AFML 8.1.ipynb

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    "### Feature Importance\n",
    "\n",
    "> \"Backtesting is not a research tool. Feature importance is.\"\n",
    ">\n",
    "> &mdash; Marco's first law of backtesting\n",
    "\n",
    "This notebook will cover exercise answer.\n",
    "\n",
    "* Exercise 8.1\n",
    "* Exercise 8.2\n",
    "* Exercise 8.3\n",
    "\n",
    "As we go along, there will be some explanations.\n",
    "\n",
    "Most of the functions below can be found under Tool/metrics\n",
    "\n",
    "This chapter itself can be quite heavy as it involves PCA as well as different metric performance measures.\n",
    "\n",
    "Contact: boyboi86@gmail.com"
   ]
  },
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     "text": [
      "Num of CPU core:  4\n",
      "Machine info:  Windows-10-10.0.18362-SP0\n",
      "Python 3.7.4 (default, Aug  9 2019, 18:34:13) [MSC v.1915 64 bit (AMD64)]\n",
      "Numpy 1.17.3\n",
      "Pandas 1.0.3\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Wei_X\\Anaconda3\\lib\\site-packages\\statsmodels\\tools\\_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
      "  import pandas.util.testing as tm\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import research as rs\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Wei_X\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:6: FutureWarning: The pandas.datetime class is deprecated and will be removed from pandas in a future version. Import from datetime module instead.\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import make_classification\n",
    "\n",
    "def test_data(n_features=40, n_informative=10, n_redundant=10, n_samples=10000):\n",
    "    # generate a random dataset for a classification problem    \n",
    "    trnsX, cont = make_classification(n_samples=n_samples, n_features=n_features, n_informative=n_informative, n_redundant=n_redundant, random_state=0, shuffle=False)\n",
    "    df0 = pd.date_range(periods=n_samples, freq=pd.tseries.offsets.BDay(), end=pd.datetime.today())\n",
    "    trnsX = pd.DataFrame(trnsX, index=df0)\n",
    "    cont = pd.Series(cont, index=df0).to_frame('bin')\n",
    "    df0 = ['I_%s' % i for i in range(n_informative)] + ['R_%s' % i for i in range(n_redundant)]\n",
    "    df0 += ['N_%s' % i for i in range(n_features - len(df0))]\n",
    "    trnsX.columns = df0\n",
    "    cont['w'] = 1.0 / cont.shape[0]\n",
    "    cont['t1'] = pd.Series(cont.index, index=cont.index)\n",
    "    return trnsX, cont\n",
    "\n",
    "X, y = test_data(n_features=20, n_informative=5, n_redundant=5, n_samples= 3000)\n",
    "\n",
    "#Take note of depreciation warning Pandas 1.0.3"
   ]
  },
  {
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       "                                 I_0       I_1       I_2       I_3       I_4  \\\n",
       "2008-12-04 18:20:31.630509 -0.737441  1.480017 -1.624384 -0.907109  1.852716   \n",
       "2008-12-05 18:20:31.630509 -0.722167  2.694209 -0.848284  1.394876 -0.676037   \n",
       "2008-12-08 18:20:31.630509 -2.464807  1.849071  0.021696  3.202498  0.194839   \n",
       "2008-12-09 18:20:31.630509  1.557030  1.290159 -1.044263 -1.673964  2.077268   \n",
       "2008-12-10 18:20:31.630509 -0.775799  1.620273 -2.026289  0.775127  0.127839   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509 -0.581578 -0.049621 -0.198635  2.023424 -0.987298   \n",
       "2020-05-29 18:20:31.630509  2.356476  0.166034 -1.223822  2.711896 -0.787449   \n",
       "2020-06-01 18:20:31.630509  0.242724 -0.258967 -0.021133  2.396409 -0.573791   \n",
       "2020-06-02 18:20:31.630509 -0.394498 -2.028831  0.196144  2.614800 -0.576834   \n",
       "2020-06-03 18:20:31.630509 -1.395280 -1.139148  1.062894  1.072333  1.738764   \n",
       "\n",
       "                                 R_0       R_1       R_2       R_3       R_4  \\\n",
       "2008-12-04 18:20:31.630509 -1.042550  0.206819 -0.282577  0.667836 -1.155404   \n",
       "2008-12-05 18:20:31.630509 -1.058662  0.937675  0.242056  0.792361  1.656174   \n",
       "2008-12-08 18:20:31.630509 -2.238507 -0.619387 -1.045632  3.676729 -0.283826   \n",
       "2008-12-09 18:20:31.630509  0.172160 -1.028541  1.640022 -1.346945 -0.755371   \n",
       "2008-12-10 18:20:31.630509 -1.718214  0.983768 -0.961620  1.657738 -0.341892   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509 -1.086323  0.039362 -0.988735  1.902968 -0.125347   \n",
       "2020-05-29 18:20:31.630509 -1.425878 -1.627161  0.338701  1.671942 -0.888587   \n",
       "2020-06-01 18:20:31.630509 -1.124627 -1.129714 -0.467224  2.034931 -0.728756   \n",
       "2020-06-02 18:20:31.630509 -1.381691 -1.298519 -1.814296  3.135303 -2.130049   \n",
       "2020-06-03 18:20:31.630509 -0.845256 -2.221103 -0.883464  2.422866 -2.565864   \n",
       "\n",
       "                                 N_0       N_1       N_2       N_3       N_4  \\\n",
       "2008-12-04 18:20:31.630509 -0.797706 -0.800303 -1.159210  0.265765 -0.692233   \n",
       "2008-12-05 18:20:31.630509 -0.471474 -0.404565  2.293856  1.553295 -0.167588   \n",
       "2008-12-08 18:20:31.630509  1.577428 -1.120976 -0.030646 -1.124057 -0.050032   \n",
       "2008-12-09 18:20:31.630509  2.145253 -1.026265  0.960892  0.286109  0.209064   \n",
       "2008-12-10 18:20:31.630509 -0.344063  0.427022 -1.974068  2.625296 -0.572037   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509  1.871046 -1.130525  0.670610 -1.306620  1.700514   \n",
       "2020-05-29 18:20:31.630509 -0.590340  0.171062 -0.029284 -0.736423  0.579844   \n",
       "2020-06-01 18:20:31.630509 -1.415538  0.701067  0.098626  1.530280  0.919778   \n",
       "2020-06-02 18:20:31.630509 -0.501588 -0.180367 -0.867517  0.067514 -0.552346   \n",
       "2020-06-03 18:20:31.630509 -1.048229  0.015849  0.198696  1.939838  2.230065   \n",
       "\n",
       "                                 N_5       N_6       N_7       N_8       N_9  \n",
       "2008-12-04 18:20:31.630509  2.031814 -0.545652  0.051393  0.162916  1.003635  \n",
       "2008-12-05 18:20:31.630509 -1.171582  0.671503  0.355732  0.164742  1.726842  \n",
       "2008-12-08 18:20:31.630509  0.093905  0.748571 -2.892617 -0.797168  1.449732  \n",
       "2008-12-09 18:20:31.630509  0.319532 -0.526978 -0.319982  0.462094 -1.778664  \n",
       "2008-12-10 18:20:31.630509 -0.509773 -0.368742  0.004224 -1.598331 -0.807513  \n",
       "...                              ...       ...       ...       ...       ...  \n",
       "2020-05-28 18:20:31.630509 -2.019744 -0.808909 -0.727355  0.202766 -1.224024  \n",
       "2020-05-29 18:20:31.630509 -0.933117  0.397632  1.639739 -2.382154  0.564313  \n",
       "2020-06-01 18:20:31.630509 -1.463967 -1.416195 -0.149276  0.083001  0.089964  \n",
       "2020-06-02 18:20:31.630509  0.638024 -0.444415  0.111936  0.936410  0.941215  \n",
       "2020-06-03 18:20:31.630509  1.074580  1.193151  1.049536  0.517009 -1.855302  \n",
       "\n",
       "[3000 rows x 20 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>bin</th>\n",
       "      <th>w</th>\n",
       "      <th>t1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2008-12-04 18:20:31.630509</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2008-12-04 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-05 18:20:31.630509</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2008-12-05 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-08 18:20:31.630509</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2008-12-08 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-09 18:20:31.630509</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2008-12-09 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-10 18:20:31.630509</th>\n",
       "      <td>0</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2008-12-10 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-28 18:20:31.630509</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2020-05-28 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-29 18:20:31.630509</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2020-05-29 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-01 18:20:31.630509</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2020-06-01 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-02 18:20:31.630509</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2020-06-02 18:20:31.630509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-03 18:20:31.630509</th>\n",
       "      <td>1</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>2020-06-03 18:20:31.630509</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3000 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                            bin         w                         t1\n",
       "2008-12-04 18:20:31.630509    0  0.000333 2008-12-04 18:20:31.630509\n",
       "2008-12-05 18:20:31.630509    0  0.000333 2008-12-05 18:20:31.630509\n",
       "2008-12-08 18:20:31.630509    0  0.000333 2008-12-08 18:20:31.630509\n",
       "2008-12-09 18:20:31.630509    0  0.000333 2008-12-09 18:20:31.630509\n",
       "2008-12-10 18:20:31.630509    0  0.000333 2008-12-10 18:20:31.630509\n",
       "...                         ...       ...                        ...\n",
       "2020-05-28 18:20:31.630509    1  0.000333 2020-05-28 18:20:31.630509\n",
       "2020-05-29 18:20:31.630509    1  0.000333 2020-05-29 18:20:31.630509\n",
       "2020-06-01 18:20:31.630509    1  0.000333 2020-06-01 18:20:31.630509\n",
       "2020-06-02 18:20:31.630509    1  0.000333 2020-06-02 18:20:31.630509\n",
       "2020-06-03 18:20:31.630509    1  0.000333 2020-06-03 18:20:31.630509\n",
       "\n",
       "[3000 rows x 3 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y #look familiar?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X0 = pd.DataFrame(data = rs.o_feat(X), index = X.index).add_prefix(\"PC_\") \n",
    "\n",
    "#always make sure your columns are str only when running mp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "If PCA is new or you are confused. I think this article can further illustrate what we are doing.\n",
    "\n",
    "[Towards Data Science: PCA using sklearn](https://towardsdatascience.com/pca-using-python-scikit-learn-e653f8989e60)\n",
    "\n",
    "While you are running SFI method using multiprocessing for parallelization, it will improve processing speed greatly but not as much as you think. Its highly dependent on your machine.\n",
    "\n",
    "For sklearn version 0.23.1, there is some base class and utilities which we can use to improve processing speed.\n",
    "\n",
    "The below is one of them (Haven't tried it, but it seems legit):\n",
    "\n",
    "[sklearn/feature_selection/variance_threshold](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.VarianceThreshold.html#sklearn.feature_selection.VarianceThreshold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x201.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x201.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[           mean         std\n",
      "PC_10  0.448667   0.0100576\n",
      "PC_11      0.47   0.0114212\n",
      "PC_12  0.470667    0.012182\n",
      "PC_13  0.450333  0.00996048] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 18:38:39.559307 33.33% mp_sfi done after 12.26 minutes. Remaining 24.53 minutes.\r"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[           mean         std\n",
      "PC_10  0.448667   0.0100576\n",
      "PC_11      0.47   0.0114212\n",
      "PC_12  0.470667    0.012182\n",
      "PC_13  0.450333  0.00996048,           mean        std\n",
      "PC_0  0.489333  0.0212122\n",
      "PC_1  0.467667  0.0188565\n",
      "PC_2  0.512667  0.0170932\n",
      "PC_3  0.674667  0.0268254\n",
      "PC_4  0.439667  0.0113573] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 18:38:44.183624 66.67% mp_sfi done after 12.34 minutes. Remaining 6.17 minutes.\r"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[           mean         std\n",
      "PC_10  0.448667   0.0100576\n",
      "PC_11      0.47   0.0114212\n",
      "PC_12  0.470667    0.012182\n",
      "PC_13  0.450333  0.00996048,           mean        std\n",
      "PC_0  0.489333  0.0212122\n",
      "PC_1  0.467667  0.0188565\n",
      "PC_2  0.512667  0.0170932\n",
      "PC_3  0.674667  0.0268254\n",
      "PC_4  0.439667  0.0113573,           mean         std\n",
      "PC_5     0.462   0.0150422\n",
      "PC_6     0.446   0.0103688\n",
      "PC_7  0.463667  0.00938616\n",
      "PC_8  0.455333   0.0113058\n",
      "PC_9  0.467667   0.0155924] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 18:40:19.381014 100.0% mp_sfi done after 13.93 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x201.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# look at the time require to run 14 columns\n",
    "\n",
    "rs.feat_imp_analysis(X = X0, \n",
    "                     y = y, \n",
    "                     sample_weight=y['w'],\n",
    "                     methods = ['MDI', 'MDA', 'SFI'],\n",
    "                     events = None,\n",
    "                     pct_embargo = 0.01,\n",
    "                     n_splits = 10,\n",
    "                     min_weight_fraction_leaf = 0.0,\n",
    "                     n_jobs = 3,\n",
    "                     scoring = \"accuracy\",\n",
    "                     output_path = None,\n",
    "                     mask_effect = False) # masking effect is False: max_feature = int(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA as an unsupervised ML\n",
    "\n",
    "**MDI:** PC_3, PC_2, PC_0, PC_1 are considered important.\n",
    "\n",
    "**MDA:** PC_2, PC_3, PC_0, PC_1 are considered important.\n",
    "    \n",
    "**SFI:** PC: PC_3, PC_2, PC_0 are considered important. (PC_1 was ranked below PC_12, PC_11)\n",
    "\n",
    "With reference to the final outcome for the 3 methods: 3, 2, 0 are consistently at the top of the rank.\n",
    "\n",
    "Firstly, we performed PCA on the initial 20 features to deduce 14 principle components (PC). This reduce dimensionality by dropping features with small eigen-values.\n",
    "\n",
    "The resulting features/ PC, are considered more \"principled\" at explaining the structure of data/ samples.\n",
    "\n",
    "**Conclusion**\n",
    "\n",
    "This result definitely proves to be more reliable since unsupervised ML (PCA) has no idea on the labels (Less bias), reduced dimensionality of feature matrix proves to be less expensive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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>PC_0</th>\n",
       "      <th>PC_1</th>\n",
       "      <th>PC_2</th>\n",
       "      <th>PC_3</th>\n",
       "      <th>PC_4</th>\n",
       "      <th>PC_5</th>\n",
       "      <th>PC_6</th>\n",
       "      <th>PC_7</th>\n",
       "      <th>PC_8</th>\n",
       "      <th>PC_9</th>\n",
       "      <th>...</th>\n",
       "      <th>N_0</th>\n",
       "      <th>N_1</th>\n",
       "      <th>N_2</th>\n",
       "      <th>N_3</th>\n",
       "      <th>N_4</th>\n",
       "      <th>N_5</th>\n",
       "      <th>N_6</th>\n",
       "      <th>N_7</th>\n",
       "      <th>N_8</th>\n",
       "      <th>N_9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2008-12-04 18:20:31.630509</th>\n",
       "      <td>0.104914</td>\n",
       "      <td>0.327937</td>\n",
       "      <td>0.606040</td>\n",
       "      <td>1.855273</td>\n",
       "      <td>-0.979098</td>\n",
       "      <td>0.200974</td>\n",
       "      <td>0.647791</td>\n",
       "      <td>-0.389390</td>\n",
       "      <td>-1.322507</td>\n",
       "      <td>-1.090359</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.797706</td>\n",
       "      <td>-0.800303</td>\n",
       "      <td>-1.159210</td>\n",
       "      <td>0.265765</td>\n",
       "      <td>-0.692233</td>\n",
       "      <td>2.031814</td>\n",
       "      <td>-0.545652</td>\n",
       "      <td>0.051393</td>\n",
       "      <td>0.162916</td>\n",
       "      <td>1.003635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-05 18:20:31.630509</th>\n",
       "      <td>-0.608805</td>\n",
       "      <td>-0.047821</td>\n",
       "      <td>-1.961944</td>\n",
       "      <td>0.814204</td>\n",
       "      <td>-1.052428</td>\n",
       "      <td>1.606602</td>\n",
       "      <td>-1.543159</td>\n",
       "      <td>-1.638999</td>\n",
       "      <td>-0.049770</td>\n",
       "      <td>0.269656</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.471474</td>\n",
       "      <td>-0.404565</td>\n",
       "      <td>2.293856</td>\n",
       "      <td>1.553295</td>\n",
       "      <td>-0.167588</td>\n",
       "      <td>-1.171582</td>\n",
       "      <td>0.671503</td>\n",
       "      <td>0.355732</td>\n",
       "      <td>0.164742</td>\n",
       "      <td>1.726842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-08 18:20:31.630509</th>\n",
       "      <td>1.765604</td>\n",
       "      <td>1.167851</td>\n",
       "      <td>-1.688129</td>\n",
       "      <td>-0.418782</td>\n",
       "      <td>1.554633</td>\n",
       "      <td>0.115834</td>\n",
       "      <td>-2.359531</td>\n",
       "      <td>0.807408</td>\n",
       "      <td>-1.680377</td>\n",
       "      <td>-0.210083</td>\n",
       "      <td>...</td>\n",
       "      <td>1.577428</td>\n",
       "      <td>-1.120976</td>\n",
       "      <td>-0.030646</td>\n",
       "      <td>-1.124057</td>\n",
       "      <td>-0.050032</td>\n",
       "      <td>0.093905</td>\n",
       "      <td>0.748571</td>\n",
       "      <td>-2.892617</td>\n",
       "      <td>-0.797168</td>\n",
       "      <td>1.449732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-09 18:20:31.630509</th>\n",
       "      <td>-2.173660</td>\n",
       "      <td>0.937350</td>\n",
       "      <td>1.197696</td>\n",
       "      <td>2.544038</td>\n",
       "      <td>1.662623</td>\n",
       "      <td>0.598929</td>\n",
       "      <td>1.420659</td>\n",
       "      <td>0.868989</td>\n",
       "      <td>-0.718842</td>\n",
       "      <td>1.667454</td>\n",
       "      <td>...</td>\n",
       "      <td>2.145253</td>\n",
       "      <td>-1.026265</td>\n",
       "      <td>0.960892</td>\n",
       "      <td>0.286109</td>\n",
       "      <td>0.209064</td>\n",
       "      <td>0.319532</td>\n",
       "      <td>-0.526978</td>\n",
       "      <td>-0.319982</td>\n",
       "      <td>0.462094</td>\n",
       "      <td>-1.778664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-10 18:20:31.630509</th>\n",
       "      <td>0.803209</td>\n",
       "      <td>-0.033160</td>\n",
       "      <td>-0.651124</td>\n",
       "      <td>1.108180</td>\n",
       "      <td>-2.126057</td>\n",
       "      <td>0.552412</td>\n",
       "      <td>0.618779</td>\n",
       "      <td>2.030640</td>\n",
       "      <td>-1.623105</td>\n",
       "      <td>-0.830248</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.344063</td>\n",
       "      <td>0.427022</td>\n",
       "      <td>-1.974068</td>\n",
       "      <td>2.625296</td>\n",
       "      <td>-0.572037</td>\n",
       "      <td>-0.509773</td>\n",
       "      <td>-0.368742</td>\n",
       "      <td>0.004224</td>\n",
       "      <td>-1.598331</td>\n",
       "      <td>-0.807513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-28 18:20:31.630509</th>\n",
       "      <td>0.339355</td>\n",
       "      <td>0.278173</td>\n",
       "      <td>-0.342509</td>\n",
       "      <td>-0.162521</td>\n",
       "      <td>1.717780</td>\n",
       "      <td>-0.871551</td>\n",
       "      <td>-0.527051</td>\n",
       "      <td>1.209593</td>\n",
       "      <td>1.178983</td>\n",
       "      <td>2.045547</td>\n",
       "      <td>...</td>\n",
       "      <td>1.871046</td>\n",
       "      <td>-1.130525</td>\n",
       "      <td>0.670610</td>\n",
       "      <td>-1.306620</td>\n",
       "      <td>1.700514</td>\n",
       "      <td>-2.019744</td>\n",
       "      <td>-0.808909</td>\n",
       "      <td>-0.727355</td>\n",
       "      <td>0.202766</td>\n",
       "      <td>-1.224024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-29 18:20:31.630509</th>\n",
       "      <td>-0.312508</td>\n",
       "      <td>1.581586</td>\n",
       "      <td>0.049642</td>\n",
       "      <td>0.064116</td>\n",
       "      <td>-1.826597</td>\n",
       "      <td>0.630899</td>\n",
       "      <td>-0.771501</td>\n",
       "      <td>1.018517</td>\n",
       "      <td>2.031080</td>\n",
       "      <td>-0.492896</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.590340</td>\n",
       "      <td>0.171062</td>\n",
       "      <td>-0.029284</td>\n",
       "      <td>-0.736423</td>\n",
       "      <td>0.579844</td>\n",
       "      <td>-0.933117</td>\n",
       "      <td>0.397632</td>\n",
       "      <td>1.639739</td>\n",
       "      <td>-2.382154</td>\n",
       "      <td>0.564313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-01 18:20:31.630509</th>\n",
       "      <td>0.195953</td>\n",
       "      <td>1.119644</td>\n",
       "      <td>-0.118879</td>\n",
       "      <td>-0.513685</td>\n",
       "      <td>-1.398517</td>\n",
       "      <td>-0.393876</td>\n",
       "      <td>0.162924</td>\n",
       "      <td>-0.871914</td>\n",
       "      <td>0.090534</td>\n",
       "      <td>-0.348632</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.415538</td>\n",
       "      <td>0.701067</td>\n",
       "      <td>0.098626</td>\n",
       "      <td>1.530280</td>\n",
       "      <td>0.919778</td>\n",
       "      <td>-1.463967</td>\n",
       "      <td>-1.416195</td>\n",
       "      <td>-0.149276</td>\n",
       "      <td>0.083001</td>\n",
       "      <td>0.089964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-02 18:20:31.630509</th>\n",
       "      <td>1.376577</td>\n",
       "      <td>1.112966</td>\n",
       "      <td>0.640255</td>\n",
       "      <td>-1.748633</td>\n",
       "      <td>-0.372117</td>\n",
       "      <td>-0.584097</td>\n",
       "      <td>0.154735</td>\n",
       "      <td>-0.619561</td>\n",
       "      <td>-0.439227</td>\n",
       "      <td>-0.560638</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.501588</td>\n",
       "      <td>-0.180367</td>\n",
       "      <td>-0.867517</td>\n",
       "      <td>0.067514</td>\n",
       "      <td>-0.552346</td>\n",
       "      <td>0.638024</td>\n",
       "      <td>-0.444415</td>\n",
       "      <td>0.111936</td>\n",
       "      <td>0.936410</td>\n",
       "      <td>0.941215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-03 18:20:31.630509</th>\n",
       "      <td>0.869378</td>\n",
       "      <td>2.033419</td>\n",
       "      <td>0.721858</td>\n",
       "      <td>-0.066690</td>\n",
       "      <td>0.638049</td>\n",
       "      <td>2.158430</td>\n",
       "      <td>1.622026</td>\n",
       "      <td>-0.377836</td>\n",
       "      <td>1.358085</td>\n",
       "      <td>-0.281309</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.048229</td>\n",
       "      <td>0.015849</td>\n",
       "      <td>0.198696</td>\n",
       "      <td>1.939838</td>\n",
       "      <td>2.230065</td>\n",
       "      <td>1.074580</td>\n",
       "      <td>1.193151</td>\n",
       "      <td>1.049536</td>\n",
       "      <td>0.517009</td>\n",
       "      <td>-1.855302</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3000 rows × 34 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                PC_0      PC_1      PC_2      PC_3      PC_4  \\\n",
       "2008-12-04 18:20:31.630509  0.104914  0.327937  0.606040  1.855273 -0.979098   \n",
       "2008-12-05 18:20:31.630509 -0.608805 -0.047821 -1.961944  0.814204 -1.052428   \n",
       "2008-12-08 18:20:31.630509  1.765604  1.167851 -1.688129 -0.418782  1.554633   \n",
       "2008-12-09 18:20:31.630509 -2.173660  0.937350  1.197696  2.544038  1.662623   \n",
       "2008-12-10 18:20:31.630509  0.803209 -0.033160 -0.651124  1.108180 -2.126057   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509  0.339355  0.278173 -0.342509 -0.162521  1.717780   \n",
       "2020-05-29 18:20:31.630509 -0.312508  1.581586  0.049642  0.064116 -1.826597   \n",
       "2020-06-01 18:20:31.630509  0.195953  1.119644 -0.118879 -0.513685 -1.398517   \n",
       "2020-06-02 18:20:31.630509  1.376577  1.112966  0.640255 -1.748633 -0.372117   \n",
       "2020-06-03 18:20:31.630509  0.869378  2.033419  0.721858 -0.066690  0.638049   \n",
       "\n",
       "                                PC_5      PC_6      PC_7      PC_8      PC_9  \\\n",
       "2008-12-04 18:20:31.630509  0.200974  0.647791 -0.389390 -1.322507 -1.090359   \n",
       "2008-12-05 18:20:31.630509  1.606602 -1.543159 -1.638999 -0.049770  0.269656   \n",
       "2008-12-08 18:20:31.630509  0.115834 -2.359531  0.807408 -1.680377 -0.210083   \n",
       "2008-12-09 18:20:31.630509  0.598929  1.420659  0.868989 -0.718842  1.667454   \n",
       "2008-12-10 18:20:31.630509  0.552412  0.618779  2.030640 -1.623105 -0.830248   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509 -0.871551 -0.527051  1.209593  1.178983  2.045547   \n",
       "2020-05-29 18:20:31.630509  0.630899 -0.771501  1.018517  2.031080 -0.492896   \n",
       "2020-06-01 18:20:31.630509 -0.393876  0.162924 -0.871914  0.090534 -0.348632   \n",
       "2020-06-02 18:20:31.630509 -0.584097  0.154735 -0.619561 -0.439227 -0.560638   \n",
       "2020-06-03 18:20:31.630509  2.158430  1.622026 -0.377836  1.358085 -0.281309   \n",
       "\n",
       "                            ...       N_0       N_1       N_2       N_3  \\\n",
       "2008-12-04 18:20:31.630509  ... -0.797706 -0.800303 -1.159210  0.265765   \n",
       "2008-12-05 18:20:31.630509  ... -0.471474 -0.404565  2.293856  1.553295   \n",
       "2008-12-08 18:20:31.630509  ...  1.577428 -1.120976 -0.030646 -1.124057   \n",
       "2008-12-09 18:20:31.630509  ...  2.145253 -1.026265  0.960892  0.286109   \n",
       "2008-12-10 18:20:31.630509  ... -0.344063  0.427022 -1.974068  2.625296   \n",
       "...                         ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509  ...  1.871046 -1.130525  0.670610 -1.306620   \n",
       "2020-05-29 18:20:31.630509  ... -0.590340  0.171062 -0.029284 -0.736423   \n",
       "2020-06-01 18:20:31.630509  ... -1.415538  0.701067  0.098626  1.530280   \n",
       "2020-06-02 18:20:31.630509  ... -0.501588 -0.180367 -0.867517  0.067514   \n",
       "2020-06-03 18:20:31.630509  ... -1.048229  0.015849  0.198696  1.939838   \n",
       "\n",
       "                                 N_4       N_5       N_6       N_7       N_8  \\\n",
       "2008-12-04 18:20:31.630509 -0.692233  2.031814 -0.545652  0.051393  0.162916   \n",
       "2008-12-05 18:20:31.630509 -0.167588 -1.171582  0.671503  0.355732  0.164742   \n",
       "2008-12-08 18:20:31.630509 -0.050032  0.093905  0.748571 -2.892617 -0.797168   \n",
       "2008-12-09 18:20:31.630509  0.209064  0.319532 -0.526978 -0.319982  0.462094   \n",
       "2008-12-10 18:20:31.630509 -0.572037 -0.509773 -0.368742  0.004224 -1.598331   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509  1.700514 -2.019744 -0.808909 -0.727355  0.202766   \n",
       "2020-05-29 18:20:31.630509  0.579844 -0.933117  0.397632  1.639739 -2.382154   \n",
       "2020-06-01 18:20:31.630509  0.919778 -1.463967 -1.416195 -0.149276  0.083001   \n",
       "2020-06-02 18:20:31.630509 -0.552346  0.638024 -0.444415  0.111936  0.936410   \n",
       "2020-06-03 18:20:31.630509  2.230065  1.074580  1.193151  1.049536  0.517009   \n",
       "\n",
       "                                 N_9  \n",
       "2008-12-04 18:20:31.630509  1.003635  \n",
       "2008-12-05 18:20:31.630509  1.726842  \n",
       "2008-12-08 18:20:31.630509  1.449732  \n",
       "2008-12-09 18:20:31.630509 -1.778664  \n",
       "2008-12-10 18:20:31.630509 -0.807513  \n",
       "...                              ...  \n",
       "2020-05-28 18:20:31.630509 -1.224024  \n",
       "2020-05-29 18:20:31.630509  0.564313  \n",
       "2020-06-01 18:20:31.630509  0.089964  \n",
       "2020-06-02 18:20:31.630509  0.941215  \n",
       "2020-06-03 18:20:31.630509 -1.855302  \n",
       "\n",
       "[3000 rows x 34 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X0 = pd.concat([X0, X], axis=1) # same dataset so can reuse X\n",
    "\n",
    "X0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x489.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x489.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[           mean         std\n",
      "PC_12  0.470667    0.012182\n",
      "PC_13  0.450333  0.00996048\n",
      "I_0       0.512   0.0270933\n",
      "I_1    0.682667  0.00885438\n",
      "I_2    0.532333   0.0338134\n",
      "I_3    0.447667   0.0102312\n",
      "I_4    0.525333   0.0298224\n",
      "R_0       0.555   0.0222972\n",
      "R_1       0.475   0.0161881\n",
      "R_2    0.484667   0.0163449\n",
      "R_3    0.481333   0.0138098] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 20:06:27.990713 33.33% mp_sfi done after 27.51 minutes. Remaining 55.02 minutes.\r"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[           mean         std\n",
      "PC_12  0.470667    0.012182\n",
      "PC_13  0.450333  0.00996048\n",
      "I_0       0.512   0.0270933\n",
      "I_1    0.682667  0.00885438\n",
      "I_2    0.532333   0.0338134\n",
      "I_3    0.447667   0.0102312\n",
      "I_4    0.525333   0.0298224\n",
      "R_0       0.555   0.0222972\n",
      "R_1       0.475   0.0161881\n",
      "R_2    0.484667   0.0163449\n",
      "R_3    0.481333   0.0138098,          mean         std\n",
      "R_4  0.473667   0.0113573\n",
      "N_0  0.452667   0.0090652\n",
      "N_1     0.464   0.0162672\n",
      "N_2  0.467333   0.0158591\n",
      "N_3  0.449667   0.0137635\n",
      "N_4  0.471667  0.00975534\n",
      "N_5  0.432667  0.00988602\n",
      "N_6     0.466  0.00946103\n",
      "N_7  0.455333   0.0107621\n",
      "N_8  0.468333    0.010025\n",
      "N_9     0.455   0.0104907] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 20:10:15.659872 66.67% mp_sfi done after 31.3 minutes. Remaining 15.65 minutes.\r"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[           mean         std\n",
      "PC_12  0.470667    0.012182\n",
      "PC_13  0.450333  0.00996048\n",
      "I_0       0.512   0.0270933\n",
      "I_1    0.682667  0.00885438\n",
      "I_2    0.532333   0.0338134\n",
      "I_3    0.447667   0.0102312\n",
      "I_4    0.525333   0.0298224\n",
      "R_0       0.555   0.0222972\n",
      "R_1       0.475   0.0161881\n",
      "R_2    0.484667   0.0163449\n",
      "R_3    0.481333   0.0138098,          mean         std\n",
      "R_4  0.473667   0.0113573\n",
      "N_0  0.452667   0.0090652\n",
      "N_1     0.464   0.0162672\n",
      "N_2  0.467333   0.0158591\n",
      "N_3  0.449667   0.0137635\n",
      "N_4  0.471667  0.00975534\n",
      "N_5  0.432667  0.00988602\n",
      "N_6     0.466  0.00946103\n",
      "N_7  0.455333   0.0107621\n",
      "N_8  0.468333    0.010025\n",
      "N_9     0.455   0.0104907,            mean         std\n",
      "PC_0   0.489333   0.0212122\n",
      "PC_1   0.467667   0.0188565\n",
      "PC_2   0.512667   0.0170932\n",
      "PC_3   0.674667   0.0268254\n",
      "PC_4   0.439667   0.0113573\n",
      "PC_5      0.462   0.0150422\n",
      "PC_6      0.446   0.0103688\n",
      "PC_7   0.463667  0.00938616\n",
      "PC_8   0.455333   0.0113058\n",
      "PC_9   0.467667   0.0155924\n",
      "PC_10  0.448667   0.0100576\n",
      "PC_11      0.47   0.0114212] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 20:10:41.765237 100.0% mp_sfi done after 31.74 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x489.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#now i have 34 columns instead of 14 columns, look at the time required when running with 4 cores only.\n",
    "\n",
    "rs.feat_imp_analysis(X = X0, \n",
    "                     y = y, \n",
    "                     sample_weight=y['w'],\n",
    "                     methods = ['MDI', 'MDA', 'SFI'],\n",
    "                     events = None,\n",
    "                     pct_embargo = 0.01,\n",
    "                     n_splits = 10,\n",
    "                     min_weight_fraction_leaf = 0.0,\n",
    "                     n_jobs = 3,\n",
    "                     scoring = \"accuracy\",\n",
    "                     output_path = None,\n",
    "                     mask_effect = False) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mixing features with principle components\n",
    "\n",
    "**MDI Summary:**\n",
    "\n",
    "PC: PC_3,PC_2,PC_0, PC_1 are still considered important.\n",
    "\n",
    "Features: I_1, R_0, I_4, I_0, I_2, R_1, R_2, R_3 are considered important.\n",
    "\n",
    "For MDI, subsitution effect can be notice as principle components suffered a drop in ranking, however MDI still considered these PCs important. All PCs that was deemed important from initial test are still considered important.\n",
    "\n",
    "While new features that were informative or redundant were mostly ranked important and above noise features.\n",
    "\n",
    "With exception to R_4, I_3 which missed marginally from the dotted vertical red line.\n",
    "\n",
    "**MDA Summary:**\n",
    "\n",
    "PC: PC_3, PC_0, PC_4, PC_5 only were found above first noise features (N_4).\n",
    "\n",
    "Features:  I_4, I_1, I_2, R_0, I_3 were still found above first noise features (N_4).\n",
    "\n",
    "In view of substitution effects, MDA deem critical features as redundant and start to rank noise features higher. When dealing with critical but identical features, MDA will considered them unimportant (Since MDA based performance on Out-of-Sample score). \n",
    "\n",
    "As a result PC_2, PC_1 as well as the remaining informative and redundant features were mostly ranked below first noise feature (N_4). \n",
    "\n",
    "To make it worse, some of these critical features were deemed unimportant and deterimental to model.\n",
    "\n",
    "**SFI Summary:** \n",
    "\n",
    "PC: PC_3, PC_2, PC_0 are ranked before then first noise feature (N_4) while PC_1 was ranked below N_8 (lower than N_4).\n",
    "\n",
    "Features: I_3 was the only one that was ranked below first noise feature (N_4), while the remaining informative and redundant features was still above the first noise feature (N_4). (SFI also based performance on Out-of-Sample score).\n",
    "\n",
    "However, SFI was the only method that ranked first principle feature (I_1) above principle components at the top.\n",
    "\n",
    "### Conclusion\n",
    "\n",
    "When features collection suffers high redundancy, substitution effects will reflect in the inconsistent ranking outcome from MDA against the other 2 methods.\n",
    "\n",
    "With reference to the above, only the below labels was considered important in all 3 methods.\n",
    "\n",
    "* PC_0\n",
    "* PC_3\n",
    "* I_4\n",
    "* I_1\n",
    "* I_2\n",
    "\n",
    "Whenever strong mismatch outcome is observed. \n",
    "\n",
    "It is a sign where features collection is suffering from high feature redundancy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1 = X0.drop(['PC_0', 'PC_3', 'I_4', 'I_1', 'I_2'], axis = 'columns')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC_1</th>\n",
       "      <th>PC_2</th>\n",
       "      <th>PC_4</th>\n",
       "      <th>PC_5</th>\n",
       "      <th>PC_6</th>\n",
       "      <th>PC_7</th>\n",
       "      <th>PC_8</th>\n",
       "      <th>PC_9</th>\n",
       "      <th>PC_10</th>\n",
       "      <th>PC_11</th>\n",
       "      <th>...</th>\n",
       "      <th>N_0</th>\n",
       "      <th>N_1</th>\n",
       "      <th>N_2</th>\n",
       "      <th>N_3</th>\n",
       "      <th>N_4</th>\n",
       "      <th>N_5</th>\n",
       "      <th>N_6</th>\n",
       "      <th>N_7</th>\n",
       "      <th>N_8</th>\n",
       "      <th>N_9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2008-12-04 18:20:31.630509</th>\n",
       "      <td>0.327937</td>\n",
       "      <td>0.606040</td>\n",
       "      <td>-0.979098</td>\n",
       "      <td>0.200974</td>\n",
       "      <td>0.647791</td>\n",
       "      <td>-0.389390</td>\n",
       "      <td>-1.322507</td>\n",
       "      <td>-1.090359</td>\n",
       "      <td>1.531310</td>\n",
       "      <td>1.040459</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.797706</td>\n",
       "      <td>-0.800303</td>\n",
       "      <td>-1.159210</td>\n",
       "      <td>0.265765</td>\n",
       "      <td>-0.692233</td>\n",
       "      <td>2.031814</td>\n",
       "      <td>-0.545652</td>\n",
       "      <td>0.051393</td>\n",
       "      <td>0.162916</td>\n",
       "      <td>1.003635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-05 18:20:31.630509</th>\n",
       "      <td>-0.047821</td>\n",
       "      <td>-1.961944</td>\n",
       "      <td>-1.052428</td>\n",
       "      <td>1.606602</td>\n",
       "      <td>-1.543159</td>\n",
       "      <td>-1.638999</td>\n",
       "      <td>-0.049770</td>\n",
       "      <td>0.269656</td>\n",
       "      <td>-0.867187</td>\n",
       "      <td>-0.157241</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.471474</td>\n",
       "      <td>-0.404565</td>\n",
       "      <td>2.293856</td>\n",
       "      <td>1.553295</td>\n",
       "      <td>-0.167588</td>\n",
       "      <td>-1.171582</td>\n",
       "      <td>0.671503</td>\n",
       "      <td>0.355732</td>\n",
       "      <td>0.164742</td>\n",
       "      <td>1.726842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-08 18:20:31.630509</th>\n",
       "      <td>1.167851</td>\n",
       "      <td>-1.688129</td>\n",
       "      <td>1.554633</td>\n",
       "      <td>0.115834</td>\n",
       "      <td>-2.359531</td>\n",
       "      <td>0.807408</td>\n",
       "      <td>-1.680377</td>\n",
       "      <td>-0.210083</td>\n",
       "      <td>0.966765</td>\n",
       "      <td>1.929211</td>\n",
       "      <td>...</td>\n",
       "      <td>1.577428</td>\n",
       "      <td>-1.120976</td>\n",
       "      <td>-0.030646</td>\n",
       "      <td>-1.124057</td>\n",
       "      <td>-0.050032</td>\n",
       "      <td>0.093905</td>\n",
       "      <td>0.748571</td>\n",
       "      <td>-2.892617</td>\n",
       "      <td>-0.797168</td>\n",
       "      <td>1.449732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-09 18:20:31.630509</th>\n",
       "      <td>0.937350</td>\n",
       "      <td>1.197696</td>\n",
       "      <td>1.662623</td>\n",
       "      <td>0.598929</td>\n",
       "      <td>1.420659</td>\n",
       "      <td>0.868989</td>\n",
       "      <td>-0.718842</td>\n",
       "      <td>1.667454</td>\n",
       "      <td>-0.285337</td>\n",
       "      <td>0.326614</td>\n",
       "      <td>...</td>\n",
       "      <td>2.145253</td>\n",
       "      <td>-1.026265</td>\n",
       "      <td>0.960892</td>\n",
       "      <td>0.286109</td>\n",
       "      <td>0.209064</td>\n",
       "      <td>0.319532</td>\n",
       "      <td>-0.526978</td>\n",
       "      <td>-0.319982</td>\n",
       "      <td>0.462094</td>\n",
       "      <td>-1.778664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-10 18:20:31.630509</th>\n",
       "      <td>-0.033160</td>\n",
       "      <td>-0.651124</td>\n",
       "      <td>-2.126057</td>\n",
       "      <td>0.552412</td>\n",
       "      <td>0.618779</td>\n",
       "      <td>2.030640</td>\n",
       "      <td>-1.623105</td>\n",
       "      <td>-0.830248</td>\n",
       "      <td>-0.219950</td>\n",
       "      <td>-1.861995</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.344063</td>\n",
       "      <td>0.427022</td>\n",
       "      <td>-1.974068</td>\n",
       "      <td>2.625296</td>\n",
       "      <td>-0.572037</td>\n",
       "      <td>-0.509773</td>\n",
       "      <td>-0.368742</td>\n",
       "      <td>0.004224</td>\n",
       "      <td>-1.598331</td>\n",
       "      <td>-0.807513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-28 18:20:31.630509</th>\n",
       "      <td>0.278173</td>\n",
       "      <td>-0.342509</td>\n",
       "      <td>1.717780</td>\n",
       "      <td>-0.871551</td>\n",
       "      <td>-0.527051</td>\n",
       "      <td>1.209593</td>\n",
       "      <td>1.178983</td>\n",
       "      <td>2.045547</td>\n",
       "      <td>0.586069</td>\n",
       "      <td>-0.166173</td>\n",
       "      <td>...</td>\n",
       "      <td>1.871046</td>\n",
       "      <td>-1.130525</td>\n",
       "      <td>0.670610</td>\n",
       "      <td>-1.306620</td>\n",
       "      <td>1.700514</td>\n",
       "      <td>-2.019744</td>\n",
       "      <td>-0.808909</td>\n",
       "      <td>-0.727355</td>\n",
       "      <td>0.202766</td>\n",
       "      <td>-1.224024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-05-29 18:20:31.630509</th>\n",
       "      <td>1.581586</td>\n",
       "      <td>0.049642</td>\n",
       "      <td>-1.826597</td>\n",
       "      <td>0.630899</td>\n",
       "      <td>-0.771501</td>\n",
       "      <td>1.018517</td>\n",
       "      <td>2.031080</td>\n",
       "      <td>-0.492896</td>\n",
       "      <td>-0.521698</td>\n",
       "      <td>0.585276</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.590340</td>\n",
       "      <td>0.171062</td>\n",
       "      <td>-0.029284</td>\n",
       "      <td>-0.736423</td>\n",
       "      <td>0.579844</td>\n",
       "      <td>-0.933117</td>\n",
       "      <td>0.397632</td>\n",
       "      <td>1.639739</td>\n",
       "      <td>-2.382154</td>\n",
       "      <td>0.564313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-01 18:20:31.630509</th>\n",
       "      <td>1.119644</td>\n",
       "      <td>-0.118879</td>\n",
       "      <td>-1.398517</td>\n",
       "      <td>-0.393876</td>\n",
       "      <td>0.162924</td>\n",
       "      <td>-0.871914</td>\n",
       "      <td>0.090534</td>\n",
       "      <td>-0.348632</td>\n",
       "      <td>0.101497</td>\n",
       "      <td>-2.099143</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.415538</td>\n",
       "      <td>0.701067</td>\n",
       "      <td>0.098626</td>\n",
       "      <td>1.530280</td>\n",
       "      <td>0.919778</td>\n",
       "      <td>-1.463967</td>\n",
       "      <td>-1.416195</td>\n",
       "      <td>-0.149276</td>\n",
       "      <td>0.083001</td>\n",
       "      <td>0.089964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-02 18:20:31.630509</th>\n",
       "      <td>1.112966</td>\n",
       "      <td>0.640255</td>\n",
       "      <td>-0.372117</td>\n",
       "      <td>-0.584097</td>\n",
       "      <td>0.154735</td>\n",
       "      <td>-0.619561</td>\n",
       "      <td>-0.439227</td>\n",
       "      <td>-0.560638</td>\n",
       "      <td>0.943997</td>\n",
       "      <td>0.111793</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.501588</td>\n",
       "      <td>-0.180367</td>\n",
       "      <td>-0.867517</td>\n",
       "      <td>0.067514</td>\n",
       "      <td>-0.552346</td>\n",
       "      <td>0.638024</td>\n",
       "      <td>-0.444415</td>\n",
       "      <td>0.111936</td>\n",
       "      <td>0.936410</td>\n",
       "      <td>0.941215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-03 18:20:31.630509</th>\n",
       "      <td>2.033419</td>\n",
       "      <td>0.721858</td>\n",
       "      <td>0.638049</td>\n",
       "      <td>2.158430</td>\n",
       "      <td>1.622026</td>\n",
       "      <td>-0.377836</td>\n",
       "      <td>1.358085</td>\n",
       "      <td>-0.281309</td>\n",
       "      <td>0.543545</td>\n",
       "      <td>-2.592930</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.048229</td>\n",
       "      <td>0.015849</td>\n",
       "      <td>0.198696</td>\n",
       "      <td>1.939838</td>\n",
       "      <td>2.230065</td>\n",
       "      <td>1.074580</td>\n",
       "      <td>1.193151</td>\n",
       "      <td>1.049536</td>\n",
       "      <td>0.517009</td>\n",
       "      <td>-1.855302</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3000 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                PC_1      PC_2      PC_4      PC_5      PC_6  \\\n",
       "2008-12-04 18:20:31.630509  0.327937  0.606040 -0.979098  0.200974  0.647791   \n",
       "2008-12-05 18:20:31.630509 -0.047821 -1.961944 -1.052428  1.606602 -1.543159   \n",
       "2008-12-08 18:20:31.630509  1.167851 -1.688129  1.554633  0.115834 -2.359531   \n",
       "2008-12-09 18:20:31.630509  0.937350  1.197696  1.662623  0.598929  1.420659   \n",
       "2008-12-10 18:20:31.630509 -0.033160 -0.651124 -2.126057  0.552412  0.618779   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509  0.278173 -0.342509  1.717780 -0.871551 -0.527051   \n",
       "2020-05-29 18:20:31.630509  1.581586  0.049642 -1.826597  0.630899 -0.771501   \n",
       "2020-06-01 18:20:31.630509  1.119644 -0.118879 -1.398517 -0.393876  0.162924   \n",
       "2020-06-02 18:20:31.630509  1.112966  0.640255 -0.372117 -0.584097  0.154735   \n",
       "2020-06-03 18:20:31.630509  2.033419  0.721858  0.638049  2.158430  1.622026   \n",
       "\n",
       "                                PC_7      PC_8      PC_9     PC_10     PC_11  \\\n",
       "2008-12-04 18:20:31.630509 -0.389390 -1.322507 -1.090359  1.531310  1.040459   \n",
       "2008-12-05 18:20:31.630509 -1.638999 -0.049770  0.269656 -0.867187 -0.157241   \n",
       "2008-12-08 18:20:31.630509  0.807408 -1.680377 -0.210083  0.966765  1.929211   \n",
       "2008-12-09 18:20:31.630509  0.868989 -0.718842  1.667454 -0.285337  0.326614   \n",
       "2008-12-10 18:20:31.630509  2.030640 -1.623105 -0.830248 -0.219950 -1.861995   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509  1.209593  1.178983  2.045547  0.586069 -0.166173   \n",
       "2020-05-29 18:20:31.630509  1.018517  2.031080 -0.492896 -0.521698  0.585276   \n",
       "2020-06-01 18:20:31.630509 -0.871914  0.090534 -0.348632  0.101497 -2.099143   \n",
       "2020-06-02 18:20:31.630509 -0.619561 -0.439227 -0.560638  0.943997  0.111793   \n",
       "2020-06-03 18:20:31.630509 -0.377836  1.358085 -0.281309  0.543545 -2.592930   \n",
       "\n",
       "                            ...       N_0       N_1       N_2       N_3  \\\n",
       "2008-12-04 18:20:31.630509  ... -0.797706 -0.800303 -1.159210  0.265765   \n",
       "2008-12-05 18:20:31.630509  ... -0.471474 -0.404565  2.293856  1.553295   \n",
       "2008-12-08 18:20:31.630509  ...  1.577428 -1.120976 -0.030646 -1.124057   \n",
       "2008-12-09 18:20:31.630509  ...  2.145253 -1.026265  0.960892  0.286109   \n",
       "2008-12-10 18:20:31.630509  ... -0.344063  0.427022 -1.974068  2.625296   \n",
       "...                         ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509  ...  1.871046 -1.130525  0.670610 -1.306620   \n",
       "2020-05-29 18:20:31.630509  ... -0.590340  0.171062 -0.029284 -0.736423   \n",
       "2020-06-01 18:20:31.630509  ... -1.415538  0.701067  0.098626  1.530280   \n",
       "2020-06-02 18:20:31.630509  ... -0.501588 -0.180367 -0.867517  0.067514   \n",
       "2020-06-03 18:20:31.630509  ... -1.048229  0.015849  0.198696  1.939838   \n",
       "\n",
       "                                 N_4       N_5       N_6       N_7       N_8  \\\n",
       "2008-12-04 18:20:31.630509 -0.692233  2.031814 -0.545652  0.051393  0.162916   \n",
       "2008-12-05 18:20:31.630509 -0.167588 -1.171582  0.671503  0.355732  0.164742   \n",
       "2008-12-08 18:20:31.630509 -0.050032  0.093905  0.748571 -2.892617 -0.797168   \n",
       "2008-12-09 18:20:31.630509  0.209064  0.319532 -0.526978 -0.319982  0.462094   \n",
       "2008-12-10 18:20:31.630509 -0.572037 -0.509773 -0.368742  0.004224 -1.598331   \n",
       "...                              ...       ...       ...       ...       ...   \n",
       "2020-05-28 18:20:31.630509  1.700514 -2.019744 -0.808909 -0.727355  0.202766   \n",
       "2020-05-29 18:20:31.630509  0.579844 -0.933117  0.397632  1.639739 -2.382154   \n",
       "2020-06-01 18:20:31.630509  0.919778 -1.463967 -1.416195 -0.149276  0.083001   \n",
       "2020-06-02 18:20:31.630509 -0.552346  0.638024 -0.444415  0.111936  0.936410   \n",
       "2020-06-03 18:20:31.630509  2.230065  1.074580  1.193151  1.049536  0.517009   \n",
       "\n",
       "                                 N_9  \n",
       "2008-12-04 18:20:31.630509  1.003635  \n",
       "2008-12-05 18:20:31.630509  1.726842  \n",
       "2008-12-08 18:20:31.630509  1.449732  \n",
       "2008-12-09 18:20:31.630509 -1.778664  \n",
       "2008-12-10 18:20:31.630509 -0.807513  \n",
       "...                              ...  \n",
       "2020-05-28 18:20:31.630509 -1.224024  \n",
       "2020-05-29 18:20:31.630509  0.564313  \n",
       "2020-06-01 18:20:31.630509  0.089964  \n",
       "2020-06-02 18:20:31.630509  0.941215  \n",
       "2020-06-03 18:20:31.630509 -1.855302  \n",
       "\n",
       "[3000 rows x 29 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x417.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iIiJShk6xiYiIiJShDpKIiIhIGTU+Bik+Pt5KTEys6dWKiIiI1Li1a9fmWZZ1RlWAGu8gJSYmkpOTU9OrFZEQFxsbi9vt9jpv69atXH/99Zw6dYqTJ09y//33c/fddwc4QhGpj4wxW71N11VsYSQrq64jEPHt1Cnfx+jJk+fy5JP/Jjo6hoICN7/85UXExw8nPj4hoDGK+Cstra4jkNqmDpKI1LmoqOiS54WFJyhdQ1dEJPDUQRKRoLB37zYeeeR/2LFjE3fd9ZSyR1WUkpFW1yHUD83qOoB6oI5Pi+gqNhEJCuec05Y5c9bx8sub+OCDeRw4sKfihUREaokySCISVOLjE0hMTCI39xP69RtR1+GEHNfMrLoOoV7QGKTwpwySiNS5ffu2c+JEAQBHjx5k/frVtG17QR1HJSL1mTJIYUS/aCSYRUT4PkY//PAbJk6ciDEGy7KYMmUSt9+eHND4REQ8qYMkIgHh6x5IAIMGDWLdunUBjEZEpHw6xSYiIiJShjJIIhIwubm5jB49utS0mJgY1qxZU0cRiYh4pw6SSC2LiIggOTmZoqIi2rdvz/z582nWzPtNVFwuF/fccw9HjhwhIiKCyZMnc9NNNwU44tqTnJyMy+Wq6zBERCqkDlIYUamR4BQd3ZCZM+1OwZNPjmXSpBe49dbJXttu29aIe+/9B23adCIvbyd33dWLxo0HExuru9IFE10QIRL+1EESCaCkpL5s3ux7MHLbtp1LnsfHJ9Cs2TkcOrRPHSQRkQBTB0kkQE6dOsXnny/n6qvH+dX+m2/+S1FRIQkJHWo5stoVlqUvwrW/qjS0SAl1kERqWWFhAXfckcLu3Vvo3LkXvXoNqnCZ/ft38eSTo3n44XmcdZYuNhURCTR1kERqWXR0Q156yYXbfZhHHx3GW2+9wA03/Npn+2PHjvDII//D7bdPpWvXSwMYae0Ix9IXGoMkEv7001QkQGJjm3L//c/xxhszKCo66bXNyZOFTJlyHVddNYa0tPQARygiIsWUQQoj+lUbnDxLbKSl9WDJku7s2rXgjPsBAbz88hvk5q7i9On9fPrpXADmzp1LSkpK4AIWERGMZVk1usLevXtbOTk5NbpOERERkdpgjFlrWVbvstN1ik1ERESkDJ1iE6kDKrkhIhLc1EGSesGz3EeXLl2YN28ejRo1Yvfu3WRkZJCdnU1MTAyJiYnMnDmTzp07e13PkCFD+Oyzz7j88stZunRpleNRyQ0RkeCmDlIY0T3efPMs9zF16igmTZpNevoE7rvvOgYPHsucOQsA2LTJxbJle9i503sHadCgB7niinz+9a+/an9XQBcNiEgo0xgkqXe6dUtlx45NfPHFx0RGRjF8+N0l8zp2TKFbt1Sfy/bqNZBGjc4ORJgiIlKHlEGSeuXUqSLWrHmPiy8ewg8/rKdz516VWj4lIw23+xBN9m4LzxIaNSlcy3HUNKUiRYKSMkhSLxSX+7jrrt60atXO73poIiJSPymDJPVCcbkPT4mJSaxatahS63HNzGKTK4sjr8/A9WTVB2nXBxqDJCKhTB2kMKIvJN8872ZdrF+/AbzxxqNs3Pgid955JwDZ2dnk5+fTr1+/ctf30Ufa3yIi4Uyn2KTeMsbw5ptv8uGHH9KhQweSkpLIzMwkISHB5zKpqamkp6ezfPly2rRpw/vvvx/AiEVEJFBUakRERETqLZUaEREREfGTxiCJlKEyICIiog6ShIyaKBficrm45557OHLkCBEREUyePJmbbrqpVBuVAREREY1BCiPhfr+5oUNjee89N2CXC+ncuZdTLuQyBg8eW3JH7E2bXOTnH/V6R+xt277DGEObNp3Iy9vJXXf1Yt68b4iNDd+7GupqOxER33yNQVIGSUJSt26pbN68zme5EF/atv0pqxQfn0CzZudw6NC+sO4giYhI5amDJCHHV7mQypb+WJt/hMgdm7j6qTs4y5haiDRIqO93pnBPt4pItekqNgkZNVkuZPfJE9z94wZmtb0gvDtHIiJSJcogScioqFyIa2aWX+s5duwIEyakMerheUSlpRPuw7E1BklEpPI0SFtCRmxsLG63u9Q0y7K49NJLueOOO/wqF1JYWMjQoUO55ppryMjICEjcIiISvHSjSAlLlS0X8sYbb7Bq1Srmzp1LSkoKKSkpuqRfRETOoAySiIiI1FvKIImIiIj4SYO0JSypXIiIiFSHOkgStDxLi7Rv35758+fTrJnvm/rMmzePqVOnAvDYY49pbJGIiFSZOkhhJNzufRcd3ZCZM+1OzpNPjmXSpBe49dbJXtseOXKARx55gtmzczDGcNddvYiLG87ZZzcPZMi1Rpfqi4gEljpIocjHt2XKocCGUdsiCgtK7o49OG8nX639iJScD722XXRwL1edOM4Vj18PwFUnjrPnvp+T2vycQIVbu3Q37Pon3H7xiIQYDdKWoHfKsljlPsjQJi18ttl18gRtomNKXp8XHcOukycCEZ6IiIQhZZBCkY9fli7vk0NWwcAIersPsXv3Fjp37kXzpz7AFRHhte2OBU9x8uQJXKMfA2DXP35PgwaNcN04MZAh1xqdYhMRCSxlkCRoFZcWWbBgK0VFhbz11gs+27Zs2Ya9e7eVvN63bzstWni/WaSIiEhFdKNICVqepUW++OILrr32WjZv3kxUVNQZbQ8cOECvXr34/PPPAejZsydr164lLi4uoDGLiEho0Y0iJaT16NGD7t27s2DBAq/z4+LimDJlCn369KFPnz48/vjj6hyJiEiVKYMkIiIi9ZYySCIiIiJ+UgdJAiY2Nrbc+fPmzaNTp0506tSJefPmeW2Tm5tLSkpKqccll1xSG+GKiEg9plNsEjCeg67LOnDgAL179yYnx74Tdq9evVi7di3Nm4fHnbBFRCQ4+TrFpvsghZFgv/HuqVO+Y1y+/H2Skgaxbp09sDopaRDPPLOMgQNvDlyAlaR7E4mIhC91kIJNNb51g73UiGfpkLI+2buN7tbpkvnd9mwleu1HpPzrr4ELsLJU/iN0BPuvBxEJOhqDJEHB24leE/AoREREbMogBZtq/NIN9lIjp4bG4pqZ5XXeyeWv8aUrC9dEO2O07um7SElJw6VTbCIiUgeUQZKg0KfPYHJyPuDo0YMcPXqQnJwP6NNncF2HJSIi9ZQySGEk2DMaERHlxRhHXt4UJkzoA8Af/vA4w4frTtgiIlI3dJm/iIiI1Fu6k7aIiIiIn3SKTQIqNzeX0aNHl5oWExPDmjVr6igiERGRM6mDJH6LiIggOTmZoqIi2rdvz/z582nWrPybAR05coQuXbpw3XXXMWvWLJKTk3G5XAGKWEREpGrUQQojtX0vvOjohsycaXdunnxyLJMmvcCtt04ud5nnn5/ChRf2Y8eO2o8v2Aepi4hI6NAYJKmSpKS+7Nu3o9w23367loMH99Cnz1UBikpERKRmKIMkFSou/1FcKuSUZTFz69eMjjvXZ+mQ05bFY5u/ZHa7C1n16nT25x8l5Yf1tRtoKJT+UMkLEZGQoA6S+K3g9GlSv83hx8LjpDQ6m/5nN/fZ9qX9OxnUJI420Q0CGKGIiEjNUAdJKlRcHiR6aCzPv+fG7T7Mo48OI/OKG7jhhl97XeaDqaPIzf2Ev+zeQkGBm6KiQo51vZTx46fXWpwagyQiIjVFHSSptNjYptx//3M89ti1XHvtPURGRp3R5rHHXil5vmzZXL79NqdWO0ciIiI1SR2kMFLbGRTPUiFpaT1YsqQ7u3YtOOO+RmVt2QJutzI8IiISOlRqREREROotlRoRERER8ZNOsUm1qHSIiIiEI2WQpELGGCZOnFjyesaMGWRmZgKUlA7xfBR3jhYtWoQxBp1yFRGRUKMMUhiprXsQRkXF8Oqri7niikdo2jSezZuhoKD87eXnH+X3v3+OLl0uYe1ae5B2TdOgbxERqS3KIEmFIiIiGTZsPAsXPuv3Mn//+xRGjnyIaN0oUkREQpAySOKXX/ziXsaN68bIkQ9V2Hbjxi/Yu3cbffsO451pt9L56btIaXR2zQdV26VFVBZERKTeUgZJ/NK4cROuumoMixc/V26706dP88ILE/jVr54OUGQiIiI1Txkk8duIERmMH9+ToUN/6bNNfv5RfvhhPRlOEdsDhcdJP7CLaRP/ygUXnHGbiWrRGCQREakt6iCJ35o0iSMt7UbefXcOQ4fe7rVNbGxT3n47r+R1RkYa99wzo8Y7RyIiIrVJHaQwUlsZFc8SI126TKR9+1kkJvq3vWbNoFcv6K3+kYiIhBB1kKRCbo9r9Fu1akV+fr7fy2ZpoLOIiIQgDdIWERERKUMZJKmyadOmsXDhwlLT0tPTmTx5ch1FJCIiUjPUQRIiIiJITk6mqKiI9u3bM3/+fJo1836Toa1bt3L99ddz6tQpTp48yf3338/dd98d4IhFRERqlzpIYaSqw32ioxsyc6YLgCefHMukSS9w663es0AnT57Lk0/+m+joGAoK3PzylxcRHz+c+PiESm9Xl+mLiEiw0hgkKSUpqS/79u3wOT8qKpro6BgACgtPYFmnAxWaiIhIwCiDJCVOnTrF93+fwui4c0lxbvTozfbC49z0w3p+OFHAEwnnc+XUW6q2wdouFeJJV9OJiEglqIMkFBYWcMcdKezevYVextD/7Obltm8T3YDVF/Rm18kT3PrDV1zbtCXnREUHKFoREZHapw6SEB3dkJdecuF2H+bRR4eRecUN3HDDr/1a9pw//pLXLv0f+vUbUentagySiIgEK41BkhKxsU25//7neOONGRQVnfTaZt++7Zw4UQDA0aMHWb9+NW3bXhDIMEVERGqdMkhhpKoZGc9SImlpPViypDu7di1g9OjRZ7T98MNvmDhxIsYYLMtiypRJ3H57cpVjFhERCUbGsqwaXWHv3r2tnJycGl2niIiISG0wxqy1LOuMiqE6xSYiIiJShk6xiVe5ublnnGKLiYlhzZo1dRSRiIhI4KiDVI8ZY3jggQd4+umnAZgxYwZut5vMzEySk5NxuVyl2m/dupWBAweyb98+4uLiePnll2nTpk1dhC4iIlKr1EEKI5W9F2JUVAyvvrqYK654hKZN49m8GQoKfK8nM3MSl146hiFDxvL55yu4/fZHePTR+ZXapi7tFxGRUKAxSPVYREQkw4aNZ+HCZ/1qv2XL1/TqNRCAHj36s3r127UZnoiISJ1RBqme+8Uv7mXcuG6MHPmQzzbFZUd6H85jc0Yag1q24V+H9pGff5R29/2cuMgo/zdYk+VFVD5ERERqiTJI9Vzjxk246qoxLF78XIVtf59wPquPHeaKb9ey+thhEqKiiTAmAFGKiIgEljJIwogRGYwf35OhQ3/pdb5rZlbJ84nOvwUFbv455kJ+eP7TSm1LY5BERCQUKIMkNGkSR1rajbz77pxy2x0+nMfp06cBeOWVJxk69PZAhCciIhJwyiCFkcpmZzxLjHTpMpH27WeRmOh7PYsWZXHXXY9gjOGKK67ghRdeICam6vGKiIgEK5UaERERkXpLpUZERERE/KRTbHKGadOmsXDhwlLT0tPTmTx5ch1FJCIiEljKIIWpiIgIUlJSuOiii0hPTyc/Px+A3bt3M3LkSDp06EDXrl25+uqr+e6770otO3nyZFwuFy6Xi9atW7Nlyxb+85//lGoza9YsOnbsiDGGvLy8gL0vERGRQFAGKYx43jcxOrohM2fatdSmTh3FpEmzSU+fwH33XcfgwWOZM2cBAJs2uVi2bA87d3b2us5Bgx7kiivy+de//lpq/TExP2fq1GFkZKSxejU0bVp6OV3OLyIioUwdpHqgW7dUNm9exxdffExkZBTDh99dMq9jx5Ryl+3VayAuV9YZ0zt16lHTYYqIiAQNdZDC3KlTRaxZ8x4XXzyEH35YT+fOvby2Ky4n4o3bfYgme7d5bRN9YDcXTb6WFmXLjdRkSZFiKi0iIiIBojFIYaqwsIA77kjhrrt606pVO66+elxdhyQiIhIylEEKU9HRDXnpJVepaYmJSaxatchre89yImVtcmVx5PUZuJ5cesa8wpGJrJ/2Nk2bxpearjFIIiISytRBCiOenRLPu2QX69dvAG+88SgbN77InXfeCUB2djb5+fn067gbTs0AACAASURBVNev3HV/9JH3Tk+DBvDzn0N8/JnzREREQpVOsdUjxhjefPNNPvzwQzp06EBSUhKZmZkkJCT4XCY1NZX09HSWL19OmzZteP/99wF47rnnaNOmDdu3b6dbt27ccccdgXobIiIitU6lRkRERKTeUqkRERERET9pDJKQm5vL6NGjS02LiYlhzZo1dRSRiIhI3VIGqR7wLDtyzTXXcOjQoVLzk5OTS0qLFJcX+fbbbxk2bFgdRSwiIlK3lEEKI77uo+hZduTJJ8cyadIL3Hqr78KzvsqLlKVL+UVEJFwpg1TPJCX1Zd++HeW26dVrII0anR2giERERIKPMkjVEWQplJRD3qdHFBaQkpHGKcti5tavGR13brmlRaD88iIlaqOcSKhR+RMRkbCkDlI9UHD6NKnf5vBj4XFSGp1N/7Ob13VIIiIiQU0dpOoIsuyBK8v79OihsTz/nhu3+zCPPjqMzCtu4IYbfl3uusorL1IsyBJoIiIiNUYdpDDiq8PyU9mRppx33nNce+21PPPMPURFRZW7Pl/lRURERMKdBmnXMz169KB79+4sWLDAZxtf5UVERETqC5UaERERkXpLpUZERERE/KQxSPWUyouIiIj4pg5SGImIiCA5OZmioiK6dOnCvHnzaNSoEbt37yYjI4Ps7GxiYmJITExk5syZuFyuctcD0K5dO5YsWRLItyEiIlLnNAYpjDRsGMt777kBmDp1FJ079yI9fQL33XcZgwePZfjwuwHYtMlFfv5RunVL9bqeoUN/Wk8xXc0mIiLhyNcYJGWQwkzxna+vztvJV64sjr4/j6Z7tvL4igWwwr5yLaWCdRTfebuU2rprdpDdS0pERAQ0SDssFVkWHx09QNcGjfnm+DFSGsZWavnjp0/T/7u1DNr4Oe8czqulKEVERIKXMkhhpLCwgN5uuyBbt4E30+2ep1myZDb7dv+A695n/V7PgrydxMcnsHPn9zzwwACY+jajRnWorbBFRESCjjpIYSQ6uiEvvVR64HViYhKrVi2q1Hri4xMASEg4n5SUNDZt+gJQB0lEROoPdZDCyE8lRX7Sr98A3njjUTZufJE777wTgOzsbPLz8+nXr98Z6zh48CCNGjUiJiaGvLw8Nm9ezTPPPBSA6EVERIKHxiCFOWMMb775Jh9++CEdOnQgKSmJzMxMEhISvLb/5ptv6N27N927d6d///48/PDDdO3aNcBRi4iI1C1d5i8iIiL1lkqNiIiIiPhJHaQQFxERQUpKChdddBHp6enk5+cDsHv3bkaOHEmHDh3o2rUrV199Nd99913Jcrm5uaSkpJCSkkLHjh1p2LAhjRs3JiUlhQYNGvDWW2/V1VsSERGpczrFFuJiY2Nxu+27Xo8aNYpevXoxYcIELrvsMsaOHcvdd9t3z3a5XBw9epTUVO93zy524MABOnbsyPbt22nUqFGtxy8iIlKXdCfteqBVq1RWrlwHfEx+fhQXXni3x42q7ftnl3fj6rQ0WLRoEUOHDlXnSERE6jV1kEJdQQGkpVFkWWxwfcXAs+M4mfMBPy88fma5kIo0gwVffskDbdpUv/iaSoiIiEgI0xikEFdw+jQpOTn0XruWNlExjI5rXeV17TpxgtxjxxjcvHkNRigiIhJ6lEEKcQ0bN8bljEHKyoKvgci1y1n9jydwzcyq1Lq+/PJPXJecTNTf/lbjcYqIiIQSZZDCUM+eAygsPMHSpS+WTNuwIRuXa2W5y7322mvcfPPNtR2eiIhI0FMGKYz8NGzIsHz5m2RkZDBu3HQaNGhAYmIiM2fOpFMn78tu2bKFbdu2eS0/IiIiUt/oMn8RERGpt3QnbRERERE/6RRbPZKbm8vo0aNLTYuJiWHNmjV1FJGIiEhwUgYphFS1rEix5ORkXC4XV111FSdPnuTEiRNccskl1PRpVhERkVCnDlIIadiwIS6Xi/Xr1xMdHc3s2bOxLIvrrruOtLQ05szZzJ///DXXX/8Hli3bQ1bWmfdr/Pe//83q1atZt24d69evJzs7m5Ury7+6TUREpL7RKbYQlZqayrp16/j444+Jiori7rt/KivSsWOKz+WMMRw/fpzCwkIsy+LkyZO0atUqMEGLiIiECHWQgoU/pT08yoq899VXDImLY/0HH9Dr+HFISyPlkI/lmv30tC/Qf+9ezj37bCzgvvPOo8s991QtZpUTERGRMKVTbCHEs6xIu5gYxrWufFmRTQUFfJOfz/a+fdnRty8rDh5k1SFfPSsREZH6SRmkYOFHNqZhbGxJWZFiScuXs+iJJyArC5ePVXgmp9586ikuPX6c2ClTABj6u9/xWYMGXPHQQ1WLW0REJAwpgxTiBgwYwIkTJ3jxRf/KirRr146VK1dSVFTEyZMnWblyJV26dAlUuCIiIiFBGaQQZ4zhzTftsiLTp1dcVmTEiBGsWLGC5ORkjDEMGTKEa665JvCBi4iIBDGVGhEREZF6S6VGRERERPykU2xhSmVFREREqk4ZpCBWndIixWVFXC4XrVu3ZsuWLbRs2bJUm3HjxtG9e3e6devGiBEjcJe5Qk5ERKS+UgcpiFVUWmTz5s18/fXX/OEPf2DPnp9Ki5QtMfLggw8yf/78M9b/7LPP8uWXX7Ju3TratWvHrFmzAvTOREREgps6SCEiNTWVTZs2lSotUiwlJYXU1FSfyw4cOJCzzz77jOlNmjQBwLIsCgoKMMbUfOAiIiIhSGOQglHxnR0rKC1S1hmlRjxKjHDoEGzbdsZyv9ywgXcPHKBro0Y8nZwM771Xeh0qJyIiIvWQMkhBrCZKi1Tk/114ITv79qVL48a8vm9fja9fREQkFCmDFIycrE1FpUXKKltqpFSyKCsLZsyApUvPWC4CuGnlSp566il+6WW+iIhIfaMMUojxVlokOzublSu9lxbxxbIsNm3aVPL8X//6FxdeeGGNxioiIhKqlEEKMZUtLQL2AO8NGzbgdrtp06YNc+bMYdCgQYwdO5YjR45gWRbdu3fnL3/5S2DfjIiISJBSqRERERGpt1RqRERERMRPOsUWJlRaREREpOYogxQijDFMnDix5PWMGTPIzMwsee1ZWsTlcrFkyRIaNWpEjx496NatG++++24dRC0iIhKa1EEKETExMSxevJi8vDy/2k+dOpUbb7yRL774ggULFvCrX/2qliMUEREJH+oghYjIyEjGjx/Ps88+61d7YwxHjhwB4PDhwyQkJNRmeCIiImFFV7EFCy+lQzzFfvIJO/v2pVtODl/27s2Lu3bhPnWKzMREr+13nTjBVbm5HDx5kmOnT/NRt2708lKP7QwqLSIiIvWIrmILA00iIxnTqhXP7dhRYdvX9u7ltlat2N63L+9edBGjN2zgdA13hkVERMKVrmILFhVlbmJjISuLjAMH6NmzJ78cMwYsCzwGanuak5TEsmXLoG1b+gLHzz+fvIULOeecc2o6chERkbCjDFKIiYuL48Ybb2TOnDnltmvXrh3Lly8H4JtvvuH48eO0bNkyECGKiIiEPHWQQtDEiRMrvJrt6aef5sUXX6R79+7cfPPNzJ07F2NMgCIUEREJbRqkLSIiIvWWBmmLiIiI+EmDtEPctGnTWLhwYalp6enpTJ48uY4iEhERCX3KIAWxisqLAEyePLlUiZFHH32UV155haSkJG655ZYARywiIhIelEEKYsXlRR555BHi4+MB2LLF9x0BzjtvI08++SSrV6+mefPm7N27N2CxioiIhBNlkIJYZcuLvPjii9x77700b94cQPc8EhERqSJlkOpSBeVFKCjg3nfeoVtODg+tXAm7dtH62ClSXFlem8/cvh4aNuTnEydyyrLITExkyLp1NR62iIhIuFMHKch5lhdpeFb5Cb8iy2JjQQFZ3buz/cQJUl0u1h86RLNmzQIUrYiISHhQB6kuVaG8yO4fLFy3ZXpt3mbB3Vx66aVE3XYb7YELBg5k48aN9OnTp6YjFxERCWvqIIUAz/Iit99+u88zc8eP/4LXXnuN2267jby8PL777jvOP//8gMYqIiISDjRIO0T4U15k8ODBtGjRgq5du9K/f3+eeuopWrRoEaAIRUREwodKjYiIiEi9pVIjIiIiIn7SGKQQpPIiIiIitUsdpCASERFBcnIyRUVFdOnShXnz5tGoUSN2795NRkYG2dnZxMTEkJiYyBtvvEHnzp29rufHH3/kjjvuYNu2bRhjePfdd0lMTAzsmxEREQlhGoMURGJjY3G73QCMGjWKXr16MWHCBC677DL69h3L8OF3A7Bpk4v8/KN065Zaavniq9vS0tKYPHkygwYNwu12c9ZZZ9GoUaNAvhUREZGQ4GsMkjJIQSo1NZV169bx8ccfExUVVdI5AujYMcXncl9//TVFRUUMGjQIsDtdIiIiUjnqIFVVRWVCqqKgANLSKLIs3vvqK4bExbH+gw/odfw4KRl+bK8ZfJeXR7Ndu7i+ZUt+OH6cK5s1Y/r55xNhTOViqegmliIiImFMV7EFkYLTp0nJyaH32rW0i4lhXOvWlV5HkWXxyeHDzDj/fLJ79uT748eZu3t3LUQrIiISvpRBqqpayLA0jI3F5YxBKpa0fDmLnngC1+8q3l5aGrT57DN6PPww5zvx/WL+fD777DPGvfBCjccrIiISrpRBCnIDBgzgxIkTbNz4ImlpdieoceNsjFlZ8rr4AdCnTx8OHjzIvn37AFixYgVdu3atk9hFRERClTpIQc4Yw5tvvsmHH35Ihw4dSEpKIjMzk4SEBK/tIyIimDFjBgMHDiQ5ORnLsrjzzjsDHLWIiEho02X+IiIiUm+p1IiIiIiInzRIO0Tl5uYyevToUtNiYmJYs2ZNHUUkIiISPpRBCkLGGCZOnFjyesaMGWRmZpZqk5ycjMvlwuVysWbNGi644AL279/PJZdcwpYtWwIbsIiISJhRBikIxcTEsHjxYh555BHi4+PZvNm+h6SvOwu89dYcCgqas2nTJhYsWMBvfvMbXn/99YDGLCIiEk6UQQpCkZGRjB8/nmeffdav9qtXv83gwWMBGDFiBMuXL6emB9+LiIjUJ8ogVUVtlBnxVFDAve+8Q7ecHB5auZKE73dx7PQpUlxZXpu7v80m7YUHYGEMkUDTY8fYf/nlxEdFVX7bKjEiIiKiDFKwahIZyZhWrXhux46KG3tJFlWy8pqIiIh4UAapKmo7yxIbC1lZZBw4QM+ePek/eAyWZeG6LdN78wcHk3VbJkn39qWoqIjDrVsT9+mnUNkCtSIiIgKogxTU4uLiuPHGG1mwYA633367zzN7t902nNzceUBfFi1axIABAzDqHImIiFSZTrEFuYkTJ5KXl1dum3HjxrF//346duzIM888w/Tp0wMUnYiISHhSBikIud3ukuetWrUiPz+/3PYNGjRg4cKFtR2WiIhIvaEMkoiIiEgZyiCFkGnTpp2RKUpPT2fy5Ml1FJGIiEh4UgcpCBljeOCBB3j66acBu9SI2+0mMzPTa2do9uzZvPDCC0RERBAbG8vf/vY3unbtGuiwRUREwoY6SEHIs9TI+vUVlxpp2/YWnn/+btLSYMmSJTzwwAMsW7YskCGLiIiEFXWQalsV7rodefIk443h2V69eLB5ez7Zu63cO2mXaAbH9u7F7N5deru6O7aIiEilqIMUpO5NSKBbTg7jm7T1q/2LeTuY/e12Ci2LFd261XJ0IiIi4U0dpNpWlexNbCxNPv2UMY8/zhPbo4iJaUhBgdvnnbQB+gAPpsGrr77K1PffZ968eVUMWERERHSZfxDLyMjg3XfncPz4Mb+XGTlyJG+99VYtRiUiIhL+lEEKYnFxcYwZU3GpkY0bN9KpUycA3nnnnZLnIiIiUjXqIAW5iRMnMmvWrHLbzJo1i48++oioqCiaN2+u02siIiLVZCzLqtEV9u7d28rJyanRdYqIiIjUBmPMWsuyepedrjFIIiIiImWog1RHIiIiSElJ4aKLLiI9Pb2kIO3u3bsZOXIkHTp0oGvXrlx99dV89913gF1qJCUlpdSjU6dONGvWjGHDhpVa/w8//MAll1xCp06duOmmmygsLAz4exQREQlV6iDVkYYNG+JyuVi/fj3R0dHMnj0by7K47rrrSEtLY/PmzXz99df84Q9/YM+ePQBMnjwZl8tV6jF79mzmz59/xvp/85vfMGHCBDZu3Ejz5s2ZM2dOoN+iiIhIyNIg7SCQmprKunXr+Pjjj4mKiuLCC+/2uH1SCuD7dkoREQPZvDmL/ft/mmZZFitWrODVV18FYOzYsWRmZnLPPffU1lsQEREJK+ogVUcVyoiUKCiAtDSKLIv3vvqKIXFxrP/gA3odP05KRuXW63YfosnebSXx7D95kmbHjhF55ZUAtDl+nB25uVWPVUREpJ7RKbY6UnD6NCk5OfReu5Z2MTGMa926xtbt7cpEY0yNrV9ERCTcKYNUHdUoAtswNhaX211qWtLy5Sx64glcv6vceje5sjjy+gzIWgpAvGVxqGVLij76iMjISLb/5z8kZGZWOVYREZH6RhmkIDJgwABOnDjB0qUvlkzbsCEbl2tlpdZjjKF///4sWrQIgHnz5nHttdfWaKwiIiLhTDeKrCOxsbG4y2SQAHbu3ElGRgZr166lQYMGJCYmMnPmTJ/lQ1JTU9mwYQNut5sWLVowZ84cBg8ezPfff8/IkSM5cOAAPXr04OWXXyYmJqa235aIiEhI8XWjSHWQREREpN7SnbRFRERE/KRB2iEgNzeX0aNHl5oWExPDmjVr6igiERGR8KYOUhAxxvDAAw/w9NNPAzBjxgzcbjeZmZm4XK4z2k+YMIGPP/4YgPz8fPbu3cuhQ4cCGrOIiEg4UgcpiMTExLB48WKuuOIRmjaNZ/Nm+36Svu4mcO21z1J8cdrixc/jdn8RsFhFRETCmcYgBZHIyEjGjx/PwoXPVnrZFSte4+abb66FqEREROofZZCqojolRspTUMC977zDRf/NYdqXK0nYv4tjp0+R4soqd7EfC4+Tt/ELBkydCtOmVbydatzgUkREpD5QBinINImMZGRcK/6Wt8PvZRYf2svwpvFEqJyIiIhIjVAGqSpqKwMTGwtZWVy+5ADjx/dk6JAxWJaF67bMchd75c4e/O+jL8B9l9VOXCIiIvWMMkhBqEmTONLSbuTdd+dU2PbHH7/l6NGDJCX1DUBkIiIi9YMySEEoLQ26dJlI+/azSEwsf8hTZuZr3HbbSPr31+k1ERGRmqJSIyIiIlJvqdSIiIiIiJ90ii0ETJs2jYULF5aalp6ezuTJk+soIhERkfCmU2x1ICIiguTkZIqKiujSpQvz5s2jUaNG7N69m4yMDLKzs4mJiSExMZGZM2fSuXNnr+sZMmQIn332GZdffjlLly4tmT5q1ChycnKIiori4osv5q9//StRUVGBensiIiIhQ6fYgkjDhg1xuVysX7+e6OhoZs+ejWVZDBx4HQkJacyZs5k///lrrr/+DyxbtoesLLw+Bg16kIcems/+/aXvPDBq1Cg2bNhAbm4uBQUFvPTSS3XwLkVEREKXTrHVsdTUVNatW8fHH39MZGQUw4ffXTKvY8eUcpft1WsgLi932b766qtLnl988cVs3769xuIVERGpD9RB8qa2SokUKyiAtDSKLIv3vvqKIXFxrP/gA35++DgpGZXbttt9iCZ7t9nLNSs97+Tp08z/4gv+1KEDrF5d/opUfkRERKSETrHVgYLTp0nJyaH32rW0i4lhXOvWtbKdX23cyBVNm5LarFnFjUVERKSEMkje1HI2pWFsLC63u9S0pOXLmfPAE7hmVm7bm1xZHHl9Bq4nl5ZKfD3xxBPsa9aMvy5eDGepHywiIlIZ+uYMEgMGDKCw8ARLl75YMm3DhmxcrpWVXtdLL73E+++/z2uvvcZZ6hyJiIhUmi7zrwOxsbG4y2SQAHbu3ElGRgZr166lQYMGJZf5d+rUyet6UlNT2bBhA263mxYtWjBnzhwGDx5MZGQkP/vZzzj77LMBuP7663n88cdr9T2JiIiEIl+X+auDJCIiIvWW7oMkIiIi4icN0g5yubm5jB49utS0mJgY1qxZU0cRiYiIhD91kOpQTZUcAThy5AhdunThuuuuY9asWQF8FyIiIuFHHaQ6VFxyJCsLpk4dxaRJs0lPn8B9913H4MFjmTNnAQCbNrlYtmwPO3f67iA9//wU+vXrF6DIRUREwpvGIAWJbt1S2bFjE1984b3kSLduqT6X/fbbtRw8uIerrroqEKGKiIiEPWWQKqsmy5A4JUcuOmjxf1u+YuDZcZzM+YCfF/pfcuS0ZfHY5i+Z3e5CcqZPh6NHYf16lQ4RERGpBmWQ6lBxyZH+362lTVQMo+MqX3Lkpf07GdQkjjbRDWohQhERkfpJGaTKqsHMTHHJkeJVfg1Erl3O6n/4X3Lkg6mjyM39hL/s3kJRkZvCwkJiL72U6TUWpYiISP2jDlKQ6dlzAC+99ChLl77IsGF3AnbJkePH80lJOXMQ9mOPvVLyfMuWueTk5DB9urpHIiIi1aEOUhAoPazJsHz5m2RkZDBu3PQyJUfKX8/cubUXo4iISH2iUiMiIiJSb6nUiIiIiIifdIotRKjkiIiISOAog1QHjDFMnDix5PWMGTPIzMz02f6ZZ57hpptu4vTp07Ro0YK3334bl8ulzpGIiEgtUQYpAMreGSAqKoZXX13MFVc8QtOm8WzebN8z0tcdBIzpwTPP5NCgQSPefvsv3HbbQ/z2t6+f0a4m72EpIiJSnymDVAciIiIZNmw8Cxc+61f7Hj3606BBIwC6dr2Uffu212Z4IiIi9Z4ySMVqMf2Scqj064jCAqZ89g6Xf5vDtC9XkrB/F8dOnyLFlVXhul7ZvpFfREWTkpHm980kRUREpHKUQaojTSIiGRnXir/l7fB7mdcP7sFVcJT7W7atxchEREREGaRitVjctWxi6NTQWFwzs7j8yAHGj+/J0CFjsCwL122ZPtexdu1HPPfc/cx8eRPfND+n1mIVERERdZACouzZu4iI4mlxfPrpjSxYMIfbb7/d51m+L774gj//+S4++mgZnTqpcyQiIlLbdIqtjk2cOJG8vLxy2zz44IO43W7S09NJSUlh+PDhAYpORESkflIGqQ643e6S561atSI/P7/c9h999FFthyQiIiIelEESERERKUMZpCAybdo0Fi5cWGpaeno6kydPrqOIRERE6idlkAKsvDIjkydPxuVylXqkpqbSs2dPIiMjWbRoUR1FLSIiUr8og1SLvN05oLJlRnbvbse9987l9ddn8NVXEB/ve3sqNSIiIlIzlEEKsMqWGWndOpEOHbpx1ln6qERERAJFGSRvaigVU7bECFS+zIjKiYiIiASe0hJ1oCplRkRERCRwlEHypobKjnhLClWlzIiIiIgEljpItcjbmbrKlhkpNncuJCVpILaIiEgg6BRbHfKnzEh2djZt2rRh4cKF3HXXXSQlJQUoOhERkfpLGaQAq2yZkT59+rB9+/baDktEREQ8KIMkIiIiUoYySEFCZUZERESChzJItaS8kiLenHfeeezY8dNl//fdd586RyIiInVEGSQ/VfbK/8qWFNmwAS6//Cb+939nVXmbusJNRESkZtSPDlIN9By83RW7PNGnTnInhlXjezHl3PZ8sncbm68aXe04REREpPbpFFstuiM+gYUH93D4VJFf7Vet+ifjxnXjt78dwd6922o5OhEREfGlfmSQauDO2D5Kpfl0amgs3z//KWl/f5wnIqOIiWkIBW6f7fv2vYYBA24mOjqGJUtmM336WJ55ZkX1ghYREZEqUQaplo0YkcG7787h+PFj5bZr2rQF0dExAPzP/9zJd9+tDUR4IiIi4kX9yCDVgMoOY6psSZFdu3Zx7rnnAvDmm0u46KIuGnQtIiJSR9RBCoCJEycya9ascts899xzLFmyhMjISOLi4pg7d25gghMREZEzGMuyanSFvXv3tnJycmp0nSIiIiK1wRiz1rKs3mWnawySiIiISBk6xRZgKikiIiIS/NRBqkEREREkJydTVFREly5dmDdvHo0aNWL37t1kZGSQnZ1NTEwMiYmJzJw5k86dO3tdz29+8xveeecdAKZMmcJNN90UyLchIiJS76mDVIHK3EIpOrohM2e6AJg6dRSTJs0mPX0C9913HYMHj2XOnAUAbNrkYtmyPezceWYH6T//eYflyz/nT39yUVh4goyMfsTGDqVx4yYVbl9XvYmIiNSM0OwgBbAnUJkSIxGFBaRkpAFwdd5OvnJlcfT9eTTds5XHVyyAFXYHKaWcdSy49H/o3r0fERGRNGwYSYcO3fnvf5fRv/+NVX8TIiIiUikapF0LiiyLj44eoGuDxnxz/BgpDWP9XrZDh+6sWfMex4/nc/hwHi7Xx+zbp7IjIiIigRSaGaQaKB3ir8qUGCkYGEFvt51y6jbwZrrd8zRLlsxm3+4fcN37rF/r6AN8+2029913Gc2ataRr176cdVZofkwiIiKhSt+8NSg6uiEvveQqNS0xMYlVqxZVaj233jqZW2+1r2r7/e9voU2bTjUWo4iIiFRMHaQKVGa400/lRX7Sr98A3njjUTZufJE777wTgOzsbPLz8+nXr98Z6zh16hSHDh2iRYsWrFu3jj171jFp0lVE6pMSEREJGH3t1jJjDG+++SYZGRlMnz6dBg0alFzm783JkydJTU0FoEmTJrz88stEqnckIiISUCo1IiIiIvWWr1IjNd5BMsbsA7YC8UBeja5cKqJ9Hnja54Gl/R142ueBpf0deD+zLKtl2Yk13kEqWbExOd56ZGIzxiQD88tMPmFZ1iXVWKf2eYBpnweW9nfgaZ8HlvZ38NDgljpiWVYu5d8zUkREROqIbhQpIiIiUkZtdpD+VovrFu+0zwNP+zywtL8DT/s8sLS/g0StjUESERERCVU6xSYiIiJSRrU6SMaY3rL9uwAABFpJREFUOGPMh8aYjc6/zX20G+u02WiMGesxPcsY860xxuU8zqlOPOHMGDPE2VebjDEPe5kfY4x53Zm/xhiT6DHvEWf6t8aYwYGMO1RVdX8bYxKNMQUex/TsQMceqvzY51cYYz43xhQZY0aUmef1b4z4Vs39fcrjGF8SuKhDmx/7/AFjzNfGmHXGmOXGmJ95zNMxHmiWZVX5Afwf8LDz/GHgj17axAHfO/82d543d+ZlAb2rE0N9eAARwGbgfCAa+BLoWqbNr4DZzvORwOvO865O+xigvbOeiLp+T8H8qOb+TgTW1/V7CLWHn/s8EegG/AMY4THd598YPWp+fzvz3HX9HkLt4ec+7w80cp7f4/F3Rcd4HTyqe4rtWmCe83we8AsvbQYDH1qWdcCyrIPAh8CQam63vrkY2GRZ1veWZRUCC7D3vSfPz2IRMNAYY5zpCyzLOmFZ1g/AJmd94lt19rdUTYX73LKsLZZlrQNOl1lWf2Mqrzr7W6rGn33+sWVZ+c7Lz4A2znMd43Wguh2kVpZl7QJw/vV2iuw8YJvH6+3OtGL/z0nTTtEXjE8V7cNSbSzLKgIOAy38XFZKq87+BmhvjPnCGLPSGJNa28GGieocpzrGK6+6+6yBMSbHGPOZMcbbD2M5U2X3+TjgvSouKzWgwhtFGmM+Alp7mTXZz2146/QUXzo3yrKsHcaYs4F/AqOx07lSWnn7sKI2/iwrpVVnf+8C2lmWtd8Y0wt4yxiTZFnWkZoOMsxU5zjVMV551d1n7SzL2mmMOR9YYYzJtSxrcw3FFq783ufGmFuB3kC/yi4rNafCDJJlWVdalnWRl8fbwB5jzLkAzr97vaxiO9DW43UbYKez7h3Ov0eBV9GpH1987kNvbYwxkUBT4ICfy0ppVd7fzqnM/QCWZa3FHnPQudYjDn3VOU51jFdetfaZZVnFf8O/xx5L2qMmgwtTfu1zY8yV2AmI4ZZlnajMslKzqnuKbQlQPJp+LPC2lzbvA1cZY5o7V7ldBbxvjIk0xsQDGGOigGHA+mrGE66ygU7GmPbGmGjsQcFlrxzx/CxGACssy7Kc6SOdq67aA52A/wYo7lBV5f1tjGlpjIkAcH5dd8IeUCnl82ef++L1b0wtxRkuqry/nf0c4zyPB34OfF1rkYaPCve5MaYH8FfszpFnwkHHeF2ozghv7DEXy4GNzr9xzvTewEse7W7HHhy8CfilM60xsBZYB3wF/AldXVXevr4a+A47IzHZmfY77P9IAA2Ahc4+/i9wvseyk53lvgWG1vV7CYVHVfc3cINzPH8JfA5cU9fvJVQefuzzPti/pI/x/9u5YxuEoRiKoncu1mFDaoZAijIERXagSRGZJg0gpHMkly6+ZX29yrVV66H37Y9Rn5l3damWfceX6vrrt/xLnZj5vXpWj71uh147/uVySRsAYHBJGwBgEJAAAAYBCQBgEJAAAAYBCQBgEJAAAAYBCQBgEJAAAIYX1kgAUwdDX+cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x417.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[         mean         std\n",
      "N_1     0.464   0.0162672\n",
      "N_2  0.467333   0.0158591\n",
      "N_3  0.449667   0.0137635\n",
      "N_4  0.471667  0.00975534\n",
      "N_5  0.432667  0.00988602\n",
      "N_6     0.466  0.00946103\n",
      "N_7  0.455333   0.0107621\n",
      "N_8  0.468333    0.010025\n",
      "N_9     0.455   0.0104907] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 21:05:41.332963 33.33% mp_sfi done after 26.8 minutes. Remaining 53.6 minutes.\r"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[         mean         std\n",
      "N_1     0.464   0.0162672\n",
      "N_2  0.467333   0.0158591\n",
      "N_3  0.449667   0.0137635\n",
      "N_4  0.471667  0.00975534\n",
      "N_5  0.432667  0.00988602\n",
      "N_6     0.466  0.00946103\n",
      "N_7  0.455333   0.0107621\n",
      "N_8  0.468333    0.010025\n",
      "N_9     0.455   0.0104907,            mean         std\n",
      "PC_12  0.470667    0.012182\n",
      "PC_13  0.450333  0.00996048\n",
      "I_0       0.512   0.0270933\n",
      "I_3    0.447667   0.0102312\n",
      "R_0       0.555   0.0222972\n",
      "R_1       0.475   0.0161881\n",
      "R_2    0.484667   0.0163449\n",
      "R_3    0.481333   0.0138098\n",
      "R_4    0.473667   0.0113573\n",
      "N_0    0.452667   0.0090652] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 21:05:46.939736 66.67% mp_sfi done after 26.9 minutes. Remaining 13.45 minutes.\r"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[         mean         std\n",
      "N_1     0.464   0.0162672\n",
      "N_2  0.467333   0.0158591\n",
      "N_3  0.449667   0.0137635\n",
      "N_4  0.471667  0.00975534\n",
      "N_5  0.432667  0.00988602\n",
      "N_6     0.466  0.00946103\n",
      "N_7  0.455333   0.0107621\n",
      "N_8  0.468333    0.010025\n",
      "N_9     0.455   0.0104907,            mean         std\n",
      "PC_12  0.470667    0.012182\n",
      "PC_13  0.450333  0.00996048\n",
      "I_0       0.512   0.0270933\n",
      "I_3    0.447667   0.0102312\n",
      "R_0       0.555   0.0222972\n",
      "R_1       0.475   0.0161881\n",
      "R_2    0.484667   0.0163449\n",
      "R_3    0.481333   0.0138098\n",
      "R_4    0.473667   0.0113573\n",
      "N_0    0.452667   0.0090652,            mean         std\n",
      "PC_1   0.467667   0.0188565\n",
      "PC_2   0.512667   0.0170932\n",
      "PC_4   0.439667   0.0113573\n",
      "PC_5      0.462   0.0150422\n",
      "PC_6      0.446   0.0103688\n",
      "PC_7   0.463667  0.00938616\n",
      "PC_8   0.455333   0.0113058\n",
      "PC_9   0.467667   0.0155924\n",
      "PC_10  0.448667   0.0100576\n",
      "PC_11      0.47   0.0114212] this out\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2020-06-03 21:07:17.541403 100.0% mp_sfi done after 28.41 minutes. Remaining 0.0 minutes.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x417.6 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# dropped important labels while using remaining labels to run feat importance.\n",
    "\n",
    "rs.feat_imp_analysis(X = X1, \n",
    "                     y = y, \n",
    "                     sample_weight=y['w'],\n",
    "                     methods = ['MDI', 'MDA', 'SFI'],\n",
    "                     events = None,\n",
    "                     pct_embargo = 0.01,\n",
    "                     n_splits = 10,\n",
    "                     min_weight_fraction_leaf = 0.0,\n",
    "                     n_jobs = 3,\n",
    "                     scoring = \"accuracy\",\n",
    "                     output_path = None,\n",
    "                     mask_effect = False) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Removal of key features\n",
    "\n",
    "After we removed the below important features/ PC: \n",
    "\n",
    "1. PC_0, PC_3\n",
    "2. I_4, I_1, I_2\n",
    "\n",
    "**MDI Summary:**\n",
    "\n",
    "PC: PC_2, PC_1 are still considered important (Improvement in ranking).\n",
    "\n",
    "All informative and redundant features were ranked above noise features, plus all these features (Including PC_2 and PC_1) were considered important.\n",
    "\n",
    "**MDA Summary:**\n",
    "\n",
    "PC: PC_2, PC_1 were found above first noise features (N_4).\n",
    "\n",
    "Features:  I_3, R_2, R_0, I_0, R_4 were still found above first noise features (N_4).\n",
    "\n",
    "All informative features (including PC_2 and PC_1) were ranked above first noise features. Significant improvement in overall ranking outcome. (Reduction in substitution effects)\n",
    "\n",
    "**SFI Summary:** \n",
    "\n",
    "PC: only PC_2 was ranked before first noise feature (N_4) while PC_1 was still ranked below N_8 (lower than N_4).\n",
    "\n",
    "Features: R_0, R_2, R_3, R_3, R_4 was the only one that was ranked below first noise feature (N_4), while the remaining informative and redundant features was still above the first noise feature (N_4).\n",
    "\n",
    "I_3 still remained only one that was ranked below first noise feature (N_4), since SFI derive performance via OOS (Similar to MDA). Hence it can conclude all features are unimportant.\n",
    "\n",
    "Overall, SFI has the least change/ improvement in terms of feature importance ranking, since SFI does not suffer from substitution effects since individual features are considered one at a time.\n",
    "\n",
    "### Conclusion\n",
    "\n",
    "After we removed the common important features among all 3 methods, there is a significant ranking improvement in informative features and principle components that were considered important.\n",
    "\n",
    "As we removed the important labels, there was also a reduction in substitution effect across the samples. Hence reflecting an improvement in ranking outcome for informative features and key principle components.\n",
    "\n",
    "With reference to SFI, the improvement seems limited as both I_3 and PC_1 were still considered \"unimportant\", after removing common \"important\" features. Both MDA and SFI based performance on OOS, therefore first principle features were able to be ranked at the top and important principle component can be considered \"unimportant\" (Below Noise features).\n",
    "\n",
    "At the same time, overall OOB score and OOS score also reduced (This may mean in reduction in overall bias), variance on each features does reflect an increase (Bias vs Variance trade-off).\n",
    "\n",
    "In short, whenever we believed that features collection are suffering from high substitution effects. Remove the common \"important\" labels may improve overall reliability of feature importance ranking (Bias reduction), however SFI on the other hand may not experience much improvement since this method is immuned substitution effects."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Parallel vs Stacked features analysis\n",
    "\n",
    "As seen above on the amount of time to run all the codes (even with parallelization).\n",
    "\n",
    "> Reliable and efficient research result is a combination of 4 key factors:\n",
    "> 1. your cognitive abilities\n",
    "> 2. your curiosity\n",
    "> 3. your data samples\n",
    "> 4. your tools\n",
    ">\n",
    "> When it comes to efficiency, your tools probably takes the cake.\n",
    ">\n",
    "> &mdash; Undefeated's first principle of quantitative research\n",
    "\n",
    "I will be skipping some exercises since my machine cannot handle such workload, you may refer to mlfinlab answers. \n",
    "\n",
    "It seems correct with my understanding.\n",
    "\n",
    "Running parallel features analysis will give a big boost to speed, at the same time an increase in OOB and OOS score (Due to substitution effect, especially for large data set even with sample weight balanced) as compared to stacked feature analysis.\n",
    "\n",
    "Since such ranking are derived from either OOS or OOB performance evaluation, if the score is unreliable (bias). It would be best to use stacked features.\n",
    "\n",
    "**Note**\n",
    "\n",
    "If you intend to run parallel feature analysis, only use mulitprocessing for parent process. Otherwise it will run into error, since daemon process cannot fork from child."
   ]
  }
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