, LassoCV, ElasticNetCV, RidgeCV, Ridge, Lasso\n",
    "from sklearn.ensemble import RandomForestRegressor, GradientBoostingRegressor\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import cross_val_score, KFold, GridSearchCV\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "import patsy\n",
    "import warnings\n",
    "from sklearn.base import BaseEstimator, clone\n",
    "import statsmodels.api as sm\n",
    "warnings.simplefilter('ignore')\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "ec6ec82b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# simple scalar regression \"population\" dgp\n",
    "n = 10000\n",
    "W = np.random.uniform(0, 1, size=(n, 1))\n",
    "y = np.exp(2 * W[:, 0])\n",
    "grid = np.linspace(0, 1, 1000).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "e9ff9106",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit BLPs with polynomial features\n",
    "dtr = lambda d: DecisionTreeRegressor(max_depth=d)\n",
    "pred1 = dtr(5).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "0eeb4458",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# even 3rd degree polynomial is good enough\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "4ca961c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now let's go to finite sample and noisy data\n",
    "n = 5000\n",
    "W = np.random.uniform(0, 1, size=(n, 1))\n",
    "y = np.exp(2 * W[:, 0]) + np.random.normal(0, 5, size=n)\n",
    "grid = np.linspace(0, 1, 1000).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "01b46d81",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit BLPs with polynomial features\n",
    "dtr = lambda d: DecisionTreeRegressor(max_depth=d)\n",
    "pred1 = dtr(5).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "2a343ccf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It is very noisy!\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "581f2f6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit BLPs with polynomial features\n",
    "dtr = lambda d: RandomForestRegressor(n_estimators=1000, max_depth=d)\n",
    "pred1 = dtr(10).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "ad125ed1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It is very noisy!\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "9910e0dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "from econml.grf import RegressionForest\n",
    "\n",
    "# Let's fit BLPs with polynomial features\n",
    "dtr = lambda d: RegressionForest(n_estimators=1000, \n",
    "                                 honest=True,\n",
    "                                 max_samples=.5,\n",
    "                                 inference=False,\n",
    "                                 max_depth=d, min_samples_split=2, min_samples_leaf=1)\n",
    "pred1 = dtr(10).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "9d915966",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It is very noisy!\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "43daf9d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit BLPs with polynomial features\n",
    "dtr = lambda d: GradientBoostingRegressor(n_estimators=1000, max_depth=d, n_iter_no_change=5)\n",
    "pred1 = dtr(2).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "9fcc1914",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It is very noisy!\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "ebece18b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neural_network import MLPRegressor\n",
    "# Let's fit BLPs with polynomial features\n",
    "dtr = lambda d: MLPRegressor()\n",
    "pred1 = dtr(2).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "b6813ebc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It is very noisy!\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "01b499b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import StackingRegressor\n",
    "# Let's fit BLPs with polynomial features\n",
    "est1 = ('nnet', MLPRegressor())\n",
    "est2 = ('ols', LinearRegression())\n",
    "est3 = ('polylasso', make_pipeline(PolynomialFeatures(degree=3, include_bias=False), LassoCV()))\n",
    "est4 = ('rf', RandomForestRegressor(min_samples_leaf=20))\n",
    "est5 = ('gbf', GradientBoostingRegressor(n_estimators=50, max_depth=2, n_iter_no_change=5))\n",
    "stack = StackingRegressor([est1, est2, est3, est4, est5], final_estimator=LinearRegression(), n_jobs=-1)\n",
    "pred1 = stack.fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "455d234d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It is very noisy!\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "894c344e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[flaml.automl.automl: 02-09 13:00:13] {2715} INFO - task = regression\n",
      "[flaml.automl.automl: 02-09 13:00:13] {2717} INFO - Data split method: uniform\n",
      "[flaml.automl.automl: 02-09 13:00:13] {2720} INFO - Evaluation method: cv\n",
      "[flaml.automl.automl: 02-09 13:00:13] {2847} INFO - Minimizing error metric: 1-r2\n",
      "[flaml.automl.automl: 02-09 13:00:13] {2993} INFO - List of ML learners in AutoML Run: ['lgbm', 'rf', 'xgboost', 'extra_tree', 'xgb_limitdepth']\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3322} INFO - iteration 0, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3460} INFO - Estimated sufficient time budget=500s. Estimated necessary time budget=4s.\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3507} INFO -  at 0.1s,\testimator lgbm's best error=0.9386,\tbest estimator lgbm's best error=0.9386\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3322} INFO - iteration 1, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3507} INFO -  at 0.1s,\testimator lgbm's best error=0.9386,\tbest estimator lgbm's best error=0.9386\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3322} INFO - iteration 2, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3507} INFO -  at 0.1s,\testimator lgbm's best error=0.9003,\tbest estimator lgbm's best error=0.9003\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3322} INFO - iteration 3, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3507} INFO -  at 0.2s,\testimator lgbm's best error=0.8960,\tbest estimator lgbm's best error=0.8960\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3322} INFO - iteration 4, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3507} INFO -  at 0.2s,\testimator lgbm's best error=0.8960,\tbest estimator lgbm's best error=0.8960\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3322} INFO - iteration 5, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3507} INFO -  at 0.3s,\testimator lgbm's best error=0.8960,\tbest estimator lgbm's best error=0.8960\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3322} INFO - iteration 6, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3507} INFO -  at 0.3s,\testimator lgbm's best error=0.8946,\tbest estimator lgbm's best error=0.8946\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3322} INFO - iteration 7, current learner xgboost\n",
      "[flaml.automl.automl: 02-09 13:00:13] {3507} INFO -  at 0.3s,\testimator xgboost's best error=1.0563,\tbest estimator lgbm's best error=0.8946\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3322} INFO - iteration 8, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3507} INFO -  at 0.4s,\testimator lgbm's best error=0.8910,\tbest estimator lgbm's best error=0.8910\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3322} INFO - iteration 9, current learner lgbm\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3507} INFO -  at 0.5s,\testimator lgbm's best error=0.8910,\tbest estimator lgbm's best error=0.8910\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3322} INFO - iteration 10, current learner xgboost\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3507} INFO -  at 0.5s,\testimator xgboost's best error=1.0563,\tbest estimator lgbm's best error=0.8910\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3322} INFO - iteration 11, current learner xgboost\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3507} INFO -  at 0.6s,\testimator xgboost's best error=0.9255,\tbest estimator lgbm's best error=0.8910\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3322} INFO - iteration 12, current learner xgboost\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3507} INFO -  at 0.6s,\testimator xgboost's best error=0.8967,\tbest estimator lgbm's best error=0.8910\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3322} INFO - iteration 13, current learner xgboost\n",
      "[flaml.automl.automl: 02-09 13:00:14] {3507} INFO -  at 0.7s,\testimator xgboost's best error=0.8967,\tbest estimator lgbm's best error=0.8910\n",
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      "[flaml.automl.automl: 02-09 13:00:23] {3771} INFO - retrain extra_tree for 0.1s\n",
      "[flaml.automl.automl: 02-09 13:00:23] {3778} INFO - retrained model: ExtraTreesRegressor(max_features=0.8284621129934027, max_leaf_nodes=18,\n",
      "                    n_estimators=10, n_jobs=-1, random_state=12032022)\n",
      "[flaml.automl.automl: 02-09 13:00:23] {3023} INFO - fit succeeded\n",
      "[flaml.automl.automl: 02-09 13:00:23] {3024} INFO - Time taken to find the best model: 4.670956373214722\n"
     ]
    }
   ],
   "source": [
    "from flaml import AutoML\n",
    "\n",
    "automl = AutoML(task='regression', time_budget=10, early_stop=True,\n",
    "                eval_method='cv', n_splits=3, metric='r2',\n",
    "                verbose=3)\n",
    "automl.fit(W, y)\n",
    "pred1 = automl.predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "f0c86c8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It is very noisy!\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1d9a15e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}