Collinear features and their effect on linear models (Perturbation Test).ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "86Tvnj5UblTy"
   },
   "source": [
    "## Collinear features and their effect on linear models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:40.319195Z",
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    "tags": []
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import SGDClassifier\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:40.746813Z",
     "iopub.status.busy": "2022-07-23T08:34:40.746621Z",
     "iopub.status.idle": "2022-07-23T08:34:52.114123Z",
     "shell.execute_reply": "2022-07-23T08:34:52.113228Z",
     "shell.execute_reply.started": "2022-07-23T08:34:40.746792Z"
    },
    "id": "VMoYWIayblUB",
    "tags": []
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('/home/ubuntu/drive_kodakandlasrikar99/aaic/task_d.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.148164Z",
     "iopub.status.busy": "2022-07-23T08:34:52.147810Z",
     "iopub.status.idle": "2022-07-23T08:34:52.158708Z",
     "shell.execute_reply": "2022-07-23T08:34:52.158059Z",
     "shell.execute_reply.started": "2022-07-23T08:34:52.148141Z"
    },
    "id": "RfStXG4tblUI",
    "outputId": "14f2c468-5e09-4544-e045-e75097200c65",
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "      <th>x*x</th>\n",
       "      <th>2*y</th>\n",
       "      <th>2*z+3*x*x</th>\n",
       "      <th>w</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.581066</td>\n",
       "      <td>0.841837</td>\n",
       "      <td>-1.012978</td>\n",
       "      <td>-0.604025</td>\n",
       "      <td>0.841837</td>\n",
       "      <td>-0.665927</td>\n",
       "      <td>-0.536277</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.894309</td>\n",
       "      <td>-0.207835</td>\n",
       "      <td>-1.012978</td>\n",
       "      <td>-0.883052</td>\n",
       "      <td>-0.207835</td>\n",
       "      <td>-0.917054</td>\n",
       "      <td>-0.522364</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.207552</td>\n",
       "      <td>0.212034</td>\n",
       "      <td>-1.082312</td>\n",
       "      <td>-1.150918</td>\n",
       "      <td>0.212034</td>\n",
       "      <td>-1.166507</td>\n",
       "      <td>0.205738</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.364174</td>\n",
       "      <td>0.002099</td>\n",
       "      <td>-0.943643</td>\n",
       "      <td>-1.280666</td>\n",
       "      <td>0.002099</td>\n",
       "      <td>-1.266540</td>\n",
       "      <td>-0.665720</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.737687</td>\n",
       "      <td>1.051772</td>\n",
       "      <td>-1.012978</td>\n",
       "      <td>-0.744934</td>\n",
       "      <td>1.051772</td>\n",
       "      <td>-0.792746</td>\n",
       "      <td>-0.735054</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "          x         y         z       x*x       2*y  2*z+3*x*x         w  \\\n",
       "0 -0.581066  0.841837 -1.012978 -0.604025  0.841837  -0.665927 -0.536277   \n",
       "1 -0.894309 -0.207835 -1.012978 -0.883052 -0.207835  -0.917054 -0.522364   \n",
       "2 -1.207552  0.212034 -1.082312 -1.150918  0.212034  -1.166507  0.205738   \n",
       "3 -1.364174  0.002099 -0.943643 -1.280666  0.002099  -1.266540 -0.665720   \n",
       "4 -0.737687  1.051772 -1.012978 -0.744934  1.051772  -0.792746 -0.735054   \n",
       "\n",
       "   target  \n",
       "0       0  \n",
       "1       0  \n",
       "2       0  \n",
       "3       0  \n",
       "4       0  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.161087Z",
     "iopub.status.busy": "2022-07-23T08:34:52.160695Z",
     "iopub.status.idle": "2022-07-23T08:34:52.164501Z",
     "shell.execute_reply": "2022-07-23T08:34:52.163567Z",
     "shell.execute_reply.started": "2022-07-23T08:34:52.161066Z"
    },
    "id": "hxzG24juXS33",
    "tags": []
   },
   "outputs": [],
   "source": [
    "features=list(data.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.166487Z",
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    "id": "gO4XQo-TXXxU",
    "outputId": "76936bdc-3b7b-4820-c88d-91306360d65e",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['x', 'y', 'z', 'x*x', '2*y', '2*z+3*x*x', 'w', 'target']"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.172450Z",
     "iopub.status.busy": "2022-07-23T08:34:52.171942Z",
     "iopub.status.idle": "2022-07-23T08:34:52.177001Z",
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    },
    "id": "JIIuomCkblUP",
    "tags": []
   },
   "outputs": [],
   "source": [
    "X = data.drop(['target'], axis=1).values\n",
    "Y = data['target'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 625
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.178858Z",
     "iopub.status.busy": "2022-07-23T08:34:52.178490Z",
     "iopub.status.idle": "2022-07-23T08:34:52.576718Z",
     "shell.execute_reply": "2022-07-23T08:34:52.576020Z",
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    "id": "aQBOjsyOoknB",
    "outputId": "11f5bf0e-3eaf-4363-8750-a299907bb62c",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:title={'center':'data correlation '}>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "plt.title('data correlation ')\n",
    "sns.heatmap(data.corr(),annot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### from above correlation matrix ,Clearly we have collinear features "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.577746Z",
     "iopub.status.busy": "2022-07-23T08:34:52.577587Z",
     "iopub.status.idle": "2022-07-23T08:34:52.582018Z",
     "shell.execute_reply": "2022-07-23T08:34:52.580868Z",
     "shell.execute_reply.started": "2022-07-23T08:34:52.577726Z"
    },
    "id": "FfYJhVFKw0rF",
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from scipy.stats import uniform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Perturbation Test on Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hyperparamater Tuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.583841Z",
     "iopub.status.busy": "2022-07-23T08:34:52.583459Z",
     "iopub.status.idle": "2022-07-23T08:34:52.587686Z",
     "shell.execute_reply": "2022-07-23T08:34:52.586673Z",
     "shell.execute_reply.started": "2022-07-23T08:34:52.583812Z"
    },
    "id": "4aVsN4d_xzLb",
    "tags": []
   },
   "outputs": [],
   "source": [
    "distributions = dict(alpha=[1e-05, 0.001, 0.1, 1, 100, 1000],penalty=['l2', 'l1'],loss=['log'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.589736Z",
     "iopub.status.busy": "2022-07-23T08:34:52.589156Z",
     "iopub.status.idle": "2022-07-23T08:34:52.593313Z",
     "shell.execute_reply": "2022-07-23T08:34:52.592290Z",
     "shell.execute_reply.started": "2022-07-23T08:34:52.589708Z"
    },
    "id": "36wJ3qGUokw9",
    "tags": []
   },
   "outputs": [],
   "source": [
    "classifier=SGDClassifier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.595038Z",
     "iopub.status.busy": "2022-07-23T08:34:52.594870Z",
     "iopub.status.idle": "2022-07-23T08:34:52.598319Z",
     "shell.execute_reply": "2022-07-23T08:34:52.597736Z",
     "shell.execute_reply.started": "2022-07-23T08:34:52.595019Z"
    },
    "id": "HrpZyaHMyHlk",
    "tags": []
   },
   "outputs": [],
   "source": [
    "clf=GridSearchCV(classifier, distributions,n_jobs=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:52.599168Z",
     "iopub.status.busy": "2022-07-23T08:34:52.599027Z",
     "iopub.status.idle": "2022-07-23T08:34:55.026649Z",
     "shell.execute_reply": "2022-07-23T08:34:55.025869Z",
     "shell.execute_reply.started": "2022-07-23T08:34:52.599151Z"
    },
    "id": "b9BUcNu9yQES",
    "outputId": "7a7f0049-d9e2-43f1-e1f1-10c76d954c28",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'alpha': 1e-05, 'loss': 'log', 'penalty': 'l1'}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "search = clf.fit(X,Y)\n",
    "search.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:34:55.028251Z",
     "iopub.status.busy": "2022-07-23T08:34:55.028067Z",
     "iopub.status.idle": "2022-07-23T08:34:55.034830Z",
     "shell.execute_reply": "2022-07-23T08:34:55.033868Z",
     "shell.execute_reply.started": "2022-07-23T08:34:55.028227Z"
    },
    "id": "e62IwRaBzC9O",
    "tags": []
   },
   "outputs": [],
   "source": [
    "classifier=SGDClassifier(loss='log',alpha=1e-05,penalty='l2').fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:38:57.772995Z",
     "iopub.status.busy": "2022-07-23T08:38:57.772470Z",
     "iopub.status.idle": "2022-07-23T08:38:57.781332Z",
     "shell.execute_reply": "2022-07-23T08:38:57.780313Z",
     "shell.execute_reply.started": "2022-07-23T08:38:57.772966Z"
    },
    "id": "ND9AnTosj7yH",
    "outputId": "f2294782-5bcf-430b-b3a2-09cf140e6612",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best model accuracy  1.0\n"
     ]
    }
   ],
   "source": [
    "print('best model accuracy ',accuracy_score(Y,classifier.predict(X)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:38:58.220490Z",
     "iopub.status.busy": "2022-07-23T08:38:58.219733Z",
     "iopub.status.idle": "2022-07-23T08:38:58.223861Z",
     "shell.execute_reply": "2022-07-23T08:38:58.223247Z",
     "shell.execute_reply.started": "2022-07-23T08:38:58.220464Z"
    },
    "id": "nix61sQdj7yI",
    "tags": []
   },
   "outputs": [],
   "source": [
    "weights1=classifier.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weights that i got after training logistic regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:38:59.044962Z",
     "iopub.status.busy": "2022-07-23T08:38:59.044314Z",
     "iopub.status.idle": "2022-07-23T08:38:59.049211Z",
     "shell.execute_reply": "2022-07-23T08:38:59.048609Z",
     "shell.execute_reply.started": "2022-07-23T08:38:59.044934Z"
    },
    "id": "SIU-CtMJj7yI",
    "outputId": "5c0acab3-bddd-493e-b1fc-5bdad54c3443",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 15.01197032, -30.0910642 ,  51.18027933,  11.94656492,\n",
       "        -30.0910642 ,  16.93112518,   2.34211046]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding noise to the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:38:59.546136Z",
     "iopub.status.busy": "2022-07-23T08:38:59.545507Z",
     "iopub.status.idle": "2022-07-23T08:38:59.549566Z",
     "shell.execute_reply": "2022-07-23T08:38:59.548907Z",
     "shell.execute_reply.started": "2022-07-23T08:38:59.546110Z"
    },
    "id": "LvPTAacUj7yI",
    "tags": []
   },
   "outputs": [],
   "source": [
    "X_noise=X.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:39:04.059471Z",
     "iopub.status.busy": "2022-07-23T08:39:04.058976Z",
     "iopub.status.idle": "2022-07-23T08:39:04.062594Z",
     "shell.execute_reply": "2022-07-23T08:39:04.061891Z",
     "shell.execute_reply.started": "2022-07-23T08:39:04.059444Z"
    },
    "id": "WX2-Bnotj7yI",
    "tags": []
   },
   "outputs": [],
   "source": [
    "X_noise=X_noise+10**-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:39:05.013396Z",
     "iopub.status.busy": "2022-07-23T08:39:05.012571Z",
     "iopub.status.idle": "2022-07-23T08:39:05.018341Z",
     "shell.execute_reply": "2022-07-23T08:39:05.017325Z",
     "shell.execute_reply.started": "2022-07-23T08:39:05.013366Z"
    },
    "id": "aNnh6SBZj7yJ",
    "tags": []
   },
   "outputs": [],
   "source": [
    "classifier=SGDClassifier(loss='log',alpha=1e-05,penalty='l2').fit(X_noise,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:39:15.119864Z",
     "iopub.status.busy": "2022-07-23T08:39:15.119249Z",
     "iopub.status.idle": "2022-07-23T08:39:15.123052Z",
     "shell.execute_reply": "2022-07-23T08:39:15.122407Z",
     "shell.execute_reply.started": "2022-07-23T08:39:15.119837Z"
    },
    "id": "wCBFJfR0j7yJ",
    "tags": []
   },
   "outputs": [],
   "source": [
    "weights2=classifier.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weights that i got after training Logistic regression on data+noise dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:39:15.196762Z",
     "iopub.status.busy": "2022-07-23T08:39:15.196221Z",
     "iopub.status.idle": "2022-07-23T08:39:15.203994Z",
     "shell.execute_reply": "2022-07-23T08:39:15.203187Z",
     "shell.execute_reply.started": "2022-07-23T08:39:15.196738Z"
    },
    "id": "tUWrcbnxj7yJ",
    "outputId": "fe18ada5-c8bc-4de9-c6a9-525f269b1c30",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 34.3403421 , -27.01104891,  71.1804098 ,  29.63471763,\n",
       "        -27.01104891,  35.25971146,  25.03145155]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:39:15.206087Z",
     "iopub.status.busy": "2022-07-23T08:39:15.205699Z",
     "iopub.status.idle": "2022-07-23T08:39:15.209493Z",
     "shell.execute_reply": "2022-07-23T08:39:15.208542Z",
     "shell.execute_reply.started": "2022-07-23T08:39:15.206067Z"
    },
    "id": "s8skpzubj7yJ",
    "tags": []
   },
   "outputs": [],
   "source": [
    "diff_weights=abs(weights1-weights2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:39:19.676379Z",
     "iopub.status.busy": "2022-07-23T08:39:19.675755Z",
     "iopub.status.idle": "2022-07-23T08:39:19.679745Z",
     "shell.execute_reply": "2022-07-23T08:39:19.679147Z",
     "shell.execute_reply.started": "2022-07-23T08:39:19.676351Z"
    },
    "id": "0_7idiu_j7yJ",
    "tags": []
   },
   "outputs": [],
   "source": [
    "p_diff_weights=abs((weights1-weights2)/weights1)*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Absolute percentage deviation of weights "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:39:19.866279Z",
     "iopub.status.busy": "2022-07-23T08:39:19.866066Z",
     "iopub.status.idle": "2022-07-23T08:39:19.871843Z",
     "shell.execute_reply": "2022-07-23T08:39:19.870679Z",
     "shell.execute_reply.started": "2022-07-23T08:39:19.866256Z"
    },
    "id": "8vRRTcFaMlzB",
    "outputId": "3d9d92ee-e8ec-42e7-84a2-9ceefe7e404a",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[128.75306425,  10.23564762,  39.07780641, 148.06057499,\n",
       "         10.23564762, 108.2537993 , 968.75623563]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_diff_weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:39:20.242297Z",
     "iopub.status.busy": "2022-07-23T08:39:20.241840Z",
     "iopub.status.idle": "2022-07-23T08:39:20.248140Z",
     "shell.execute_reply": "2022-07-23T08:39:20.246976Z",
     "shell.execute_reply.started": "2022-07-23T08:39:20.242269Z"
    },
    "id": "WKhoH5pKj7yJ",
    "outputId": "021d2992-e3a1-46f9-e900-a29ad590bd4c",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top features :\n",
      "w\n",
      "x*x\n",
      "x\n",
      "2*z+3*x*x\n",
      "z\n",
      "2*y\n",
      "y\n"
     ]
    }
   ],
   "source": [
    "print('Top features :')\n",
    "for i in np.argsort(p_diff_weights[0])[::-1]:\n",
    "  print(features[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now model told the above features as colinear features, if we rerun the cell again it may say other features because , z and 2*z , 3*x and x are collinear with each other , and 2*z+3*x*x is colinear with z and x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SR8OWAv6iZEQ"
   },
   "source": [
    "# Observation\n",
    "\n",
    "### As the difference of their weights are high after and before pertubation test , we can say that we have colinear features in the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Lai8wXU1pmSb"
   },
   "source": [
    "# Perturbation Test on SVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:38.797279Z",
     "iopub.status.busy": "2022-07-23T08:44:38.796844Z",
     "iopub.status.idle": "2022-07-23T08:44:47.259521Z",
     "shell.execute_reply": "2022-07-23T08:44:47.258748Z",
     "shell.execute_reply.started": "2022-07-23T08:44:38.797253Z"
    },
    "id": "Rs9hHvNgjYPi",
    "tags": []
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('/home/ubuntu/drive_kodakandlasrikar99/aaic/task_d.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:47.261090Z",
     "iopub.status.busy": "2022-07-23T08:44:47.260780Z",
     "iopub.status.idle": "2022-07-23T08:44:47.271502Z",
     "shell.execute_reply": "2022-07-23T08:44:47.270892Z",
     "shell.execute_reply.started": "2022-07-23T08:44:47.261067Z"
    },
    "id": "bw8Dg-cCjYPk",
    "outputId": "7b6109d8-e9da-4f2e-dfc4-d8d2a1814e28",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "      <th>x*x</th>\n",
       "      <th>2*y</th>\n",
       "      <th>2*z+3*x*x</th>\n",
       "      <th>w</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.581066</td>\n",
       "      <td>0.841837</td>\n",
       "      <td>-1.012978</td>\n",
       "      <td>-0.604025</td>\n",
       "      <td>0.841837</td>\n",
       "      <td>-0.665927</td>\n",
       "      <td>-0.536277</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.894309</td>\n",
       "      <td>-0.207835</td>\n",
       "      <td>-1.012978</td>\n",
       "      <td>-0.883052</td>\n",
       "      <td>-0.207835</td>\n",
       "      <td>-0.917054</td>\n",
       "      <td>-0.522364</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.207552</td>\n",
       "      <td>0.212034</td>\n",
       "      <td>-1.082312</td>\n",
       "      <td>-1.150918</td>\n",
       "      <td>0.212034</td>\n",
       "      <td>-1.166507</td>\n",
       "      <td>0.205738</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.364174</td>\n",
       "      <td>0.002099</td>\n",
       "      <td>-0.943643</td>\n",
       "      <td>-1.280666</td>\n",
       "      <td>0.002099</td>\n",
       "      <td>-1.266540</td>\n",
       "      <td>-0.665720</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.737687</td>\n",
       "      <td>1.051772</td>\n",
       "      <td>-1.012978</td>\n",
       "      <td>-0.744934</td>\n",
       "      <td>1.051772</td>\n",
       "      <td>-0.792746</td>\n",
       "      <td>-0.735054</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y         z       x*x       2*y  2*z+3*x*x         w  \\\n",
       "0 -0.581066  0.841837 -1.012978 -0.604025  0.841837  -0.665927 -0.536277   \n",
       "1 -0.894309 -0.207835 -1.012978 -0.883052 -0.207835  -0.917054 -0.522364   \n",
       "2 -1.207552  0.212034 -1.082312 -1.150918  0.212034  -1.166507  0.205738   \n",
       "3 -1.364174  0.002099 -0.943643 -1.280666  0.002099  -1.266540 -0.665720   \n",
       "4 -0.737687  1.051772 -1.012978 -0.744934  1.051772  -0.792746 -0.735054   \n",
       "\n",
       "   target  \n",
       "0       0  \n",
       "1       0  \n",
       "2       0  \n",
       "3       0  \n",
       "4       0  "
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:47.272455Z",
     "iopub.status.busy": "2022-07-23T08:44:47.272295Z",
     "iopub.status.idle": "2022-07-23T08:44:47.275951Z",
     "shell.execute_reply": "2022-07-23T08:44:47.275290Z",
     "shell.execute_reply.started": "2022-07-23T08:44:47.272435Z"
    },
    "id": "KMbgfuzEjYPl",
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from scipy.stats import uniform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hyperparamater Tuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:47.277588Z",
     "iopub.status.busy": "2022-07-23T08:44:47.277409Z",
     "iopub.status.idle": "2022-07-23T08:44:47.281101Z",
     "shell.execute_reply": "2022-07-23T08:44:47.280496Z",
     "shell.execute_reply.started": "2022-07-23T08:44:47.277569Z"
    },
    "id": "2mvYohMUjYPl",
    "tags": []
   },
   "outputs": [],
   "source": [
    "distributions = dict(alpha=[1e-05, 0.001, 0.1, 1, 100, 1000],penalty=['l2', 'l1'],loss=['hinge'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:47.282142Z",
     "iopub.status.busy": "2022-07-23T08:44:47.281863Z",
     "iopub.status.idle": "2022-07-23T08:44:47.286227Z",
     "shell.execute_reply": "2022-07-23T08:44:47.285658Z",
     "shell.execute_reply.started": "2022-07-23T08:44:47.282120Z"
    },
    "id": "mSIky2nfjYPm",
    "tags": []
   },
   "outputs": [],
   "source": [
    "classifier=SGDClassifier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:47.287317Z",
     "iopub.status.busy": "2022-07-23T08:44:47.286983Z",
     "iopub.status.idle": "2022-07-23T08:44:47.290759Z",
     "shell.execute_reply": "2022-07-23T08:44:47.290261Z",
     "shell.execute_reply.started": "2022-07-23T08:44:47.287292Z"
    },
    "id": "ZuLrahEgjYPn",
    "tags": []
   },
   "outputs": [],
   "source": [
    "clf=GridSearchCV(classifier, distributions,n_jobs=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:47.292359Z",
     "iopub.status.busy": "2022-07-23T08:44:47.291986Z",
     "iopub.status.idle": "2022-07-23T08:44:49.606455Z",
     "shell.execute_reply": "2022-07-23T08:44:49.605444Z",
     "shell.execute_reply.started": "2022-07-23T08:44:47.292332Z"
    },
    "id": "GWp2gA9AjYPn",
    "outputId": "52daa05d-04f3-4e39-f39a-e5a52f3ddb67",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'alpha': 1e-05, 'loss': 'hinge', 'penalty': 'l2'}"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "search = clf.fit(X,Y)\n",
    "search.best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:49.607965Z",
     "iopub.status.busy": "2022-07-23T08:44:49.607772Z",
     "iopub.status.idle": "2022-07-23T08:44:49.613009Z",
     "shell.execute_reply": "2022-07-23T08:44:49.612332Z",
     "shell.execute_reply.started": "2022-07-23T08:44:49.607941Z"
    },
    "id": "NCSL0IuejYPo",
    "tags": []
   },
   "outputs": [],
   "source": [
    "classifier=SGDClassifier(loss='hinge',alpha=1e-05,penalty='l2').fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:49.614053Z",
     "iopub.status.busy": "2022-07-23T08:44:49.613880Z",
     "iopub.status.idle": "2022-07-23T08:44:49.619989Z",
     "shell.execute_reply": "2022-07-23T08:44:49.618689Z",
     "shell.execute_reply.started": "2022-07-23T08:44:49.614034Z"
    },
    "id": "cOTCHHLejYPp",
    "outputId": "8bb6d159-c677-4f1f-8ee6-1f2e8fe43b9e",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best model accuracy  1.0\n"
     ]
    }
   ],
   "source": [
    "print('best model accuracy ',accuracy_score(Y,classifier.predict(X)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:49.623047Z",
     "iopub.status.busy": "2022-07-23T08:44:49.622827Z",
     "iopub.status.idle": "2022-07-23T08:44:49.626630Z",
     "shell.execute_reply": "2022-07-23T08:44:49.625619Z",
     "shell.execute_reply.started": "2022-07-23T08:44:49.623027Z"
    },
    "id": "nEQJC4p_jYPq",
    "tags": []
   },
   "outputs": [],
   "source": [
    "weights1=classifier.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weights that i got after training SVM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:49.627669Z",
     "iopub.status.busy": "2022-07-23T08:44:49.627517Z",
     "iopub.status.idle": "2022-07-23T08:44:49.632487Z",
     "shell.execute_reply": "2022-07-23T08:44:49.631918Z",
     "shell.execute_reply.started": "2022-07-23T08:44:49.627650Z"
    },
    "id": "XXjm7RDpjYPq",
    "outputId": "97d0ac9e-f91c-4997-98ce-bbb5cf9a6f6e",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 27.24967259, -29.88431733,  53.73569211,  23.45672205,\n",
       "        -29.88431733,  27.59889366,  28.15885083]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding noise to the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:49.633411Z",
     "iopub.status.busy": "2022-07-23T08:44:49.633254Z",
     "iopub.status.idle": "2022-07-23T08:44:49.636330Z",
     "shell.execute_reply": "2022-07-23T08:44:49.635761Z",
     "shell.execute_reply.started": "2022-07-23T08:44:49.633392Z"
    },
    "id": "1hDBbKyVjYPr",
    "tags": []
   },
   "outputs": [],
   "source": [
    "X_noise=X.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:49.803791Z",
     "iopub.status.busy": "2022-07-23T08:44:49.803500Z",
     "iopub.status.idle": "2022-07-23T08:44:49.806490Z",
     "shell.execute_reply": "2022-07-23T08:44:49.805909Z",
     "shell.execute_reply.started": "2022-07-23T08:44:49.803771Z"
    },
    "id": "FFF0NxCbjYPs",
    "tags": []
   },
   "outputs": [],
   "source": [
    "X_noise=X_noise+10**-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:44:49.807367Z",
     "iopub.status.busy": "2022-07-23T08:44:49.807216Z",
     "iopub.status.idle": "2022-07-23T08:44:49.812052Z",
     "shell.execute_reply": "2022-07-23T08:44:49.811427Z",
     "shell.execute_reply.started": "2022-07-23T08:44:49.807349Z"
    },
    "id": "HtfD52y3jYPt",
    "tags": []
   },
   "outputs": [],
   "source": [
    "classifier=SGDClassifier(loss='hinge',alpha=1e-05,penalty='l2').fit(X_noise,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:45:27.655458Z",
     "iopub.status.busy": "2022-07-23T08:45:27.654941Z",
     "iopub.status.idle": "2022-07-23T08:45:27.658827Z",
     "shell.execute_reply": "2022-07-23T08:45:27.657991Z",
     "shell.execute_reply.started": "2022-07-23T08:45:27.655431Z"
    },
    "id": "64vjjk12jYPu",
    "tags": []
   },
   "outputs": [],
   "source": [
    "weights2=classifier.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weights that i got after training SVM on data+noise dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:45:28.573836Z",
     "iopub.status.busy": "2022-07-23T08:45:28.573313Z",
     "iopub.status.idle": "2022-07-23T08:45:28.581079Z",
     "shell.execute_reply": "2022-07-23T08:45:28.579678Z",
     "shell.execute_reply.started": "2022-07-23T08:45:28.573808Z"
    },
    "id": "NJM7nyvejYPu",
    "outputId": "131b34e0-9110-4dad-f062-23fa2e840e16",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 20.05994552, -32.00111772,  83.48343588,  17.11657262,\n",
       "        -32.00111772,  25.48103013,  30.04310468]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:45:30.311421Z",
     "iopub.status.busy": "2022-07-23T08:45:30.310810Z",
     "iopub.status.idle": "2022-07-23T08:45:30.314512Z",
     "shell.execute_reply": "2022-07-23T08:45:30.313711Z",
     "shell.execute_reply.started": "2022-07-23T08:45:30.311395Z"
    },
    "id": "YGu77IMYjYPv",
    "tags": []
   },
   "outputs": [],
   "source": [
    "diff_weights=abs(weights1-weights2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-07-23T08:45:30.638435Z",
     "iopub.status.busy": "2022-07-23T08:45:30.637899Z",
     "iopub.status.idle": "2022-07-23T08:45:30.641980Z",
     "shell.execute_reply": "2022-07-23T08:45:30.640709Z",
     "shell.execute_reply.started": "2022-07-23T08:45:30.638410Z"
    },
    "id": "cGkuof4nkur2",
    "tags": []
   },
   "outputs": [],
   "source": [
    "p_diff_weights=abs((weights1-weights2)/weights1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Absolute percentage deviation of weights "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:45:31.633975Z",
     "iopub.status.busy": "2022-07-23T08:45:31.633327Z",
     "iopub.status.idle": "2022-07-23T08:45:31.641479Z",
     "shell.execute_reply": "2022-07-23T08:45:31.640330Z",
     "shell.execute_reply.started": "2022-07-23T08:45:31.633946Z"
    },
    "id": "CwsdrKmXlDzc",
    "outputId": "646393ff-0e6e-43e6-a2f6-86174065f2df",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.26384637, 0.07083315, 0.55359376, 0.27029137, 0.07083315,\n",
       "        0.07673726, 0.06691515]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_diff_weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "execution": {
     "iopub.execute_input": "2022-07-23T08:45:32.874936Z",
     "iopub.status.busy": "2022-07-23T08:45:32.874348Z",
     "iopub.status.idle": "2022-07-23T08:45:32.880136Z",
     "shell.execute_reply": "2022-07-23T08:45:32.879201Z",
     "shell.execute_reply.started": "2022-07-23T08:45:32.874906Z"
    },
    "id": "dRzAvGf_lHGk",
    "outputId": "a4286c06-7de5-42b3-f18d-c0f9e5686e72",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top colinear features\n",
      "z\n",
      "x*x\n",
      "x\n",
      "2*z+3*x*x\n",
      "2*y\n",
      "y\n",
      "w\n"
     ]
    }
   ],
   "source": [
    "print('Top colinear features')\n",
    "for i in np.argsort(p_diff_weights[0])[::-1]:\n",
    "  print(features[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now model told the above features as colinear features, if we rerun the cell again it may say other features because , z and 2*z , 3*x and x are collinear with each other , and 2*z+3*x*x is colinear with z and x "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cQD0zrBu6BXa"
   },
   "source": [
    "# Observation\n",
    "\n",
    "### As the absolute percentage difference of their weights are high after and before pertubation test , we can say that we have colinear features in the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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