{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "84e21b5e",
   "metadata": {},
   "source": [
    "# Homework 6 (Due 11/15/2024 at 11:59pm)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "caee7a09",
   "metadata": {},
   "source": [
    "\n",
    "## Name:\n",
    "\n",
    "## ID:\n",
    "\n",
    "**Submission instruction:**\n",
    "- Download the file as .ipynb (see top right corner on the webpage).\n",
    "- Write your name and ID in the field above.\n",
    "- Answer the questions in the .ipynb file in either markdown or code cells.\n",
    "- Before submission, make sure to rerun all cells by clicking `Kernel` -> `Restart & Run All` and check all the outputs.\n",
    "- Upload the .ipynb file to Gradescope."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32c0348a",
   "metadata": {},
   "source": [
    "**Q1.** How to predict the future? Can we use past temperatures to predict future temperatures? Can we use past stock prices to predict future stock prices? \n",
    "\n",
    "These are examples of time series data. If we collect the temperature data, then we only have a sequence of numbers. Compared with the penguins dataset, it seems that we have very limited number of features. However, in time series data, each observation is linked to previous ones.\n",
    "\n",
    "Let's first generate a synthetic time series data.\n",
    "\n",
    "$$ y = \\sin(2\\pi t/60) + \\exp(t/90) + \\epsilon $$\n",
    "\n",
    "where $\\epsilon$ is a random noise.\n",
    "\n",
    "This is an example of a time series data with a long term trend with seasonality. This could be a model for the temperature data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cd34480f-1141-4dba-81ac-7353c0297bcb",
   "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>Time</th>\n",
       "      <th>Value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1.176405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1.155717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.328256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1.567001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1.638939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>175</td>\n",
       "      <td>6.557907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>176</td>\n",
       "      <td>6.580767</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>177</td>\n",
       "      <td>6.768842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>178</td>\n",
       "      <td>6.973201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>179</td>\n",
       "      <td>7.204629</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>180 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Time     Value\n",
       "0       0  1.176405\n",
       "1       1  1.155717\n",
       "2       2  1.328256\n",
       "3       3  1.567001\n",
       "4       4  1.638939\n",
       "..    ...       ...\n",
       "175   175  6.557907\n",
       "176   176  6.580767\n",
       "177   177  6.768842\n",
       "178   178  6.973201\n",
       "179   179  7.204629\n",
       "\n",
       "[180 rows x 2 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Import necessary libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error\n",
    "\n",
    "\n",
    "np.random.seed(0)  # For reproducibility\n",
    "N = 180\n",
    "t = np.arange(N)\n",
    "value = np.sin(2*np.pi*t/60) + np.random.normal(0, 0.1, N) + np.exp(t/90)\n",
    "df = pd.DataFrame({'Time': t, 'Value': value})\n",
    "df\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ef2eb3a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the time series data\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(df['Time'], df['Value'], label='data')\n",
    "plt.title('data')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Value')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a722093a",
   "metadata": {},
   "source": [
    "One model of time series data is the autoregressive model, which is a linear regression model that uses the previous observations as features.\n",
    "\n",
    "$$ y_{t} = \\beta_0 + \\beta_1 y_{t-1} + \\beta_2 y_{t-2} + \\cdots + \\beta_p y_{t-p}$$\n",
    "\n",
    "where $y_{t-1}, y_{t-2}, \\cdots, y_{t-p}$ are the previous observations (also called lags), and they are used as features to predict the current observation $y_{t}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "50d210bf",
   "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>Time</th>\n",
       "      <th>Value</th>\n",
       "      <th>Value_t-1</th>\n",
       "      <th>Value_t-2</th>\n",
       "      <th>Value_t-3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1.176405</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1.155717</td>\n",
       "      <td>1.176405</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1.328256</td>\n",
       "      <td>1.155717</td>\n",
       "      <td>1.176405</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1.567001</td>\n",
       "      <td>1.328256</td>\n",
       "      <td>1.155717</td>\n",
       "      <td>1.176405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1.638939</td>\n",
       "      <td>1.567001</td>\n",
       "      <td>1.328256</td>\n",
       "      <td>1.155717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>175</td>\n",
       "      <td>6.557907</td>\n",
       "      <td>6.221304</td>\n",
       "      <td>6.101900</td>\n",
       "      <td>6.103135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>176</td>\n",
       "      <td>6.580767</td>\n",
       "      <td>6.557907</td>\n",
       "      <td>6.221304</td>\n",
       "      <td>6.101900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>177</td>\n",
       "      <td>6.768842</td>\n",
       "      <td>6.580767</td>\n",
       "      <td>6.557907</td>\n",
       "      <td>6.221304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>178</td>\n",
       "      <td>6.973201</td>\n",
       "      <td>6.768842</td>\n",
       "      <td>6.580767</td>\n",
       "      <td>6.557907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>179</td>\n",
       "      <td>7.204629</td>\n",
       "      <td>6.973201</td>\n",
       "      <td>6.768842</td>\n",
       "      <td>6.580767</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>180 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Time     Value  Value_t-1  Value_t-2  Value_t-3\n",
       "0       0  1.176405        NaN        NaN        NaN\n",
       "1       1  1.155717   1.176405        NaN        NaN\n",
       "2       2  1.328256   1.155717   1.176405        NaN\n",
       "3       3  1.567001   1.328256   1.155717   1.176405\n",
       "4       4  1.638939   1.567001   1.328256   1.155717\n",
       "..    ...       ...        ...        ...        ...\n",
       "175   175  6.557907   6.221304   6.101900   6.103135\n",
       "176   176  6.580767   6.557907   6.221304   6.101900\n",
       "177   177  6.768842   6.580767   6.557907   6.221304\n",
       "178   178  6.973201   6.768842   6.580767   6.557907\n",
       "179   179  7.204629   6.973201   6.768842   6.580767\n",
       "\n",
       "[180 rows x 5 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create lagged features for t-1 to t-p\n",
    "df_shift = df.copy()\n",
    "\n",
    "p = 3\n",
    "\n",
    "for lag in range(1, p+1):\n",
    "    df_shift[f'Value_t-{lag}'] = df_shift['Value'].shift(lag)\n",
    "\n",
    "df_shift\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9dc7381c",
   "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>Time</th>\n",
       "      <th>Value</th>\n",
       "      <th>Value_t-1</th>\n",
       "      <th>Value_t-2</th>\n",
       "      <th>Value_t-3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1.567001</td>\n",
       "      <td>1.328256</td>\n",
       "      <td>1.155717</td>\n",
       "      <td>1.176405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1.638939</td>\n",
       "      <td>1.567001</td>\n",
       "      <td>1.328256</td>\n",
       "      <td>1.155717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>1.459400</td>\n",
       "      <td>1.638939</td>\n",
       "      <td>1.567001</td>\n",
       "      <td>1.328256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1.751733</td>\n",
       "      <td>1.459400</td>\n",
       "      <td>1.638939</td>\n",
       "      <td>1.567001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>1.734877</td>\n",
       "      <td>1.751733</td>\n",
       "      <td>1.459400</td>\n",
       "      <td>1.638939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>175</th>\n",
       "      <td>175</td>\n",
       "      <td>6.557907</td>\n",
       "      <td>6.221304</td>\n",
       "      <td>6.101900</td>\n",
       "      <td>6.103135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>176</td>\n",
       "      <td>6.580767</td>\n",
       "      <td>6.557907</td>\n",
       "      <td>6.221304</td>\n",
       "      <td>6.101900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>177</td>\n",
       "      <td>6.768842</td>\n",
       "      <td>6.580767</td>\n",
       "      <td>6.557907</td>\n",
       "      <td>6.221304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>178</th>\n",
       "      <td>178</td>\n",
       "      <td>6.973201</td>\n",
       "      <td>6.768842</td>\n",
       "      <td>6.580767</td>\n",
       "      <td>6.557907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>179</th>\n",
       "      <td>179</td>\n",
       "      <td>7.204629</td>\n",
       "      <td>6.973201</td>\n",
       "      <td>6.768842</td>\n",
       "      <td>6.580767</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>177 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     Time     Value  Value_t-1  Value_t-2  Value_t-3\n",
       "3       3  1.567001   1.328256   1.155717   1.176405\n",
       "4       4  1.638939   1.567001   1.328256   1.155717\n",
       "5       5  1.459400   1.638939   1.567001   1.328256\n",
       "6       6  1.751733   1.459400   1.638939   1.567001\n",
       "7       7  1.734877   1.751733   1.459400   1.638939\n",
       "..    ...       ...        ...        ...        ...\n",
       "175   175  6.557907   6.221304   6.101900   6.103135\n",
       "176   176  6.580767   6.557907   6.221304   6.101900\n",
       "177   177  6.768842   6.580767   6.557907   6.221304\n",
       "178   178  6.973201   6.768842   6.580767   6.557907\n",
       "179   179  7.204629   6.973201   6.768842   6.580767\n",
       "\n",
       "[177 rows x 5 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Drop rows with NaN values\n",
    "df_shift = df_shift.dropna()\n",
    "df_shift"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ed8c82c",
   "metadata": {},
   "source": [
    "(1) Split the data into train and test sets. Instead of splitting the data randomly as we did in the penguins dataset, we will split the data in a sequential manner.\n",
    "\n",
    "We will use the first 50% of the data for training and the remaining 50% for testing.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8e4a78e0",
   "metadata": {
    "tags": [
     "sol"
    ]
   },
   "outputs": [],
   "source": [
    "# Define the split index\n",
    "split_index = int(len(df_shift) * 0.5)\n",
    "\n",
    "# Split the dataset into training and testing sets\n",
    "train_df = df_shift.iloc[:split_index]\n",
    "test_df = df_shift.iloc[split_index:]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "530a5304",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16a13f0e0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example code to plot the training and testing sets\n",
    "# need to save the training and testing dataframe as variable names train_df and test_df\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(train_df['Time'], train_df['Value'], label='Training')\n",
    "plt.plot(test_df['Time'], test_df['Value'], label='Testing')\n",
    "plt.title('Training and Testing Sets')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Value')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab75a4e8",
   "metadata": {},
   "source": [
    "(2) Fit a linear regression model to the training data and make prediction on the test data. That is, use the features `Value_t-1` ... `Value_t-p` to predict `Value`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e710f59a",
   "metadata": {
    "tags": [
     "sol"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error: 0.029921841615967348\n"
     ]
    }
   ],
   "source": [
    "\n",
    "features = [f'Value_t-{lag}' for lag in range(1, p+1)]\n",
    "target = ['Value']\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(train_df[features], train_df[target])\n",
    "predictions = model.predict(test_df[features])\n",
    "\n",
    "err = mean_squared_error(test_df[target], predictions)\n",
    "print(f'Mean Squared Error: {err}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7f524c9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example code for plotting the actual and predicted values\n",
    "# Save the predictions on the test data in a variable called `prediction` for visualization.\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(train_df['Time'], train_df['Value'], label=f'Training')\n",
    "plt.plot(test_df['Time'], test_df['Value'], label=f'Testing')\n",
    "plt.plot(test_df['Time'], predictions, label=f'Predicted')\n",
    "plt.title(f'Actual vs Predicted Values for {target}')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Value')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0de2ac16",
   "metadata": {},
   "source": [
    "(3) Try different values of p. How does the model performance change?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98ec2282",
   "metadata": {
    "tags": [
     "sol"
    ]
   },
   "source": [
    "As p increase, the testing error decrease and then increase. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ff5c37a",
   "metadata": {},
   "source": [
    "**Q2** \n",
    "\n",
    "Sometimes the number of features can be much larger than the number of samples. This is called the high-dimensional dataset.\n",
    "\n",
    "In this problem, we compare Lasso and Ridge regression on a synthetic high-dimensional dataset with n = 20 and p = 100.\n",
    "\n",
    "Each feature vector $X_0$, ... $X_{99}$ is generated from a normal distribution with mean 0 and standard deviation 1.\n",
    "\n",
    "The true model is\n",
    "\n",
    "$$ y = 3X_0 - 2X_1 + 5 X_2 $$\n",
    "\n",
    "That is, only a small number of features are actually relevant to the target variable $y$. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f8a29ca6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# DO NOT modify this cell\n",
    "# Generate synthetic high-dimensional data\n",
    "import numpy as np\n",
    "from sklearn.linear_model import Lasso, Ridge\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "np.random.seed(0)\n",
    "n = 20  # number of observations\n",
    "p = 100  # number of features\n",
    "X = np.random.randn(n, p)\n",
    "true_coef = np.concatenate([np.array([3, -2, 5]), np.zeros(p - 3)])\n",
    "y = np.dot(X, true_coef)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8f5a076",
   "metadata": {},
   "source": [
    "\n",
    "(1) Fit a Lasso and a Ridge regression model to this dataset without the intercept term and use $\\alpha=0.1$. Compute and compare the means square error of the two models. Which model has a smaller MSE?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4f97ca83",
   "metadata": {
    "tags": [
     "sol"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lasso Mean Squared Error: 0.03250277108009776\n",
      "Ridge Mean Squared Error: 5.223539906925877e-05\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Lasso Regression\n",
    "lasso = Lasso(alpha=0.1, fit_intercept=False)\n",
    "lasso.fit(X, y)\n",
    "\n",
    "# Ridge Regression\n",
    "ridge = Ridge(alpha=0.1, fit_intercept=False)\n",
    "ridge.fit(X, y)\n",
    "\n",
    "print(\"Lasso Mean Squared Error:\", mean_squared_error(y, lasso.predict(X)))\n",
    "print(\"Ridge Mean Squared Error:\", mean_squared_error(y, ridge.predict(X)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "654a89be",
   "metadata": {},
   "source": [
    "(2) Collect the coefficents of the two models. Make a bar plot of the coefficients of the two models. That is, draw a bar of length $\\beta_i$ at position i (sample plot shown below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bf7f69ad",
   "metadata": {
    "tags": [
     "sol",
     "keep"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16a2b0dd0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "lasso_coef = lasso.coef_\n",
    "ridge_coef = ridge.coef_\n",
    "\n",
    "plt.bar(range(len(lasso_coef)), lasso_coef, label='Lasso')\n",
    "plt.bar(range(len(ridge_coef)), ridge_coef, label='Ridge')\n",
    "plt.title('Lasso vs Ridge Coefficients')\n",
    "plt.legend()\n",
    "\n",
    "# Lasso is preferred in this case. While it has a higher MSE than ridge, it can recover the true coefficients by setting the irrelevant coefficients to zero. \n",
    "# Ridge, on the other hand, will make all coefficients small but non-zero."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce750fa2",
   "metadata": {},
   "source": [
    "(3) Which model is preferred in this case, and why?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e806429e",
   "metadata": {
    "tags": [
     "sol"
    ]
   },
   "source": [
    "Lasso is preferred in this case. While it has a higher MSE than ridge, it can recover the true coefficients by setting the irrelevant coefficients to zero. \n",
    "Ridge, on the other hand, will make all coefficients small but non-zero."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "math10",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}