docs/tutorials/regression_penalty.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Penalties in DLT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook continues to discuss regression problems with DLT and covers various penalties:\n",
    "\n",
    "1. `fixed-ridge`\n",
    "2. `auto-ridge`\n",
    "3. `lasso`\n",
    "\n",
    "Generally speaking, regression coefficients are more robust under full Bayesian sampling and estimation.  The default setting `estimator='stan-mcmc'` will be used in this tutorial. Besides, a fixed and small smoothing parameters are used such as `level_sm_input=0.01` and `slope_sm_input=0.01` to facilitate  high dimensional regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-28T21:49:43.395926Z",
     "start_time": "2022-04-28T21:49:40.870237Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import orbit\n",
    "from orbit.utils.dataset import load_iclaims\n",
    "from orbit.models import DLT\n",
    "from orbit.diagnostics.plot import plot_predicted_data\n",
    "from orbit.constants.palette import OrbitPalette"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-28T21:49:43.400898Z",
     "start_time": "2022-04-28T21:49:43.398300Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1.4.6\n"
     ]
    }
   ],
   "source": [
    "print(orbit.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression on Simulated Dataset\n",
    "\n",
    "A simulated dataset is used to demonstrate sparse regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:21.684510Z",
     "start_time": "2021-08-20T23:41:21.664310Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from orbit.utils.simulation import make_trend, make_regression\n",
    "from orbit.diagnostics.metrics import mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A few utilities from the package is used to generate simulated data. For details, please refer to the API doc. In brief, the process generates observations $y$ such that\n",
    "\n",
    "$$y_t = l_t + \\sum_p^{P} \\beta_p  x_{t, p}$$  \n",
    "$$\\text{ for } t = 1,2, \\cdots , T$$\n",
    "\n",
    "where\n",
    "\n",
    "$$l_t = l_{t-1} + \\delta_t$$\n",
    "$$\\delta_t \\sim N(0, \\sigma_{\\delta})$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regular Regression\n",
    "\n",
    "To begin with, the setting $P=10$ and $T=100$ is used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:21.692493Z",
     "start_time": "2021-08-20T23:41:21.686578Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,) (50, 10)\n"
     ]
    }
   ],
   "source": [
    "NUM_OF_REGRESSORS = 10\n",
    "SERIES_LEN = 50\n",
    "SEED = 20210101\n",
    "# sample some coefficients\n",
    "COEFS = np.random.default_rng(SEED).uniform(-1, 1, NUM_OF_REGRESSORS)\n",
    "trend = make_trend(SERIES_LEN, rw_loc=0.01, rw_scale=0.1)\n",
    "x, regression, coefs = make_regression(series_len=SERIES_LEN, coefs=COEFS)\n",
    "print(regression.shape, x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:21.698022Z",
     "start_time": "2021-08-20T23:41:21.695046Z"
    }
   },
   "outputs": [],
   "source": [
    "# combine trend and the regression\n",
    "y = trend + regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:21.711159Z",
     "start_time": "2021-08-20T23:41:21.700567Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 12)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_cols = [f\"x{x}\" for x in range(1, NUM_OF_REGRESSORS + 1)]\n",
    "response_col = \"y\"\n",
    "dt_col = \"date\"\n",
    "obs_matrix = np.concatenate([y.reshape(-1, 1), x], axis=1)\n",
    "# make a data frame for orbit inputs\n",
    "df = pd.DataFrame(obs_matrix, columns=[response_col] + x_cols)\n",
    "# make some dummy date stamp\n",
    "dt = pd.date_range(start='2016-01-04', periods=SERIES_LEN, freq=\"1W\")\n",
    "df['date'] = dt\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a peek on the coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:21.717168Z",
     "start_time": "2021-08-20T23:41:21.713028Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.38372743, -0.21084054,  0.5404565 , -0.21864409,  0.85529298,\n",
       "       -0.83838077, -0.54550632,  0.80367924, -0.74643654, -0.26626975])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coefs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, `regression_penalty` is set as `fixed-ridge` i.e.\n",
    "\n",
    "$$\\beta_j ~\\sim \\mathcal{N}(\\mu_j, \\sigma_j^2)$$\n",
    "\n",
    "with a default $\\mu_j = 0$ and $\\sigma_j = 1$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fixed Ridge Penalty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:23.984750Z",
     "start_time": "2021-08-20T23:41:21.719782Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-03-19 23:42:19 - orbit - INFO - Sampling (CmdStanPy) with chains: 4, cores: 8, temperature: 1.000, warmups (per chain): 1000 and samples(per chain): 25.\n"
     ]
    },
    {
     "data": {
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       "model_id": "718785da0d334995a5720cdeeb76c61e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 1 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "model_id": "ba408d1005194e49a8c9fd0d110d269f",
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      },
      "text/plain": [
       "chain 2 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "169e11e6f9614e6792804ed95da9a8de",
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      "text/plain": [
       "chain 3 |          | 00:00 Status"
      ]
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     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "application/vnd.jupyter.widget-view+json": {
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      },
      "text/plain": [
       "chain 4 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                                                                                                                                                                                                                                                                                                                \n",
      "CPU times: user 81.8 ms, sys: 62.7 ms, total: 145 ms\n",
      "Wall time: 2.65 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<orbit.forecaster.full_bayes.FullBayesianForecaster at 0x2a317b0d0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "dlt_fridge = DLT(\n",
    "    response_col=response_col,\n",
    "    date_col=dt_col,\n",
    "    regressor_col=x_cols,\n",
    "    seed=SEED,\n",
    "    # this is default\n",
    "    regression_penalty='fixed_ridge',\n",
    "    # fixing the smoothing parameters to learn regression coefficients more effectively\n",
    "    level_sm_input=0.01,\n",
    "    slope_sm_input=0.01,\n",
    "    num_warmup=4000,\n",
    ")\n",
    "dlt_fridge.fit(df=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:24.279682Z",
     "start_time": "2021-08-20T23:41:23.987572Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 2000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef_fridge = np.quantile(dlt_fridge._posterior_samples['beta'], q=[0.05, 0.5, 0.95], axis=0 )\n",
    "lw=3\n",
    "idx = np.arange(NUM_OF_REGRESSORS)\n",
    "plt.figure(figsize=(20, 8))\n",
    "plt.title(\"Weights of the model\", fontsize=20)\n",
    "plt.plot(idx, coef_fridge[1], color=OrbitPalette.GREEN.value, linewidth=lw,  drawstyle='steps', label='Fixed-Ridge', alpha=0.5, linestyle='--')\n",
    "plt.fill_between(idx, coef_fridge[0], coef_fridge[2], step='pre', alpha=0.3, color=OrbitPalette.GREEN.value)\n",
    "plt.plot(coefs, color=\"black\", linewidth=lw,  drawstyle='steps', label=\"Ground truth\")\n",
    "plt.ylim(1, -1)\n",
    "plt.legend(prop={'size': 20})\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Auto-Ridge Penalty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Users can also set the `regression_penalty` to be `auto-ridge` in case users are not sure what to set for the `regressor_sigma_prior`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of using fixed scale in the coefficients prior, a prior can be assigned to them, i.e.\n",
    "\n",
    "$$ \\sigma_j \\sim \\text{Cauchy}^{+} {(0, \\alpha)} $$\n",
    "\n",
    "This can be done by setting `regression_penalty=\"auto_ridge\"` with the argument `auto_ridge_scale` (default of `0.5`) set the prior $\\alpha$. A higher `adapt_delta` is recommend to reduce divergence.  Check [here](https://mc-stan.org/rstanarm/reference/adapt_delta.html) for details of `adapt_delta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:29.092925Z",
     "start_time": "2021-08-20T23:41:24.281661Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-03-19 23:42:23 - orbit - INFO - Sampling (CmdStanPy) with chains: 4, cores: 8, temperature: 1.000, warmups (per chain): 1000 and samples(per chain): 25.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "405a776e3216444689757be24cd845fc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 1 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b240ceeab056426ea5dbf1ce5a15be95",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 2 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e2ecd0d452614a98afc47f18e50122e6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 3 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c53355d5716e49e7a68a5c8116e1a9e1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 4 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                                                                                                                                                                                                                                                                                                                \n",
      "CPU times: user 88.3 ms, sys: 52.6 ms, total: 141 ms\n",
      "Wall time: 4.08 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<orbit.forecaster.full_bayes.FullBayesianForecaster at 0x2a52ee510>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "dlt_auto_ridge = DLT(\n",
    "    response_col=response_col,\n",
    "    date_col=dt_col,\n",
    "    regressor_col=x_cols,\n",
    "    seed=SEED,\n",
    "    # this is default\n",
    "    regression_penalty='auto_ridge',\n",
    "    # fixing the smoothing parameters to learn regression coefficients more effectively\n",
    "    level_sm_input=0.01,\n",
    "    slope_sm_input=0.01,\n",
    "    num_warmup=4000,\n",
    ")\n",
    "dlt_auto_ridge.fit(df=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:29.312900Z",
     "start_time": "2021-08-20T23:41:29.094900Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef_auto_ridge = np.quantile(dlt_auto_ridge._posterior_samples['beta'], q=[0.05, 0.5, 0.95], axis=0 )\n",
    "lw=3\n",
    "idx = np.arange(NUM_OF_REGRESSORS)\n",
    "plt.figure(figsize=(20, 8))\n",
    "plt.title(\"Weights of the model\", fontsize=24)\n",
    "plt.plot(idx, coef_auto_ridge[1], color=OrbitPalette.GREEN.value, linewidth=lw,  drawstyle='steps', label='Auto-Ridge', alpha=0.5, linestyle='--')\n",
    "plt.fill_between(idx, coef_auto_ridge[0], coef_auto_ridge[2], step='pre', alpha=0.3, color=OrbitPalette.GREEN.value)\n",
    "plt.plot(coefs, color=\"black\", linewidth=lw,  drawstyle='steps', label=\"Ground truth\")\n",
    "plt.ylim(1, -1)\n",
    "plt.legend(prop={'size': 20})\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:29.317298Z",
     "start_time": "2021-08-20T23:41:29.314547Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fixed Ridge MSE:0.091\n",
      "Auto Ridge MSE:0.075\n"
     ]
    }
   ],
   "source": [
    "print('Fixed Ridge MSE:{:.3f}\\nAuto Ridge MSE:{:.3f}'.format(\n",
    "    mse(coef_fridge[1], coefs), mse(coef_auto_ridge[1], coefs)\n",
    "))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sparse Regrssion\n",
    "\n",
    "In reality, users usually faces a more challenging problem with a much higher $P$ to $N$ ratio with a sparsity specified by the parameter `relevance=0.5` under the simulation process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:29.329485Z",
     "start_time": "2021-08-20T23:41:29.323077Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,) (50, 50)\n"
     ]
    }
   ],
   "source": [
    "NUM_OF_REGRESSORS = 50\n",
    "SERIES_LEN = 50\n",
    "SEED = 20210101\n",
    "COEFS = np.random.default_rng(SEED).uniform(0.3, 0.5, NUM_OF_REGRESSORS)\n",
    "SIGNS = np.random.default_rng(SEED).choice([1, -1], NUM_OF_REGRESSORS)\n",
    "# to mimic a either zero or relative observable coefficients\n",
    "COEFS = COEFS * SIGNS\n",
    "trend = make_trend(SERIES_LEN, rw_loc=0.01, rw_scale=0.1)\n",
    "x, regression, coefs = make_regression(series_len=SERIES_LEN, coefs=COEFS, relevance=0.5)\n",
    "print(regression.shape, x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:29.336311Z",
     "start_time": "2021-08-20T23:41:29.331801Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.        , -0.45404565,  0.37813559,  0.        ,\n",
       "        0.        ,  0.        ,  0.48036792, -0.32535635, -0.37337302,\n",
       "       -0.42474576,  0.        , -0.37000755,  0.44887456,  0.47082836,\n",
       "        0.        ,  0.32678039,  0.37436121,  0.38932392,  0.40216056,\n",
       "        0.        ,  0.        , -0.3076828 , -0.35036047,  0.        ,\n",
       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "       -0.45838674,  0.3171478 ,  0.        ,  0.        ,  0.        ,\n",
       "        0.        ,  0.        ,  0.41599814,  0.        , -0.30964341,\n",
       "       -0.42072894,  0.36255583,  0.        , -0.39326337,  0.44455655,\n",
       "        0.        ,  0.        ,  0.30064161, -0.46083203,  0.        ])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# generated sparsed coefficients\n",
    "coefs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:29.341796Z",
     "start_time": "2021-08-20T23:41:29.338956Z"
    }
   },
   "outputs": [],
   "source": [
    "# combine trend and the regression\n",
    "y = trend + regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:29.355537Z",
     "start_time": "2021-08-20T23:41:29.344693Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 52)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_cols = [f\"x{x}\" for x in range(1, NUM_OF_REGRESSORS + 1)]\n",
    "response_col = \"y\"\n",
    "dt_col = \"date\"\n",
    "obs_matrix = np.concatenate([y.reshape(-1, 1), x], axis=1)\n",
    "# make a data frame for orbit inputs\n",
    "df = pd.DataFrame(obs_matrix, columns=[response_col] + x_cols)\n",
    "# make some dummy date stamp\n",
    "dt = pd.date_range(start='2016-01-04', periods=SERIES_LEN, freq=\"1W\")\n",
    "df['date'] = dt\n",
    "df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixed Ridge Penalty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:41.014941Z",
     "start_time": "2021-08-20T23:41:29.357833Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-03-19 23:42:27 - orbit - INFO - Sampling (CmdStanPy) with chains: 4, cores: 8, temperature: 1.000, warmups (per chain): 2000 and samples(per chain): 25.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "42b1882e010d4a29afaf9c6936d35e4d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 1 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "25e15cc74b5041ca8fb4aa78ffe32aa3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 2 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "189ba5e382bc43c89be6de2890d374c3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 3 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ee7dd760f3c54f3b81a609dd78af359c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 4 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                                                                                                                                                                                                                                                                                                                \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<orbit.forecaster.full_bayes.FullBayesianForecaster at 0x2a6375650>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dlt_fridge = DLT(\n",
    "    response_col=response_col,\n",
    "    date_col=dt_col,\n",
    "    regressor_col=x_cols,\n",
    "    seed=SEED,\n",
    "    level_sm_input=0.01,\n",
    "    slope_sm_input=0.01,\n",
    "    num_warmup=8000,\n",
    ")\n",
    "dlt_fridge.fit(df=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:41.275538Z",
     "start_time": "2021-08-20T23:41:41.017543Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+aCJJMSMz+R0BAACyDUGTHiBmJvTQujdVE4/pk+QaJbdt0zF77d+huycBAJln2pbKY9WNlhWHe5E/oRvyyquyvOImywBkTtgX1Dl7T1VVok4eeVQUyuO8uRMZlqVIIqqwP+DaaG1GYQDpuR0kBgCgu+DsvwcwbUvrarYrmoxru1UrI261e35uAEDXkbQMLdyystGymYMnysdUgd1O0OfXlJJ9M92NrOORR4XBHNmWLduTkCeQQ94xoIsJ+4KujcCQGIUBpEOQGACA9PhriKzg9/g0oXhv1RpxRZJR5QfC3HENAOhWYmZCpm073EZSScuQJHk8Hvk92TklZcgX0IzSg2SblqxtX8i7117y+DgvAAAAAAC0zpWgyZ///GfNnTtXW7Zs0fjx4/WnP/1JhxxySNqy8+bN07nnnttoWSgUUiwWc6Or6KZCvoBOGHSQqhJ12hmvUVEoTwEvMUEAQPcQMxNaV7Ndvfw5jrYTN5OKmbvuto5bSRUF8xxtrydJmIbeKf9UcTOpWiOusD+gbwyd7Nr0QwAAAACAzuH4VeUHH3xQl19+ue644w4deuihuvXWW3X88cdr1apVKikpSbtOQUGBVq1alXru8TCdAroewzK1tmZbo2XD8kvk92bnXbsAAOeYtq1e/hydWHaw8h1MUlxrxLU1VqmEZeiTyGbZDo9s6UksWdpQW55K5v1J1RcybaZDBYDO4PN4NaJgQJNlAAAATnA8aPL73/9eF1xwQWr0yB133KEFCxborrvu0lVXXZV2HY/HowEDBqR9DegqDNvU0vI1jZaV5RXLL4ImAICOyfeHVRjMdax+v9erkC/gWP0AADgh4PVrQvHeme4GAADoIRwNmiQSCS1dulRz5sxJLfN6vZo+fboWLVrU7Ho1NTUaMmSILMvSQQcdpN/85jcaM2ZM2rLxeFzxeDz1PBKJSJKSyaSSSZL9SVLSSMqyLFnWl3c7WrZs05btRjJ405LHtGUkDSU9zn8eRtKQx7Ql05Ltcfb92aYt7XaHbiyRkO1r+a7dcDMXq0zbUtIy29R2zIjLNizXtqvk7rbNGJf3157CMHblT5BpyTZd2ndc/CwbHWMtW/I6f4xNd/xx5biege9Ijzj2SK5t20zsr5lUf8xx49iT+l7atmTZihkJ7aytVsyfcLxtv9erXBcTamfke+ni8SduJvXS1g9UZ8T1wc71yguENLF4b8emft1937Esa9dvGTs7b8TJ9v2nnuvnP/yN7nR+26tpJaObLHP888zyz7InHfMy8R1x89wnJcv32YzpIdcnXP8se8h2zYT66/Bd+Xp8e/rmsR2cl+GLL75QaWmp3nzzTU2aNCm1/Morr9Qrr7yit956q8k6ixYt0urVq7X//vurqqpKv/vd7/Tqq6/qgw8+0KBBg5qUv/baa3Xdddc1WX7fffcpN9e5OzW7k5htaH7io0bLTg7up7CHnB97It12bYuvh8alXb7BrNIiY32b6wnIp4P8AzXE17vdfegOTNNUTU2N6+3m5+fL58u+E3Y4JxPHWI7r2SNhm1pibGq0bIK/VEGHErSbtqVyu67RsmJPLlOcdAK+l9nD7c+SfQdApiRtU++bWxot2983QAGHzkMkjnkAgMypq6vTWWedpaqqKhUUFLRYtsv9VZo0aVKjAMvkyZO133776a9//auuv/76JuXnzJmjyy+/PPU8EomorKxMxx13XKtvvqeoNWL66GND0WRcG9etl9E3LO/QgfK6MD1HnRFXVbxOpw05TAVBZ5PbSlIkEdUjny9WYSjX8TsuvWZSno0b27/ekL3SLvfUBuXZUdGmOpKWoRojqZ19cnTh2K/I68LFLje37UuPPa2/XTNXtdXuB01yeuXp5ltu0fnnzHa97Wy1s65ai19+TbH9eis35PxxQHL32FN/jI2bSX1YuVFhf0Dewc4eY9Mdf7yDnD+uu31Ml9w99mSEmdSmjRt25cEwkhpdNEjHjjlWeQ7mNZEab1e/L6i4ZXS4roDX12zQpT7pfL2g1y+vC7nqkpapVZEvZFuWtGanNLyP9i0apICDeccafi8Ny5QtW7G9+kgOfy9jZlJxI5n138tsPq7X7zsNjwPHjznO8eNApmT7/lPP7fMf/kZnD7ePdys/fqrR8W7c4AGunMf2hGNeJr4jtmnJXrFFnnED5PG5c1MMxx9nZGK7ZoLbn2VP2a6ZkEwm9fzzz+vYY49VINA1p4Sun6GqLRwNmvTt21c+n09bt25ttHzr1q1tzlkSCAR04IEH6tNPP037eigUUijU9EsVCAS67AfktoDHlNfrldf75R9Mr0cen8edP6C2V7bPI3/A7+jnETMTemjdm6ozEnqrYrVy/SEdM2Ccgj7ndvGQN6igL6BEOy80NbfdPT6v1NYLSR6P5PUoKVOG11ae3/l93W8nZfs8ks/r6L5jGob+9ovMBEwkKVpdq6t+9GNdMOtc+f1dLq7cLaW2o8P7TiMuHXukBsdY2yt5PZLH+WOsR7vasQxTiZqoJCmSX6mEL+hYm9KuE0wj7HNlu9Zz69iTKfWfZf1x3ev17jqHcfi43nC7Jjym/rtpSYfrmlyyjwbn9U372n/XN633wD5DNSS/X8v98/jkbybAETeTstXyQOm4beiDyEbJtmWb1fJURzWqT6kr30tJ8n95/pEXCivs8PdShlcx28j+72UWH9czdRzIlGzff+q5fv6TifeY5X+jMyaLj3dSzzrmZeo7YmvX9YWsPsb2hONPBrZrJrj+WfaQ7ZpJXfmafHv65egVwWAwqIMPPlgvvviiZs6cKUmyLEsvvviiLrnkkjbVYZqmVqxYoRNOOMHBnqK7M21L62q2K24mtTNeozojLsvh+dm9Ho8OKh6mZeVr2x04QfNqqqpVG8lMwKRepKpKFRUV6tev5Yt6QCatfe4dvXPrI0p+GTR5xKV2c3rlyf/HP+i7s7/jUovINu/uXKd3d65rsczBxcM1smBg2tee2rRMcZO/uwAAdEcBr19HDxirOjOhSKJOJ5VNUNjr8A0GAJBhtUZMhuVu/h2/15uVo/jc4vht1JdffrlmzZqlCRMm6JBDDtGtt96q2tpanXvuuZKkc845R6WlpbrhhhskSb/85S912GGHacSIEaqsrNTcuXP1+eef6/zzz3e6q0C7Dc0v0eC8fkpYe57kqDSnj2YOnthimbhp6OlN7+5xWwC6N9MwGgVM3BStrtWPL/2Rzjt7FqOxAACAKxKmode3fdxo2eEl+zo6swCc4fN4VZJTqFojroDHp8F5feXzZulIAQDQroDJ/A1LFEm4+/u9IJijk8smEDjpIMfPML7xjW9o+/btuuaaa7RlyxYdcMABeuaZZ9S/f39J0vr16/83bZSkiooKXXDBBdqyZYt69+6tgw8+WG+++aZGjx7tdFeBDvF6PJ0y9YbP65VP3GGTzl8WPqyCPkWO1R/ZWanvH32GY/WjZ7AMU/HKGskXUFV5heIOTsmzfcf2jARM6jEaC91NwOtT0Ns1h4gDAFpnydK2WFWTZU6ybVvx3W6OC3kD8riQmwsAkD0My1IkEVXYH3B+6t4vxcyEIomo66Nbsokrt2VccsklzU7H9fLLLzd6fsstt+iWW25xoVdA9xPyBjRz8ETVGglVxWt1+tBJyvVlZ9Kzhgr6FKmwuHemuwGklecPa/iKuC6+5P8Uqdr1Y35+hvsEtEf935aOCniaP52sr/fzmu2tTsnllIB8OqjPcFcS0AMd4ZFHhcEcxU1Dfo9PxaFe8oq7roFMi1tJPb7+nUbLZg6e6NoFLwBdh2kYqqmqdrXNOiMuM5w+xx+6p7AvqDwXkt3Xixl7PitOT8ZYVqAb8Xw5qsW0bcV8AeX5Q9zpBGSYYRi65JJLUgGTTLnlhfvUr68zIz8YjZXdPJ00YjKd+nr3KSzVyIK92jydpd/T/A/EE0oPajURfD3btOXfuU3+PEZFoesK+QKaUXqQao24KuO1OnPYFOX4uSgLAEBX8NKjT+mvP/9tRnKvkk8SyByCJj2Az+PVfkWDVBOLyvJWKJmTz91raDfLthQ3k4qZSfnaEagJegNp7+61bDvtxbOYmdijfgJuq6ioUFWGAyaB/BwNHDpIeaHcjPYDaElnTWcZ8rV9mi1blixuLgAAAEAHmIaRsYCJRD5JIJP4xvUAYV9QZwyZpPLaiPp8XK1Y32IS5qFd3q/4XI+vf1tLy9co7Aso4G37/vOV0gNUFMxrsjySrNMzm5Y3WR6rzMzJCNBd5fbK1znX/lA5wZxMdwUAAABoUX2umJiZVNxMqtaIqyCQwwwK6JJqqqozFjCpRz5JIDO4cg6gRZZt6ZlNyxU3MzcXYsxIKPTlCJSA1y+fp+lIqXSJGttcP6Nb0Mn+svBhFfQpcqWt/MJe8nHXEQAAADrIMkzFK2skX0BV5RWKO5i3JWYm9PSm5Upahqxcv7bGKnX1/qcqzx92rE0AANqLqywAWhQ1ExkPKjz9xXKF6/IlSUcPGKuSnMImZdIlamwrRregsxX0KVJhce9MdwOAi7zyqiRc2GQZAABd2XsLXtWCG+5SvKZOkjTfxbb9eWF5rzpX2v9UF1sF9ozTN8iRTxLoGgiaAN2IaVsqj1WrzkwokqjT+todGu0fJJ+XizJAphiW2WSZaVkZ6AnQdoZhqHpnpbzBhAx/yLV2s3lkVNDn19EDx2a6GwAAtJlhGHqqQcDE9fZrY3r2pn/KuOK3XJ1Ct8ENckDPwJ8loBtJWoYWblmppGUoZiZVa8R2DWX2OjeUOewN6py9j1J1MqZHPl+sXoEcleUVp03unk7Qmz5hb0EgVzMHT2yyvCq3Qo/sUY8Bd6WbFi5pGxnoCdA29957ry6+5BJFqqpcbzuvIF8XXn+lpp16guttA11V0jK1qmqTYmZSNcmY3tj2saYP3J8chAAcV1FRoViGAib14jV1qqioUOHA/Iz2AwCAhjgTB9Ain9erofklqkrUaWBObxWF8pTbCXclez0ehdPMlRv3Ozd/LpCNOjp9XnvyA2V6ir6ewDJMxatqVGtHtH37dtU5NK+3YRj69re/7UjdbVEbqdFff/5bHXnycVk74gTdn1de9QsXKGoklO8PK8cflEfOJSg2bVMrKzekbooJ+fw6asBoBfmpBgAAAGQEZ+I9QMxM6ImNS1UTi+rj5Hold+zU4QNGc/cauo0ZpQekhr8GvOn325A3kHbkSltU5TG6Bd2LZduKJHfdFfhpZIs+rd7S7jrakx+IvD/O8cqr8pc+0MK5/1KiJqpnJf0h051yWG2kRjVV1UxrgC4rxx/URfscr6pEnfL8YRWF8hTypR85CwDdWbrcW7e+cL/69u3rWJvbd2zXZdPPcqx+AAA6A1fNewDTtvRR5UZFk3FttKpkRBOylJ3z7VuGqXhljeQLqKq8QvE0IxmckM1ztHcFYV8w7aiUhjzNjFxpC7f2E6CzJKykntm0PKN9sOzs/DviNp8tvXbzfUrURDPdFQAA0MPkpBnl37dvX0dvbGAEMwCgO+AqL7KCz+PV9pdW6h/X3Kxoda0kab6L7TNHOwA3Bb0BBb1+JazM5U6JZvEPXtMwVFNV7UpbkZ2Vqo1kdiTPP5c8I5/f51j9kZ2V+v7RZzhWPwAAAAAAnYmgCbKC3/bqX9f+IRUwcRtztHdv6e52qjVi6peBvgBt4fV4dFDxMC0rX5vRwEk2eunRp/TXn/8244EMN+T0ytN51/1Iffo7NwVHT5K0DL1X8XmjZeN7D2l2WkkAAIDOZhqGIlVV8pbnyONrOv2aE+qMuMywczfgAEAm8CsOWaGiokJVVVUZ7UO2ztFu27bqzLhqjbjiZlIxM6lcX1Aej3MJUQG0bmh+iQbn9VNit6TtbdWe/EDbwzt6RN4f0zC6RMDkww8/dHQucUmKJOr0bOVHKs4rcLSdnsS0LX0aaZxfaGxRmciEAQB7ziuvyvKKmywD8D8vPfqU/vqz36q22v1z2ZxeefL/8Q/67uzvuN42ADiBoAmAFtWZcd38wROKm0mtrNygsC+gM4ZO6nD+EACdx7sHuXyaky4/UNDXM+4cq6mqznjApKCwUCNHjpTf4VGLwUSdfDWfONoGAACdJejza0rJvpnuBtBlpW7+yUDARJKi1bX68aU/0nlnz3L8PHZ3CdPocN5er7wK+tL3N2kZ5OABejCCJshaf1n4sAr6FDlWP3O0AwA6U06vPM299WbXf2gC3UmNEXO8jYRp6J3yTxU1E1od2az8QFjj+wxVwNszAshAW1m2lRqJ7vtyFLrP4212NKtTFzadEvD4NblknybLgK6oK9z8E6mqUkVFhfr1c3ei63fKP9WG2vIOrVsSLtTRA8emfe29is+1ctOne9I1AN0Yf/GRtQr6FGXdVFkAAHc5HYBPWoY+qNyohJWUEfapd+loxc2kQj4mdQIa8nk8qjaienLDUsfbiptJvbhlxa7HVlJFwTyN7V2mgAiaAPXer/hcj69/W0vL1yjsC6QCJSMKBmhC8d5p13l928faFuvYlMplecWujzTxeb0anJfdeb8SZtPceJFEVH4j17E264yOTS0LdBWWbWe6CwBcQNAEAACgGU4H4GNmQptrPtk1/D+e1PKda3XCoAMVIhMG2smNERiZaKte2BfU0Px+Ml24UBEzkwp/GbjM8Qfl9xAsARqybEvPbFquuMnF7+4uaTcNmlTEa+SNhx1rszpR51jdaIzZN5zR0ZySALoXgibICunmmUx31wwAoHsxDEPVOyvlDSZk+EOOthXZWelo/YAT3ByBUc+ybVUkapQXCClmelos29pc4abd9ql6gt6AvJ6W2+sMPo+n2emFAEhRM8E8/1nspLIJGjyw1LH614c36aeO1Y6GmH0DADqOXwPICul+cHd0vlwAQGPp5u8OeZ0fCXHvvffq4ksuUaSqY1N5AD2BmyMwJGl97Q69t3OdDNvUh1UbWy3f2lzhn0a2tLntoNevg4qHaWh+SZvXATLFMAxVVVUpXu6VEXJ+dFadEZcZZlQU9lyvYFiFQeem5+ob7tVkmRvnlcheE4tH6ODi4R1a1ytvs6+N7z1E/RM5eqSjHQPQrRE0AQAALfJ5m/6Y8DucENkwDF1CwARok7Av6Eo7lm3ro8pdgZJMTFmVsAwtK1+rwXn9XBlxAnRUpoL+Ob3y5P/jH/Td2d9xtV1JmlF6oEI+v3ye5i9AHl6y7x4lgkd2SHcO6fR5JbJbcyNa91TA61fQx74J9FQETQAAQJdTUVGhqgwHTPIK8pVf2PRuSKCnSlhJJazMTn+asAwlrKRrgSKgvTIZ9I9W1+rHl/5I5509S36/uz/1Qz5/q99Lpy5sAug5YmZCT2xcqjojrmU71yjPH9LhJftxfAHQ6TiqAN1I0BvQV0oPUJ2RUCRRp5mDD1EOFw2AjMr1Nc2zwRQD3V9eQb4uvP5K+Vy+6ASg5/HIo5DPL4/HI8u2leMPySNG0nRXmQ76R6qqVFFRoX79+mWsD9kiZib0+Pp3Gi2bOXgiQVsgg0zb0keVGxU3k9oSrVTYF2Bq9k5Wa8RkWO5t08pYjWs5LCWms0TbcSUA6Ea8Ho+KgnkKeP2ybVv9wgXytjAEHoDzPGmmiEm3DHvuLwsfVkGfIlfayi/sRcAEaIP6KXma09pc4WOLylqsP24aenrTux3uX3cQ8gV0yuBDVWvEVRmv1ZnDpijXhYsGAAAADdUaMc3fsESRRNSV9t6a/4IeuP7PilbXutJevUxOZ4nug6sBPYDP49XQ/H6qiccU9W5XMpTPnLAAgG6noE+RCot7Z7obABpoy5Q8zQl4/WptXJ5HHhUGc5osA7oTJ4P+kZ2V+v7RZzhSNwCgZzEsS5FEVGF/wPFRdaZh6MHr/+J6wETK7HSW6D7YM3qAsC+oc/aeqvLaiF5fHVespJj5HgEAANAuXnlVllfcZJmTQr6AZpQe5GgbgNMI+gMAupOwL6g8h0e9VlXVqa66xtE2WsJ0lmgNV84BAECLYmaiybJaIyZOL4GeJejza0rJvpnuBgCgG6s1YmmXcV4JAOhKCJoA6PH8nqZJwIJeDo8AgLZjGikAAACg45jOEl0JVwWBbsSybUWSdaozEqpORrU9FlGvQJhk8HvI720aNAkQNEEbmZbVdJnddBmA7MY0UgB6Cq+86hcuUNRIKN8fVo4/SJAYQFZKd2zjeOccprNEV8JVQaAbSVhJPbNpuZKWoZiZVEWiRlfvf6ry/GHH2gx5AzptyGGqScYU8PrVK5CjgIdDB1AvZjWduippGRnoCQCgOzIsU2trtilqJlSdiGlZ+Rod3n9fbuBAl5XjD+qifY5XVaJOef6wikJ5CvkCme4WAHS6dMc2jndAz8CZOIAW+b0+jSkqU1WiTst3rlNRKE8+LyNbAABAdvLIo5DP32SZUwzb1NLyNambYrwe6ZB+IwiaAAAAABnCmXgPEDeTenHzClXH6/SBsUnJimodUjKSH2IAAKRh2bYSVlLSrpxH6abwk3b9fbVld6gNn8engNeXyoMRNw35PT4Vh3rJKwLTQL2kZWpV1aZGy/YpLFWgme9lZwj5Ajpl8KGO1Q8AXQVTDwEAkB5XzXsAwza1pPwzRZNxrTd3yqiJ6uB+e4sBhQAANLauZpuWla9V4ssp1g4uHq6RBQPTln1q0zLFzY5NxTa2qExjew9O5cGoNeKqjNfqzGFTlOMPdrj/gJMSpqF3yj9ttGxi8QgFfc79pDBtUysrNzRaNqJggAJyLmgCAD1Frj/UpmUAAPQ0BE2QFXxpEqFzpy4AoD0s224UMAHQmCVLG2rLGy07uHh4hnoDAAAAAM4gaIKsEPY1vSvXybsekV3iZrLJsjojnoGeAMikhJVsEjBJd3wA0snENFIAAAAAgM7HVeUeqrnpRHYlvkw/cVfSMmXaZrvaiZlJWXbH5nsH3JIuJ0FH8xQAAHomppEC0FMkTEOLtq9SrRHX6shm5QfCGt9nKEFiAFknaTW9BpZuGYDsQ9Ckh3p607tplxcGczSj9KC0r62q2tTkYkBrkpYhw7Y0vs8QTS7Zp939RObVGjHd/METiptJrazcoLAvoDOGTko7ugfdR60Rk2FZ7rRlxlxpB3DCsF79m33thNKD9igRPAAA3VHSNvTK1g8VN5NaXb1ZYV9AY3uXESRGt+Dm76Aag99Bnc3n8Wpofj/VGQl9Ea1Qrj/k6NTs6W4cbu/NxAC6J4ImcJxhmXph8/s6rN9IedPkHgHgrlojpvkbliiSiLrSnse01V+Sz+NxpT2gM7W03zY3MhNA92ZYptbWbGu0bFh+ifzcRQ/0KH6Pr0neJj83PXRrbv8OkqRqI6ricL5r7WW7sC+oc/aeqqpEnTzyqCiUx9TsABzBkaUHyPEFFfYFFU1mLkdD3EwqaiaU5w9nrA8AdjEsS5FEVGF/wJ0RQ6YlKapQBkYnuXF3V3WCO8gAIJsYtqml5WsaLSvLK5afu+jRTUQSdQom6hyrv9aIK242zQOWbfxen0YWDMx0NxyVTPMZpluWLVz/HSSpOJzPLA0A0A0RNOkBvB6vvlJ6gB5duzgj7Qe9fuX4Q/KIu8yBriTsCyrPH3K8HdtjyZ0B8P/j83hUbUT15IaljrdVvn2H420AAAC01WPr31avmiLH6q+ftleS4lZSOX4uCHdX6QJf2R4Mk9z7HQQA6L4ImvQQ+/ceooGBQi1c71dsrz7KC6Uf8dFSYGOfwlKNKBjQrnZrjYRiRkJnDpuiXAdPSuJmssmybL5DBkDLwr6ghub3k2l3LN9EeySCzt3JicZs21bMTHR4/YDHL583/TSRMTOhuMnfDQBA91cYzFVBKM+x+mNmUuEvp6jM8QeZsgoAAGQdgiY9iNfjVdjjl3wdG4oa8PrandzPtG3FjI5f4GorI21yLrfvbQfQlbg1DD7Xn/15LdJdDAl63T+FiFtJPbP+nQ6vP7lkHw3O65v2tcf3oF4AALqSXH/I0bvofR6PAhk4D0B2SHcOmYnzSgAAWkJWbgAA0KJ0yY+5WAIAAID2SncOyXklAKCr4S8TAABAGkGvX0Fv9o8kAgAAALqDuJnUi5tXqNaIa2XleuUHwjqk7wgCbwA6HUcVoBsJeP06esBY1ZkJRRJ1OqlsgsJeEi8CmZTuojoX2ru/oNevg4qHyetpPtcXAADIXnEzqac2LWu07ITSgxTycZ4HZIphm1pS/pniZlLra3co7Avo4OLh4lsJoLMRNEHWqjOSqjXiDtbvXN3N8Xm8KskpVK0RV8Dj0+C8vs0mNQbgjnQX1bnQ7oyQN6CZgyd2eP2Ap/nTnt3rDXoDfI4AXBH2BXXmsCmqNeKqjNfqzGFTlOcPZ7pbQI9ny1bcNJosAwAA2Y+gCRxhWKbW1mxT1EyoOhHTsvI1Orz/vq4OmaxO1CkYr3W0fgCAM0zLarLMkq2wz5nRdU7Vi66hzohLtrM3GcTMpJLWrotrHo9Hfk/TXEBoP488Cvn8TZYB6LliZkKm7XzwguM6AAA9F0ETOMKwTS0tX6OkZShmJuX1SIf0c3eeyZPKJmjwwFLH6t+Rv10/dqz2tqkxYo63UWvEFTeTSlhG64UBoJPErESTZUmOQ2inuJlQQFJVvE62z9kL7XEzqZiZ3PXYSqoomOdoe5nglVcl4cImy5wU8gV0yuBDHW0DQPcRMxNaV7Ndvfw5jreV6eO6G7/1qhPOt4HMiX+5/6ZjWKYM2+xw3dxwBCDbETRB1uoVDKswmOtY/QkH626Nz+NRtRHVkxuWOt5W3ExqZeWGXY+tpHL8nBwBPU26H1yZmKIQaC/TthWQ9JVBB6gwnO9oW7VGXFtjlUpYhj6JbJbtwl3Qbgv6/Dp64NhMdwNAD2batnr5c3Ri2cHKd3gau0wd1938rVe+fYfjbewu3Tkk55XOeGHz+zqrZHra19bWbNPS8jUdrvvMYVM6vC7QnJiZUMhsevNcOrtGI6fPZpO0TJm7BQVjbawXqEfQBOiGwr6ghub3c21YevjLP0Q5/mBWDkv3pXlPLeU+AHqadPN3M6c3upM8n7M3UkhSwOtT71C+YmZSQa9fQV+AaaQAwCH5fueP636vNyNJ3938rZcIuj/lNOeVzrCy8GYN9DxPb1qucG3bbnQqDOZoRulBaV9bVbUpdfNvvVhlTZNykUSdgi5Mve/GyEF0Pq4KAt2IbduKW/+749vn8SjkDcjjYLJin8fj6rRqmRDwNg2aBH3Z/Z7RedL9QOFHC9Dz5PpDumLMyapK1OmBtW+oKJSXkYttALqebLtzllxDznNr6qNcP3+nskXCajoyPGF1fPot7JLu2MbxrnN0hd/Mj3z+lgprervSVrURVbHDI9/RubgqCHQjcSupx9e/02jZzMETHT2p9nt8Orh4eJNlAHZJ/wOl+fmDs0V1IqYqB+/KYY5tAD2FaVnaFN2pqJFQdTKqj6s26eDi4fKnuakD3ZPbd846jVxDAHqKdEFsborpHF3hN3OOP6SikDv5qorD+eQC6mYImgBokd/r08iCgZnuBoAu5okNS1QcW+dY/ZmYYxsAMiFpG3pz2yolLUMxM6mkZWhs7zKCJt2UZVuZ7kKXuHsXQOYdM2Bcs68Nyy9RWV7xHtVvWk2PdwajW9BGPo83011Qrj+gPH8o091AF0XQBAAAtFuvYK6jd+VkYo5tAF2PYZlaW7Ot0bJh+SWOBhTCviAJbtFh0S6QaLYr3L0LIPOCvub/Vvq9Pvm1Z39Lk7bRZFmc4w/aKN008DNKD1Bhcdumy2ppmrR9Cks1omBAo2Xbwzv0SPu6iB6OoAkAAGg3p+/KYY5toOtJWobeq/i80bLxvYc4mvvMsE0tLV/TaFlZXvEeX+gBnMI0tuhO0k0Vk+cPZ6AnALDrmNQZU1gFvD4FdjtXbCmICKRD0ARZwaumw/rSLQMAAEDHmLalTyNbGi0bW1QmQpzA/6Sb6547ZwEAALoXgibICjn+ppHodMuAdOJm0yHEUSPzUysAALqPpGVo+c51qknGtK5mu3olqjW6cBB5KQBw5ywAAEA3Q9AEQI9nq2myTEuZT+IJAOg+Epahpze9q7iZ1IdVGxT2BTSqYCDTSAHIOpnINdRVxc1k2t8SbeHzeB2d3hDAnkuX2J5k90DPwF9oAC2Km0k9tWlZo2UnlB6UduoBALvUGUnVGnFX2vJ5PJ1y9yoAAEBbkGvofxZuWaGqRLRD644oGKAJxXt3co+A7OaVV/3CBYoaCeX7w8rxB1uc1nBPGXaaoEmaZU6LJOoUTNQ53k6NEXO8jUxJt584ue+g+yNoAqBFtmzFTaPJMgDNq07UKRivdactI6qh+f0InABAJzEtS5uiOxstK83pI5+XfHlATxLw+HVU/9GqNeKKm4byA2H5PD0vMAR0JTn+oC7a53hVJeqU5w+rKJTXI27ofGz92+pVU+RKW9VGVMXhfMfbSex2nam5ZZ0l3X7SE/YddBxBEwAAOtlJZRM0eGCp4+3UGDE9uWGpTJtAJgB0lqRt6M1tqxotmzl4onwiOI2uhztnnRP0+XXUgDGqStRpQ225ikJ5Cjg4BVnCNPT6to8bLTu8ZF8Ffc5dtjGtplMSM/UQ0PUUBnNVEMpzpa3icL4rN+SlmxKdadLRlRA0AQCgk/UKhlUYzM10NwAAgMtiZqLJMu6cRVtYsrQtVtVkmZOSdtN9M24lHW0TQPvl+kPK84cy3Q2gRyFoAkeEfUGdOWyKao24KuO1OnPYFOX5w4615/awPgCAs4Lephd80i0DAKCt3JirvTLedM557pzNXkcPGLdHieCBzpJu6jimkwOAjiNogqyQ7g6ZdMsAAO2XiR9hXk/TqUXSLQMAoDU+j0fVRlRPbljqeFvl23c43ga6Dkb1tF/A0/QyVLplaJ90U8c5OZ0cAGQ7/jIBAIAW8SMMALJXrRGTkSavgVPcGO2xu7AvqKH5/VzJAZYINh1pAuB/0uVocTJvC9DZEqbZaCrG5vJ/mJbVoZt5003zCMB9/GUCAAAAgB6o1ohp/oYliiSirrZbbURVHM53tU03ktpKUq6fkQcA4JSEaWjR9lWqNeJaHdms/EBY4/sMdfWGrhe3rFA49r+/YWcOm5K23KboTr25bVW7649V1nS4b2ieYZltWgbUI2gCdCMBj1+TS/ZpsgxA5gS8Tb+DYa87F2YAANgThmUpkogq7A+4FlSQpOJwvqvtAQCyQ9I29MrWDxU3k1pdvVlhX0Bje5cpIEbBo2WGnSZokmYZUM+VzGN//vOfNXToUIXDYR166KF6++23Wyz/8MMPa99991U4HNa4ceP01FNPudFNoMvzeb0anNe30T+flwSCQCalS+LJ9xIA0FYhb0AzB0/UCYMO1jEDxunifWco1xdytQ9hX1B5/pBr/wiYdB7unAUA5wS9jB4EeirHb1F/8MEHdfnll+uOO+7QoYceqltvvVXHH3+8Vq1apZKSkibl33zzTX3zm9/UDTfcoBNPPFH33XefZs6cqWXLlmns2LFOdzcrWZal8vJy7aytVlVVleLlXhkhZ+cSNi1Lm2MVihlJmTk+fVy1SQcXD5c/y+fAj+yszHQXOl3MTDQZHlqVV6G4Qz92s3Eb9nSmYShSVSVveY48PveCCfmFveTzMxLLKU5/VyvLK5oss1yYix7ucOtYXxePKl5VpR3bd8iqizvaVq0RU+3OiOJWUpZlSlmcHNgyTCVqdk3n5OQ5geT+eUim2pSkhBFXIlGnaEVEO2rbPwd6R0QSdareWSlvMCHD726gxm3Zel6Q7i7Zip07Hf3dlanviCTVGXFVJ+q0I3+7EsFcx9uT3PueZGK7VldUOVZ3e+zYscOVdiKJOpmGKWX34c41oTQBhbqKam33b3esTbfPt7wej6P1t1U2XifpKscfN5iGoZqqalfbbPj3stfAMnm5sbPdHD9r/P3vf68LLrhA5557riTpjjvu0IIFC3TXXXfpqquualL+D3/4g77yla/oxz/+sSTp+uuv1/PPP6/bbrtNd9xxh9PdzUrl5eVpA1Ru8eeF9d5V5+q+q36f9UGT7x99Rqa74IpHMt0BdBsvPfqU/vqz36q22v15WfMK8nXh9Vdq2qknuN52T5CJ413CSrreJpyR7X8v/XlhHfzDU6XvTsp0VzqVRx5tefE9vXbz/amgSSbOCbK9zR+72FZP0pPOCy6bfpbrbbr9vewp35Oe8rtr9OjRrrWV0ytP5133I33ljJNda9MNcbPpeXK6ZZ3JkyagMGbMGEfbbChT51szSg9QYXHvVsuV5vTRzMET211/VV5Fk+9+tp87Z7OXHn1Kf/35b1UbyUyumh9L2rZtm/r165eR9rszR4MmiURCS5cu1Zw5c1LLvF6vpk+frkWLFqVdZ9GiRbr88ssbLTv++OP1+OOPpy0fj8cVj//vzsFIJCJJSiaTSia5uCIp49vBqI3p2Zv+qegPf61g2JmgiZFsejeekTQcfe+Z3q49iW1ask3LuQbMpnevO73/NFRnxGVYDr6/3dSaMXlMWzIt2R7n2jUNI2MBE0mqjdTorz/7rY746v+3d+9RdlVl3u9/67JvteuWVCpUEqpyASRACCEXIEArhAABBSOR1tb3KB6POHzBIwa1haMIar+0tv2KdqvoGD2I3W9n2No2dOsRMALi4RUQg1GwIRIkJgRyp6679l7X80eoaoraVdRtrbUv388YGVBzr73n3Le555rPms9cH+mVpeU+m3H9BnmuF8t7WXSivUJ/wvww2r4gSX4gww+P9T1G7Xx2pPLfkVrnDRT15Nf+Td77P6wwUztXtlteqMf+5/eHAyZANYlrXFBuXBnp71e5+oBpiPo8qG9wILLHnojBvgHd9bn/qfVXbqip1Wfl+pioz6OTHuPFMd4q9xwzspV5zXTqWK+D+eqxkzWV+9SMuH8vIz6/THpOZEhc8xNDdVTyfOlk2hbpN/Hw4cPyfV/HHXfciPLjjjtOzz77bNn77N+/v+zx+/fvL3v87bffrttuu21U+U9/+lM1NMSzXLfS9fQkv+St1F/Q3f92t+a2tkXy+Ae7j4wqe+ihhyKrT5J831dDQ4MKhUJkdUBqaGhQw+5+BXsjnKDpPjqq6OGHfq45rbOjqzNhx3rZQUU5zO3t6Ul8cDDQ16/e//2cWlpaIqsjKNPH/uxnP4u0zteK473MeSWlGrJyC9GmdhxPqiGr3J4BBS+9lFgbopR99d8jzz0UW51xfHYkqaFOfy/dgaL6Ht2lXIRjkbhVQr8OTEcs44Iy5yXBfx5Q8FI0Kdcq4TcatSPVkNWvnnhCv7d/F1kdAxXwmS3E0BfELe6+R6qMMV7U461y53rB0/sVtEQ3P1EJr2sSoj7fS+I7Uilj5zjnJyRp27ZtsdU1WZP5XlV9+PKmm24asTKlt7dXnZ2duuSSS9Tc3JxgyyrHoUPR5ZOcjAsvvFAL5x0fyWP/6eUXY61vyDe+8Q197IYb1FsBgalalG9q1LWf/6RSqzojrSdzJDeq7LKLL41l+WKvM6gf/ukxZeyUsjHmv7cMQ5mI806bZV7XJJjLOmROYPn0VBmHs6PKLrrooljSIg59floyDWqIMMd2yne15uPv1BNf+1e5/fGf4KYas1rzsXcqdebxMmt0n4iCV1JPqaBNC89Rczr6705cnx3p2FV2H/6rv9R3bvmbijhpiFPu9OMj7X/iVin9OjAdUY8LzIOjT7HNU4+TGdG4IOnfaNQOO5/VpZ+6Rpdffpny9ujx7UwZ8Ip6200f1E++dJdK/clNCkfdF8Qt7r5H+q8x3rdv+RsVEhzjRfk8y419ov7shGGgv7j1o9r6hb/XYF+yK7PiEsf5XiLfkQoZO69fvz6W+S3XdbVt2zZdfPHFSqUq87x9KEPVREQaNJkzZ44sy9KBAwdGlB84cEAdHR1l79PR0TGp4zOZjDKZ0Sf7qVSqYt+guHV0dOjgwYM6OtCnx3/xiEpLZ6khE+0X99DhQ6Ny6dopO7L3xE6N/ihHWd+Qa665Rlf8+VW667f3qyUd/cRT0Xd0774dI8ouW7BC2Qgnv93A167el0eUndg8T6kY9qeJa8POcpuTx9WH2KGr0DKUTWeUr7ENWMu9rt988Adqnt0aWZ29R7tH5Xs1LDPSDegdY/QGrK4ZxPr5UcTP0ZChxZeu0cKLVg6n5Ym673ltf5duzMm0LRmWEenzTFRoKrSMWH67pPg+O0PWvfOtesvGS+PfALE0qMyzr+jsN5+v2fmmSOs6fPjwqJzsUfc/cUuiX09C3OMtPwz0SqlfBd9RvzOoSxas0MnN82XFsGFnr1PQ3Xt+Fcs49o28WDiiJw4/P+X7l3uPkhgXyCqzaXCEv19J/EYPKXgl9TgFvaPrLDXHtCl7EuL6niRxrjdUpxt4ChpsLW9bdOw8yI5uLJIyfK244i06+ZKz9ZsX/6CMldKVnasjfZ6J9AVxi7nvGbLunW/V6rddoJcOHYilL9izf59WLz9zZGGUfWyZx436s+P5nornzNfGf/9C7P16nGI/30vgO5Lk2Pm1v9EdHR2xbgRfyXPyk2lXpLOR6XRaq1at0gMPPKCNGzdKkoIg0AMPPKDrr7++7H3Wrl2rBx54QDfccMNw2bZt27R2bW1tpBkn0zTV3t4usyGjlpYWFdtmKR9x0KToO5E+fiWxbVtNs1vVnMlHPumd8R1lBxpHlLW0zYr8x3NO+5xIHx/1o3l264Q2zUNlMm1L2dZjfVDUfU+5/g7VzbLt2L//dimrbEugOe1z1JZnBXIUarFfj3u8VfQd/XTPs3IDT8XAlfqe0erFp0R6pfeQtFNQU38849g30pP1lfWm3u9P9D0KwtrcAyTO3+ghtldSUEprTnu7Wmo4aBLX9ySJc72hOq3AUzHiTcNfz7QtZVoblbVSsX1mMbP8MNCRYp8KviMnb6nQYGhRS1ukQf8Br35W1CXRr8cp53s6SQtHlJmqoUDmGOIaO7/2NzrOgEktifwS7s2bN+v973+/Vq9erbPOOkt33HGHBgYG9IEPfECS9L73vU8LFizQ7bffLkn62Mc+pre85S3627/9W731rW/V9773Pf3617/Wd77znaibCgAAUFfivsjBMoyaO+FDtPwg0L7BkXuPLcjNjnRCJmOmtLFrzagyVJ9yfZwTVO7mpKhvpkx15ttGlQGVyg08Pbj/6WNBf9/VgFfUzcuvUt6MPuiP6pe2bJ03d2nSzQDGFHnQ5F3vepcOHTqkW265Rfv379eKFSt03333DW/2vmfPnhERr3PPPVdbt27VZz7zGd1888066aSTdM8992jZsmVRNxUAAKAu2Kap5nROvc6gil58E4h93qAWNbYTOKlSblAmHWGZshmtM/T0y4M7R5Rt7FojS9F9hgyCe5Eo+o7u2fPEiLKNXWtq7rUuN8nNxDcmIokJxKEg8YDnqKc0oHcuWqsGq7ZSBgMAMBWxbAR//fXXj5mO6+c///mosquvvlpXX3316IOBMRganZuwXBkAAJDydlZXdq6WFwSx1dnvFfXjvdvl12hqnHrgh6MDJOXKgKlYkJs9aoXPZFTKaqC0NfoUu1wZUAmGgsR+GKpopZS3MzIMzqMBAGD0hppQbkO+pDezRPVwfG9UWT3tywOgPsWxX0I98cqsuPBjDEoB1c4yzUhXEAEAAAATxTphAHUv0OhJLT9kogsAMHGlMvskuOHooDwAVDs/CLRn4LBeHDiilwdf0bM9+8oGjgEAAKoVK00AjKvku3pw/1MjytZ1nK6MVRkpEAAAAADEZ2ivoaHNn93A07JZnbJNK+mmAahxpGYHEBeCJgDGFSpUjzM4qgwAAKAW+WGgI8W+EWVt2SZZBov0AQBIUrk07FzQWZ0c39MTR3aNKFvTdmJk+4BlrdEpQMuVAUMImgAAAADAq9zA04P7nx5RtrFrjSxOrAFEKO4JROm/gsQF31GvU9CegcM61T5elkmQGEC0AgXaO3BkRNmqtiUJtQYYjaAJAAAAAAAzwPFH72VUrmymZK203r34vMgeH/FJYgJxKEg8lGptwCvq5uVXKW9mI60XAIBKR9AEkciYo5dHNlijl1HOFDcYfSJSrgwAUB1Spq11HctGlQEAUMkCBRMqA4CZVC6FJGklAWDqmH1AJAyjzOZcZcpmilMmQFKuLEpF34mhDnc4GGQYhmyDzRYBRM8yTJ3Y3DGqLOo65+ZaIq0DAAAA8bINS6vbTtCAV1KvO6jGVJbJ/RlQ7uIiLjgCgKmjBwWmyTZNNadz6nUGVfTcSOsq+a6K/rE6SoGr1nQ+0vrqWZ9TVI9TiLyefq8YeR3AdKVMW6vbTki6GQAAAKhyGSuly49fqR6noKOlfrVm8kzuAwAqDr9MwDTl7ayu7FwtL4h+2f2AV9KBYrecwNMfel9WGIaR11mvfrT312or7o6lrj5vUG3ZxljqAgAAAACgGpVLw+4FfgItQbXxy8zZlSsDhhA0AWZA3o5no7wGO62NXWep3y3KNn6npnSWFF0RaUo3qDUTz0qetmyjslY6lrow81LG6J/Scvs6AQAAAACmrlwadi+sraBJ2kxpw4IVo8owPW5YZi/kMmVRK/qOMpNM728Z5pgr8hzfK7t32lCWGkwdQROgiqRMW2vmnKgep6A/9L6s1kxetknQJAoNdkp5O5N0M1AFLHN0Dma+lwCAiRqaHCl4jnqdgjZ2naUcF1PMiHKTTLU28eQHgfYNHh1RtiA3u+z4BABQ+UzDIBV7Dbt33w5lByaXaeTE5o4x02U/cvBZHSz2jCp3A0/rOk6fUhtxDEETRMIPWfYGAJi6MAxVCkZeHZMxUzIMI6EWAUA0hiZHUqatMAzVnm2WyabIM8Is85tRrqyauaGnXx7cOaJsY9caWSLwBiBaBP0B1DKCJohEuTyTxWByy88AAPWrFLi6Z88TI8o2dq2JLZVd0Xfkx7hvVHGSS7SBJBgaPdlcrmwmZcyUNnatGVXmh0HZ8eZEpc1U2cnzIAxV8uNP1VAPbMPSqrYlo8oAANPnlPntKlc2kwj6A6hlBE0AAMC4HN/TIwefHVF2/tylSlu1OYwo+o529x9Sk52Ltd7mdE426VRQwTLW6LRG5cpmkmEYZYOlRwZ79eD+p6f8uBsWrCib+qLXLei+fTum/LgYm21aOql5XtLNAJCwou/o+7t/qYLn6PHDz6nBzuiijtNrdlwZl3J7GpQrAwBMDL9KAOqeqdGTlOXKgHoVKBiVJ7WWT8L8MFSTndPbOlep0c7GVq9tmsrHWB8AAEDc/DDQ7v5DKvmujpb6VfBKNT2uBIDXumzBCrW0zZrUfaxxVnCdP3dp2T50wHNU9MhmMB0ETQDUvXJXNXGlE4BGO6uWdEPSzUCVaLAyo8oyNbbhdL1Km3bNbR4OAAAqUxCG6nULI8qaUw01tydXvcpa6RlNOT3W3JUfhgRNpolZQaCKFLySvrnzfhV9V789ultZO62NnWsiTY1hGaZObO4YVQbgmHJ7UQx4RbUn0BYAyTHKnMiWK0N1SZu2VrYtjnSiYmhypOA56nMHdajYq6ZUlrzwMyAoszdVuTJMztBeQwOeo57SgN65aG3ZwDEAxKHguRrwShE9djSPOx4ncEelCo1zb0cAxxA0AapIqFAFr6SS78oJPJm+oVDRnvilTFur206ItA4AAIDJaMs2jdogfjLGWjnSnGoY8bhjbRg/k4YmR9zAU9F39YrTr5uXX0W6vhngBO6EyjA5Q3sN+WGoopVS3s4QJAbqUKUE/fucgtKlgcgeG9EwZWputmVUGVApCJoAAAAAVSoIwzecBE4Ztiyz/EloudVyY5nMsVGzDFNWBFdcmmNsPA8AUWMCEdWmUoL+V3SuVte8BZE89uHGQ/pkJI+MtGVr3bxlSTcjUm7gT6gMlYmgCQAAAFCFdvcf1JNHXpATeOMed+7ck9WVn1P2tnv2PDHh+ord/aPKPE78ZpwTeOpxBuUF0W+M3O8VI69jSMl39ZN9T44ou3zBykjTzCah3CQ3E9+YiCQmENNmShsWrFDBc9TrFLSx6yzlCByjyjSlo9uH0GF/Q0yDH44eJ5crQ2UiaAKgYhV9R34MeaeTyFMKAMB0BGE4oYBJ1DxO/GaMYRgqBa7+0Puy/nX3o7EFE/q8QbVlGyOvJ1Soku+NKqs15TZkHWuTViBppmGoNZ1XyrQVhqHas83spwQAgAiaoEaUW/5JHujqVvQd7e4/pCY7F3ldR4t9o8ocP9lJKABAdfHLrArww+hWCjiBm3jARBp7bxBMnm1Yak3nFYahWjJ5ZWMKmrRlG0lJBgAAALwGQRMAFckPQzXZOb2tc5UaIw6A7cnu082vKwsUfUoMAEDtKAaj9/twKyCoEbWoN0mvN7ZhSYaUt9MEMlCx/DDQkWKfCv6xlE57Bg7rVPv4MfdOAgBUhzfaK88yLKVMq+xtJd+d8gpSxjyoRARNAIzL8T09cvDZEWXnz10aW5qBRju6/KRDmtKsSgIAVL/LFpypTJnf55Qx9m/2xq41E378nvwr+uGUWgaglriBpwf3Pz28+fOAVzy2+bPJmBoAqtVE9spb1tqpZbO6yt724P6n1OMMTrreVW1LdFLzvEnfD4gaQRMA4woU6GCxZ1QZAACoLBnLnvSVepM5vsRVgAAAIEGkZo9Gknvl9bgF/frI85KkM2YtVMqMZqo6UyalbLkyYAhBEwAAAAAAgAS5gaffvvKnEWVRTiBKxyZKe92CCp6jPndQh4q9akpl2QweqDNJ7pW3q3e/JClt2lo5e0lk9RhlUsqWKwOGEDQBAAAAAGAGlNvLKMr9jTJmalSaPa6crU5+GAxPHg5Z1tqpKN9NJ3B1374dw6nWXnH6j6Va48p9ADFKm7ZWti1mrzxUFIImiES6zEA9F2FKBy/wJ1SG6fFCX2EYasBz5IdT2+Broor+6A11AdSPlGHr3LknjyoDAKCS+eHoNLblymaKYRhsoAtApkavDipXBkxUub3yLKP8JvCStK7j9ClvBJ82UwRMUHGYfUAkynV2US7xLQXuhMowdV7oq9sZUMZMqac0oKIV/RVszemcbJOBHpA0U6Y6822jyqJkmaa68nMirQOoZlxdDgCoRpZh6pTW41XwSjpc6lPezjC5PwPS1ujpvXJlwERNdq+8TAxzRECc6EEBTEgYhsqYKb2peZ7euWit8nYm8jpt02RpOFAB0pat8+YuTboZqBFxriQs+q5q9VeEq8sBvJ4fBtNKBTbWlb5BGMp5zQVpJT+ZvPeoDVkrrasXrlWPU1DRc9WayTO5DwCoOPwyAZiUtGmrJZ0jmAEAmBTbNNWczqnXGVTRi2c1qOGHw3UnwfF9FX1nwhORk5UybVls1hupoh9HSlJ3eKLbMAzZ46S+AMZzpNinB/c/PeX7b1iwQq3p/KjyXreg+/btmEbLgMpT9B3lA1+2Wb7PLfnulFMNWYal1BiPi+khNTumKu70mah+BE2AKpIybL3luFM14JVU8j01prLj5pQEEL1yk1tpk59X4PXydlZXdq6WF8R3cuK5nh557iE1xLA6spwH9j+lbLExsonIdR3LNDfXMo0WYjxF39Hu/kNqsnOR1lPyXRX9Y8GzUuCW/awAAGbWvft26Lzscp3UPK/s7T/Z9+SUV1Uta+3Uslld02kexlAPqdlTpq11HctGlWF6yq3EnM7qTNQ+vnVAFUlbtt7ScZp6nIL2DhxRaybPFSxAwspdncagFigv7lWKrlFbJ9GIlx+GarJzelvnKjVG+Nn1g0AXzlumglfSAy8/peZ0A78jM6Tc68hrO/MyVko50gWiggURrxgEZpJlmLFfFGPIGLXpuyE2Zkd9Y8SISJQblAQsewMAADWKCcPa1Whn1ZJuiLSO2dlG9TgF7Ti6W62ZPGnXZki515HXdmbZpqX185bL5HVFBZtOKkyMbWhFRMF31OsUdEXnamVNxkPVKGOl9I6us5NuRs0pF3giGFU9CJogEuUGJYMxbvwKAKhuRd/RPXueGFG2sWsNG1+jYjFhCIzPMiwta+0cVYaZ05Zt0sauNVO+f9pMlS1vTjWUfdwBz1HBLem0172vAOLnlEklVq5sJg2tiBjwSkoZlrryc2QltI8cUIky1ujf1XJlqEwETQAAwLgc39MTR3aNKFvTdqLSFsMIYDyXLVihlrZZk56InCjSDKGapEyLHP8RswxTVgQXF5iGUfaiBT8MVfS4MA6TU/Qd/ejF7Sp4JT159I/K2xmdP/eU2MeVF3WcrnmNc8e8/fIFK6e1EXzcAo3O7FGuDAAwMZxpAah75dI0mOIKGWBIoEB7B46MKFvVtiSh1gDVI2ulx10dNdZEJAAAtcoPAz3T/aJKvqv9g93KWqlEJvfTllV2b8IhXA0OAPWNoEkdKvqu5EU7IVzwyBmK6lFuwoor6AEA09V7tDuWehpbmmTZyfxuFbySbK8US10WQSYAwAzpe6Unst+Uku/qkYPPHPujIS3TtrSuY9mEzjEtwxxzJanje2MGmBzfn3J7UVnCMFTpdSnvM2ZKhsFeGECcmBWsI/aruSVLnqtiGG1uyz6nEOnj16tBz9GW5x/SoOdo+5E/KmenddmCMyO9CsaUqc58m0q+qwGvpDe1zGcDTeA1Sv7oIHEhpglEAJXtv6+7OpZ68s2N+vAXPqULr7o8lvpeq8cpKCjFE8jo8wa1qLG95gInYRiq4Jc04JVU8l0VfVcNVprJkRkQhqNT65QrA1B/Pr7+PbHUk2rMac0Nm1S8ZGIXlp7Y3KHVbSeUve2Rg8/qYLGn7G3F7v4pt3Gm9HvFyOvoc6KvI2mlwGVvR6ACEDSpIw12RpK0aeE5slPRvvV7svv0/0RaQ30KFOhQsVcl31W/V5QX+lPOszpRacvWeXOXasArqbs0oI2dZ9XFj3VcVwdLyV4hjOkr9x2M+nsJAK810Nuvb3/2y3rzlZfE/nvyjq6zNKe9PfJ6+r2ifrx3u/wanPAu+CX97e9/pJLv6unuvcpaKV29aG1djLei9vordccqA4CouP2DeuKOH2rhupUy7fj3OonS0IoIN/B0pNSnH+5+TGnTjjTof+TQ4cgeu555ga8X+g+OKFvcOHfcFHZArWOWrg41p3NKpaLNz9mUzkb6+EDU4ro6WEr2CmEAwMyYNWuWWlpa1NNT/grQqA309qu/p08tbbNirbc53aCWdEOsdQJALTJkqCWdG1WG6WtsaVKqMSe3fzCR+t3+QTn9g8q2NsZab9qMdt7ntSsivNBXGIa6/PhVykaYCcNJ12dWk5I/fraYlGHLMstnBCn6zoQef/uRP44o68y3yRZBk+nwgtFp88qVoTIRNAGAhCV5hTAAYGbYtq2///u/13XXX6/ehAInQCUr+a4e3P/UiLJ1HafX3GbL5Sa5mfjGRGSslC5bsDLWOlOmrXUdy1TwHfU6BV3RuVpZs/ZWuVm2rTU3bNITd/wwscBJEswY0zzahiUZUt5OR7pSssGurd+Mibp332/Gvf3cuSerKz+n7G2vT/WF+HhhmaBJmTJUJmbnANS9pK8OlpK7QhgAMHP+23/7b7rsqit112/vV0u6YTg1ahR6j3bHuioSmK5QoXqcwVFltaZcEKjWAkOoHZZham6uRQNeSSnDUld+zphXq1e7xZes0cJ1K+W8GjS5bMGKyCb3y/1GX7ZgxYTO9cbbP/T8uUvH3Ai+J/+Kfji5ZgIAxkHQBDWhwRo9KVGurBaVW6ZpGaZSZvmvt+N7Yw60xlMss9l1rfCNUP/X5z+hb33mSyr0Jb+BHgCgetm2rabZrWrO5JWPMGhSTtT7ccW53xcAADPNtK3hFFktbbNi3Tsqa01/BUbaGnsKr8Q+WDUjbaaUNm05wfgpuaJtgx15ejeg0hE0QU0ot9FYlJuPVZJyyzRPbO7Q6rYTyh7/yMFndbA4+RUVp7Yer7Z006TvVw280FfzW07W//2zb+o3L/5BGSulKztXRzqI5gphAMBM43cFAACgupmGoZVti/XkkRcSCZykTVsr2xbHmt4NqEQETQBMyOFir/7Uf0hZO6V3LTo31qty4mLaljKtjcpaqdivPIpTEIZyAleWYSlllt/YreS7U06ZMd5KJwAAAACIU9ZK692Lz0u6GcCELWqcq658u5xgYhk/UsbY598bu9ZMqu60mSJgAoigCVBVcq8u6S0lkCprX+Goir6rP/UfUpoJ8aq1u//g8BUry1o7tWxWV9njHtz/1Ki84xM13kqnJESdTqbvFTZ8BhC/xpYm5ZsbNdCbXFrJ5pYWzZrFXlwAACAemTIpo2o1NbtpGDNyIWetXgw6WeXSjZGCDONh5hOoIqZhasOCFbpnz68Sqd82La2ft1zmOJvTYeqintwPwlC/fPF3ckJf6cZcpHVVEtLVAKhFlm3rw1/4lL792S8nEjjJNeX1N3f8rWyb0wkAmAlu4Gtnz74RZSe3LBhzZfhMCMNQpcBV0XdV8l0NeCU1p3J1k+oa1aeeU7NjesqtnmFFDcbDWQ5QZZbPWqjOhjb90/O/UEsmr7w9+qoBa5ygxvlzl05pI/gBz1HBLem01s5J3xcTE+fkfqoxp32b/1wn/p8f5soTAKhSF151ud585SXq7+mLtd6CV5KbtfSuk94ca71ANXADf0JlwOv5oa+nu/eOKDuxuUMpRRc0KQWu7tnzhNzAU9F3daDYrZuXX6W8nY2sTgAAqgFBE0Qia46ehC1XNlP8YHQQoFxZrTANUxkrpayVmvSEd9qa2tfeD0MVPWdK90XlcfsH9ej//L7++/s+KNVQ0KQS0tVkGhtIVzMDbMPSqrYlo8oAjGTZtlra4u1zbK+k7tJArHUC1cIPRwdIypUBAACgchE0QSQsc/RKh3JlM6UYjJ7ML1cGVIpKmNx3+wfV39On/NyGUbet6zh9WhvBS5Lje6NuK1c2k5JOV2Pns7r0L99fc+lqTJmam20ZVRYl27R0UvO8SOsAAABAvCzD1KLGdhU8Ry8NvqIGOxP5uBK17fDhw1X52AAqW23N6gBAlUh6cv+NZKzpb4hWLg1c0XdV9McPaJoyx1wR5fjeG6aXW/v29TrrrRfI6SvGkqO06Du6d98OuYGnoMHWsrZFkdcZt7Rla928ZUk3AwAAAFUua6X1vhMuUI9TkCFDrZn8lLMhTJQfBNo3eHRE2YLc7Egv7ER8Tj311KSbAKAGETQBgITEnYv+0OFD+vj698RS11ge2P+UssXGcY/pzLfpvLlLy972xJFd2jtwZEJ1pU1bK9sWa1Hj3Em3czIyvqPsQKOsV3NBAwAAAKgcbujplwd3jijb2LVGlmonTXG98MPaTcOOaAXh6Ewa5cqAIQRNACBBceaif6MVHrXGCTw9dug5zcvNGnPljBt4Ux54GzKUsVKyDEvLWjtV9F31u0WdN3epUgY/rwAAAAAwkzJNOaUac3L7BxOpv6GpUY0tTYnUjelxgtEXOJYrA4YwqwMAiETanH6Kr5nw4P6ndNmClWVv++0rf9Ku3v1TetyWdE6XLViplGlp2awuDby6MfJ5c5dGnmIAAFA7MmZKmxaeo363qJRpqymVI/g+Q8q9jry2AJLQe7S7qh+/Uli2rTU3bNITX/1XuQPFWOvONeX1gds2y6qx/SsBlMc3HZEIyyxxK1cGIFl9r/Qoa0WzLL3/lZ5IHhcAgFpim5ZOa+1Uj1PQjqO71ZrJk2d/hpR7HXltASThv6+7OukmzLiUYevcuSePKova4kvWaP4Fy9XX06ulLQt0w6lvVd7ORlpnr1PQ/d3PqC3fHGk9ACoHQRNEouCXJlQGIFlx73Fy2YIVb5iOzNTYkxlr2k7UqrYlY94ehtK/731iRFnGJFdxNSr5rn6y78kRZZcvWDlmqjUAQGWzDFMnNneMKotb0XeUmWLKUtuwZJtW2dtKvqtQoRzfn07zAKBqWKaprvycROo2bUuZ1kblW5vV3t4eedAk7RRk9f8h0jpQe8pdoBrVRauYeQRNAACxyVrpaQ0SJpL26pz2k/TkkRfkBN6U68FIbuDpt6/8aUTZGbMWKmVGN4wIFarke6PKAADVKWXaWt12QtLN0L37dig70Dil+65qW6KTmueVve0n+55UyfdU7O6fTvOAmlfyXT3w8lMa8Ep6unuPGlNZnTXnxEjHlXFrbGlSvrlRA73J9Qd59t4AgGmpnV8lAJgiU6bas80a9Bw12lnl7LQMGUk3a8Y1tjQlumleXAP3RY1z1ZVvH97UbbyVK2fMWqhlrZ1TqqcWPyNj8cNg1N4vJzXNU8YKxr2fIWPMlSFu4MsPx74a9/UBEwAAAFQ/L/T16yPPq+S72jNwWFkrpVVtS1RLa4kt29aHv/ApffuzX04kcNLQ0KBrP/9J9t4AgGmgB0Vsjhw+EtmSySOHj0TyuKgPOTutj5x8qXqcgvJ2Vq2ZfE2mABreNO+OH8YeOIl74G4axoRWtKRMu6ZO0OJ0777fvOExLemcLluwsuxtO3v26enuvTPdLAAAKk7aZLQB1JsLr7pcb77yEvX39MVab+gHatjdr9SqqV0YBtQTx/dVfE3KzpRpl00dGoahSq9elDkZxSmmA0VlIGiC2KxefmbSTQDq3uJL1mjhupVyXg2aXLZgReQ5NRm4AwCASlGaRvqsfqNHPW75i8AGX+mTE/hlH9806md1KqLlBb68cVbqvhFy6cfLsu033M9xpoV+oGBvMpkFgGrzk2cfVWb/f6Xs/LO5SzUn2zzquKLv6N59Oyb9+NMZcyB5BE0AoE4cS5VkS5atXCYjSWptmx35qhoG7tUvbaaUNu1E94lJmzZX6gKoSQNeUX/7+x+p5Lt6unuvslZKVy9ay+RmRH78vtunfN8fzmA7gKl4of+gth/545Tv/+7F55Utn5Nt1osDZG8AUF9ePybgdx6vRdAEkZg1a5ayjQ0q9hcSqT/TmNOsWfFe0QFUuoyV0ju6zk66GahCpmFoZdtiPXnkhUQCJ2nT1sq2xVypCwAAatbwBU6vK4vaqrYlCsKQoAkmreg7umfPEyPKNnatIeiPSSv6jvwwjLQOLxh/P07g9QiaIBK2bevym/5P/b+3/4NKMe+dkGrM6cJP/h+y2fQMAGbMosa56sq3y5lELtfxTvRPblmgE5s7JvQ4aTNFwAQAqpzje3rk4LMjys6fu1RpK7oxe2NLk/LNjYlsxDwk39SoxpamxOpH9UjiAqesldZJzfO0s+el4TbkmPAGEKOi72h3/yE12blI6/FztjKNDSoldHG3JOWbGRNUE2aVEZkz3vpmda07U3sP7Vd7tkl/uWxjZBvBD3hFfevZn6rXK6jH9jSvaXYk9QBAPTMNY8auHEuZllKyZuSxAACVL1Cgg8WeUWVRsmxbH/7Cp/Ttz345kcBJQ0ODrv38J2VxMReqgG1aWj9vucwymyADQFT8MFSTndPbOlepMaI5wyH2331dn7xhs3p7eiOtp5x8c6M+/IVPMSaoIpG+U0ePHtVHP/pR/ehHP5Jpmtq0aZO+9rWvqbGxccz7XHDBBXr44YdHlH34wx/WnXfeGWVTERHTtpRtbVRDrlnt7e2RBU3awkA3znqn9hWO6vfde3VaaydXyGDCHN/To4d2asAr6bnel9WYyuqM2YuUMpnQBQAAqGYXXnW53nzlJerv6Yu13tAP1LC7X6lVnbHWi9q2uHGuOvNtM/648xpmaX3Hcp3WyucVQDIa7axa0g2R1nHtNR/Upj+/Wnf99n61pBvUYGcire+1GluaCJhUmUjfrfe+9716+eWXtW3bNrmuqw984AO69tprtXXr1nHv96EPfUif//znh/9uaIj2S4PqZxqm5mZbVPRdtabzass0cYUMJswNPT184D9V8l091/eyslZKy2Z1chU8AABABLzQVxiGGvCiz2E+JNOajzXPfugHCvYOquCVpDCe8xJrBleEojLZpiU7gnMUyzBJhQqgLti2rabZrWrO5JWPMWiC6hNZ0OSZZ57RfffdpyeeeEKrV6+WJP3d3/2dLr/8cn3lK1/R/Pnzx7xvQ0ODOjomluccAAAAAFAdvNBXtzOgjJlST2lARSsVS7193qAWNbbHFlQo+Y5SknpKBYVWPJPRcT9HoFpkzJQ2dq0ZVQYAwFgiC5o8+uijam1tHQ6YSNL69etlmqYef/xxveMd7xjzvv/8z/+s//W//pc6Ojp0xRVX6LOf/eyYq01KpZJKpdLw3729x/LSua4r1534ZrX1YOj1iON1cT1XQRAoDAIpDBUGwbH3JIz2yn3f8xT6gXzPq+n333M9GX4o+YFCI9pc0MP8QIYfynM9uUZtvbZDn9cgCKQglMxQoR8qjDjPdty8wNcLAwdHlC3Oz5UdcRqy0A9G/LdmJfAdSaQvqAc13N/VmzjHPkPq4ntZL/1dTM+zXsYhoR8OnxdkZOvExuP0jgVrYkmNMeAXdd+LO+R7fmyvq+/5Skm6uGOZmjNjp6eeKUk8x3r5vaRfn1lJ9XmZ109/BaFCxbPSLU5xnnsN9euvL4vyvUyFljZ0nKGCX1JfaVBv61wlOzAiH+vVRT+QlJh/S5J6L0t+fKtrJanou7H/Ridx7jVZk2mbEYbRvGP/43/8D333u9/Vzp07R5TPnTtXt912mz7ykY+Uvd93vvMdLVy4UPPnz9fvfvc7/eVf/qXOOuss/du//VvZ42+99Vbddttto8q3bt1KWq8EFUNP/+E8M6LsyvQpyhrk70PlqZfPa708TwAAqkm9/D7Xy/MEMD76gtrBewmg2hQKBb3nPe9RT0+Pmpubxz120j3Zpz/9aX3pS18a95hnnnlm3NvHc+211w7//+mnn6558+bpoosu0vPPP68TTjhh1PE33XSTNm/ePPx3b2+vOjs7dckll7zhk683rutq27Ztuvjii5VKRbsUdcAr6plnPfW6BR0s9mputlmXnn5JZBvBD3mxcERPd+/VstZOHd8w8xvkVYpeZ1A//NNjasnEt3FVwSupp1TQpoXnqDmdi6XOuAx9Xku+q//sflFZOyWza57MmNJFxMX0XRkvvjiy7Pjon2foBwqf2i/j9A4ZVu3uNZTEdySJvqAe1HJ/V2/iHPsMqYfvZb30d3E9z0oYhziBp2CK19KZhqG0Wf608rWP6/qujJeb5Aaeip6rU1uP16WnRX9+ICX0+SkNKvvMKzrngj/T7IamyOur5e9I0ujXZ1Yl9Hm1LM5zr6TOL6X4+5966AeSUg/v5dBz3HD8CuWt6Mc9Q2zTjPXzmsS512QNZaiaiEkHTW688UZdc8014x6zZMkSdXR06ODBkWlgPM/T0aNHJ7Vfydlnny1J2rVrV9mgSSaTUSYz+gOQSqUq9g1KWhyvTaNl6urF5+rlwW79ofclval5vhozDZGlAQrCQIdLfer2B9XjD6rbH9RC26rZzeDt0D2WG9ky45uEDk2FliE7Zdfcdytl+DJNU2ZoSqYhGYYMy6i5CX5Dx57biLKYnmcoyYjz85qEBL4jifQF9aCG+7t6Fee4sC6+l/XS38X0PCthHPK/D/5BB4s9U7pvZ75N581dWva2Xx/5o/YOHPmvAuPVsYhpyDTNY99NO/rPUCKfn1frse14vie1/B1JGv36zKqEPq/WxXXuleT5Zdz9T130A0mph/fy1efYkm1US7r2syJV8pz8ZNo16aBJe3u72tvb3/C4tWvXqru7W9u3b9eqVaskSQ8++KCCIBgOhEzEjh07JEnz5s2bbFORINu0dFprp5pSORV9R29qnhfpvgmDvqM7d/5UPW5BBwZ79JujL+hNK94Vy5VrAAAAAADgjZky1Z5t1qDnqNHOKmenj02+A1Wg6Dux1mcZhrJWOtY6ARwTWaLBU045RRs2bNCHPvQh3XnnnXJdV9dff73e/e53a/78+ZKkffv26aKLLtI//uM/6qyzztLzzz+vrVu36vLLL1dbW5t+97vf6eMf/7je/OY3a/ny5VE1FQAAAAAQo4yVUo6JIKDu5Oy0PnLypepxCsrbWbVm8spEnM7JDwMdKfaNKGvLNsmq0cwUmHm2aao5nVOvM6iiF98m133eoBY1thM4ARIQ6e5M//zP/6zrr79eF110kUzT1KZ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      "text/plain": [
       "<Figure size 2000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef_fridge = np.quantile(dlt_fridge._posterior_samples['beta'], q=[0.05, 0.5, 0.95], axis=0 )\n",
    "lw=3\n",
    "idx = np.arange(NUM_OF_REGRESSORS)\n",
    "plt.figure(figsize=(20, 8))\n",
    "plt.title(\"Weights of the model\", fontsize=24)\n",
    "plt.plot(coef_fridge[1], color=OrbitPalette.GREEN.value, linewidth=lw,  drawstyle='steps', label=\"Ridge\", alpha=0.5, linestyle='--')\n",
    "plt.fill_between(idx, coef_fridge[0], coef_fridge[2], step='pre', alpha=0.3, color=OrbitPalette.GREEN.value)\n",
    "plt.plot(coefs, color=\"black\", linewidth=lw,  drawstyle='steps', label=\"Ground truth\")\n",
    "plt.legend(prop={'size': 20})\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### LASSO  Penalty\n",
    "\n",
    "In high $P$ to $N$ problems, *LASS0* penalty usually shines compared to *Ridge* penalty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:48.887761Z",
     "start_time": "2021-08-20T23:41:41.277444Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-03-19 23:42:37 - orbit - INFO - Sampling (CmdStanPy) with chains: 4, cores: 8, temperature: 1.000, warmups (per chain): 2000 and samples(per chain): 25.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "529f7ee5150a456584594c6c110fb4d9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 1 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5a2ce24f39ef404d9a8a92bebe3e67c1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 2 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2fe500f476ef48efb198572e987db37c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 3 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ffa432c9a41f40edb2fc0e2fd7c404f4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "chain 4 |          | 00:00 Status"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                                                                                                                                                                                                                                                                                                                \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<orbit.forecaster.full_bayes.FullBayesianForecaster at 0x2a63b9150>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dlt_lasso = DLT(\n",
    "    response_col=response_col,\n",
    "    date_col=dt_col,\n",
    "    regressor_col=x_cols,\n",
    "    seed=SEED,\n",
    "    regression_penalty='lasso',\n",
    "    level_sm_input=0.01,\n",
    "    slope_sm_input=0.01,\n",
    "    num_warmup=8000,\n",
    ")\n",
    "dlt_lasso.fit(df=df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:49.105834Z",
     "start_time": "2021-08-20T23:41:48.890031Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef_lasso = np.quantile(dlt_lasso._posterior_samples['beta'], q=[0.05, 0.5, 0.95], axis=0 )\n",
    "lw=3\n",
    "idx = np.arange(NUM_OF_REGRESSORS)\n",
    "plt.figure(figsize=(20, 8))\n",
    "plt.title(\"Weights of the model\", fontsize=24)\n",
    "plt.plot(coef_lasso[1], color=OrbitPalette.GREEN.value, linewidth=lw,  drawstyle='steps', label=\"Lasso\", alpha=0.5, linestyle='--')\n",
    "plt.fill_between(idx, coef_lasso[0], coef_lasso[2], step='pre', alpha=0.3, color=OrbitPalette.GREEN.value)\n",
    "plt.plot(coefs, color=\"black\", linewidth=lw,  drawstyle='steps', label=\"Ground truth\")\n",
    "plt.legend(prop={'size': 20})\n",
    "plt.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-20T23:41:49.110576Z",
     "start_time": "2021-08-20T23:41:49.107468Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fixed Ridge MSE:0.186\n",
      "LASSO MSE:0.106\n"
     ]
    }
   ],
   "source": [
    "print('Fixed Ridge MSE:{:.3f}\\nLASSO MSE:{:.3f}'.format(\n",
    "    mse(coef_fridge[1], coefs), mse(coef_lasso[1], coefs)\n",
    "))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "This notebook covers a few choices of penalty in regression regularization. A `lasso` and `auto-ridge` can be considered in highly sparse data."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "orbit311",
   "language": "python",
   "name": "orbit311"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  },
  "toc": {
   "base_numbering": 1,
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