{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "BvJ0QjgbuFtp"
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets, linear_model, model_selection\n",
    "\n",
    "# load the data\n",
    "diabetes = datasets.load_diabetes()\n",
    "\n",
    "# target\n",
    "y = diabetes.target\n",
    "\n",
    "# features\n",
    "X = diabetes.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 910,
     "status": "ok",
     "timestamp": 1571316858888,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "XKHMBvvmudNU",
    "outputId": "82434ba9-2d90-4beb-f13e-4c068d096eed"
   },
   "outputs": [],
   "source": [
    "# the first patient has index 0\n",
    "print(y[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 54
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 905,
     "status": "ok",
     "timestamp": 1571316858890,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "hlKYUSJSuhQH",
    "outputId": "3f0acc84-f9f3-4808-b89f-8e36cd4c1276"
   },
   "outputs": [],
   "source": [
    "# lets look at the first patients data\n",
    "print(\n",
    "  dict(zip(diabetes.feature_names, X[0]))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1388,
     "status": "ok",
     "timestamp": 1571316859384,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "GJtBIe3lu-df",
    "outputId": "3d8e6a86-28f8-4599-d82c-5ca85d0201a6"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# values of alpha\n",
    "x = np.linspace(1, 20, 100)\n",
    "\n",
    "# probabilities\n",
    "p_X = stats.gamma.pdf(x=x, a=1, loc=1, scale=2)\n",
    "\n",
    "plt.plot(x,p_X)\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('P(alpha)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "fvtXzLMXvdUk"
   },
   "outputs": [],
   "source": [
    "# n sample values\n",
    "n_iter = 100\n",
    "\n",
    "# sample from the gamma distribution\n",
    "samples = stats.gamma.rvs(a=1, loc=1, scale=2, size=n_iter, random_state=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1370,
     "status": "ok",
     "timestamp": 1571316859386,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "Eh1gcP2bvo9L",
    "outputId": "390e9fa3-78d1-4ed1-b9b0-a9792eac588b"
   },
   "outputs": [],
   "source": [
    "# visualise the sample distribution\n",
    "plt.hist(samples)\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('sample count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Nou_IG1IwlAu"
   },
   "outputs": [],
   "source": [
    "# we will store the results inside a dictionary\n",
    "result = {}\n",
    "\n",
    "# for each sample\n",
    "for sample in samples:\n",
    "  \n",
    "  # initialize a ridge regression estimator with alpha set to the sample value\n",
    "  reg = linear_model.Ridge(alpha=sample)\n",
    "  \n",
    "  # conduct a 10-fold cross validation scoring on negative mean squared error\n",
    "  cv = model_selection.cross_val_score(reg, X, y, cv=10, scoring='neg_mean_squared_error')\n",
    "  \n",
    "  # retain the result in the dictionary\n",
    "  result[sample] = [cv.mean()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 121
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2788,
     "status": "ok",
     "timestamp": 1571316860822,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "aqSFjq7ExSMK",
    "outputId": "515cb7ff-d8ea-41bc-dba7-ec4c79fcb843"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# convert the result dictionary to a pandas dataframe, transpose and reset the index\n",
    "df_result = pd.DataFrame(result).T.reset_index()\n",
    "\n",
    "# give the columns sensible names\n",
    "df_result.columns = ['alpha', 'mean_neg_mean_squared_error']\n",
    "\n",
    "print(df_result.sort_values('mean_neg_mean_squared_error', ascending=False).head(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 950,
     "status": "ok",
     "timestamp": 1571316908254,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "9pCIKSN6yRzS",
    "outputId": "17a1a958-82a4-4f0c-bf64-0a735517333a"
   },
   "outputs": [],
   "source": [
    "plt.scatter(df_result.alpha, df_result.mean_neg_mean_squared_error)\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('-MSE')"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "simple_demonstration_of_the_random_search_process.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}