line_regression.ipynb

{
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   "source": [
    "## 1. Line regression"
   ]
  },
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   "source": [
    "### 1.1 Ordinary Least Squares (OLS) Perspective"
   ]
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   "source": [
    "#### 1.1.1 Model Representation:"
   ]
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   "source": [
    "The linear regression model is represented as:\n",
    "$$\n",
    "\\hat{Y} = X\\theta\n",
    "$$\n",
    "where:\n",
    "- $ X $ is the design matrix with dimensions $ n \\times (m+1) $ (including the intercept term).\n",
    "- $ \\theta$ is the parameter vector with dimensions $ (m+1) \\times 1 $.\n"
   ]
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   "source": [
    "#### 1.1.2 Loss Function:"
   ]
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   "source": [
    "The mean squared error (MSE) is given by:\n",
    "- No regularization\n",
    "$$\n",
    "J(\\theta) = \\frac{1}{n}(X\\theta - Y)^T(X\\theta - Y)\n",
    "$$\n",
    "- L1 regularization\n",
    "$$\n",
    "J(\\theta) = \\frac{1}{n}(X\\theta - Y)^T(X\\theta - Y) + \\lambda \\|\\mathbf{\\theta}\\|_1\n",
    "$$\n",
    "- L2 regularization\n",
    "$$\n",
    "J(\\theta) = \\frac{1}{n}(X\\theta - Y)^T(X\\theta - Y) + \\lambda\\theta^T\\theta\n",
    "$$"
   ]
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   "source": [
    "#### 1.1.3 Objective:"
   ]
  },
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   "source": [
    "Given a dataset with $n$ samples and $m$ features, we want to find the parameter vector $\\theta$ that minimizes the mean squared error (MSE) between predicted values $\\hat{Y}$ and actual values $y$.\n",
    "$$\n",
    "\\theta = \\arg\\min_\\theta{J(\\theta)}\n",
    "$$"
   ]
  },
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   "source": [
    "#### 1.1.4 Solution:"
   ]
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    "1. **Gradient of $\\theta$:**\n",
    "    - No regularization\n",
    "$$\n",
    "\\frac{\\partial J}{\\partial \\theta} = \\frac{2}{n}X^T(X\\theta - Y)\n",
    "$$\n",
    "    - L1 regularization\n",
    "$$\n",
    "\\frac{\\partial J}{\\partial \\theta} = \\frac{2}{n}X^T(X\\theta - Y)+\\lambda \\text{sign}(\\mathbf{\\theta})\n",
    "$$\n",
    "    - L2 regularization\n",
    "$$\n",
    "\\frac{\\partial J}{\\partial \\theta} = \\frac{2}{n}X^T(X\\theta - Y)+2\\lambda\\theta\n",
    "$$\n",
    "2. **Closed-Form for $\\theta$:**\n",
    "    - No regularization\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "& \\frac{2}{n}X^T(X\\theta - T) = 0 \\\\\n",
    "& X^TX\\theta - X^TY = 0 \\\\\n",
    "& \\theta = (X^TX)^{-1}X^TY\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "    - L1 regularization\n",
    "    \n",
    "    The closed-form solution for OLS with L1 penalty doesn't have a direct analytical solution due to the non-differentiability of the L1 norm. However, it can be solved using optimization algorithms like coordinate descent or proximal gradient descent. These algorithms iteratively update the coefficients until convergence.\n",
    "    \n",
    "    - L2 regularization\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "& \\frac{2}{n}X^T(X\\theta - Y)+2\\lambda\\theta = 0 \\\\\n",
    "& (X^TX+\\lambda n I)\\theta = X^TY \\\\\n",
    "& \\theta = (X^T X + \\lambda n I)^{-1} X^TY\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$"
   ]
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   "source": [
    "### 1.2 Maximum Likelihood Estimation Perspective"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70c1b221-2439-40d2-a060-123fea2aaf04",
   "metadata": {},
   "source": [
    "#### 1.2.1 Model Representation:"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "The linear regression model is represented as:\n",
    "$$\n",
    "\\mathbf{y}^{(i)} = \\mathbf{x}^{(i)T}\\theta + \\epsilon\n",
    "$$\n",
    "where:\n",
    "- $\\mathbf{x}^{(i)}$ is the $i$th example which is a vector with dimensions $ (m+1) \\times 1 $. (including the intercept term).\n",
    "- $\\theta$ is the parameter vector with dimensions $ (m+1) \\times 1 $.\n",
    "- $\\epsilon $ is the error term assumed to be normally distributed with mean zero and variance $ \\sigma^2 $, that is  $\\epsilon\\sim{N(0,\\sigma^2)}$.\n",
    "- $\\mathbf{y}^{(i)}|\\mathbf{x}^{(i)},\\theta\\sim{N(\\mathbf{x}^{(i)T}\\theta,\\sigma^2)}$."
   ]
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   "source": [
    "#### 1.2.2 Likelihood and posterior Function:"
   ]
  },
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   "source": [
    "Under the assumption of Gaussian errors, the likelihood function of the observed data is given by the product of the probability density functions of the individual observations:\n",
    "- No regularization\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "P(X,Y|\\theta) &= P(Y|X,\\theta)*P(X|\\theta) \\\\\n",
    "&\\propto P(Y|X,\\theta) \\\\\n",
    "& = \\prod_{i=1}^{n} \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left(-\\frac{(\\mathbf{y}^{(i)} - \\mathbf{x}^{(i)}\\theta)^2}{2\\sigma^2}\\right) \\\\\n",
    "& = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp{\\left(-\\frac{\\sum_{i=1}^{n} (\\mathbf{y}^{(i)} - \\mathbf{x}^{(i)}\\theta)^2}{2\\sigma^2}\\right)} \\\\\n",
    "& = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp{\\left(-\\frac{(X\\theta - Y)^T(X\\theta - Y)}{2\\sigma^2}\\right)}\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "- L1 regularization\n",
    "\n",
    "We assume $\\theta\\sim{Laplace(0,b)}$, so the priori probability of $\\theta$ is\n",
    "$$\n",
    "P(\\theta) = \\frac{1}{2b}\\exp{(-\\frac{\\left|\\theta\\right|}{b})}\n",
    "$$\n",
    "The posterior probability of $\\theta$ is\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "P(\\theta|X,Y) &= \\frac{P(X,Y,\\theta)}{P(X,Y)} \\\\\n",
    "& \\propto P(X,Y,\\theta) \\\\\n",
    "& = P(Y|X,\\theta)*P(X|\\theta)*P(\\theta) \\\\\n",
    "& \\propto P(Y|X,\\theta)*P(\\theta) \\\\\n",
    "& = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp{\\left(-\\frac{(X\\theta - Y)^T(X\\theta - Y)}{2\\sigma^2}\\right)} * \\frac{1}{2b}\\exp{(-\\frac{\\left|\\theta\\right|}{b})} \\\\\n",
    "& = \\frac{1}{2b\\sqrt{2\\pi\\sigma^2}} \\exp{\\left(-\\frac{(X\\theta - Y)^T(X\\theta - Y)+\\frac{2\\sigma^2}{b}\\left|\\theta\\right|}{2\\sigma^2}\\right)}\\\\\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "- L2 regularization\n",
    "\n",
    "We assume $\\theta\\sim{N(0,\\Sigma)}$, so the priori probability of $\\theta$ is\n",
    "$$\n",
    "P(\\theta) = \\frac{1}{(\\sqrt{2\\pi})^m\\left|\\Sigma\\right|^\\frac{1}{2}}\\exp{(-\\frac{\\theta^T\\Sigma^{-1}\\theta}{2})}\n",
    "$$\n",
    "The posterior probability of $\\theta$ is\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "P(\\theta|X,Y) & \\propto P(Y|X,\\theta)*P(\\theta) \\\\\n",
    "& = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp{\\left(-\\frac{(X\\theta - Y)^T(X\\theta - Y)}{2\\sigma^2}\\right)} * \\frac{1}{(\\sqrt{2\\pi})^m\\left|\\Sigma\\right|^\\frac{1}{2}}\\exp{(-\\frac{\\theta^T\\Sigma^{-1}\\theta}{2})} \\\\\n",
    "&\\propto \\exp{\\left(-\\frac{(X\\theta - Y)^T(X\\theta - Y)+\\sigma^2\\theta^T\\Sigma^{-1}\\theta}{2\\sigma^2}\\right)}\\\\\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$"
   ]
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   "source": [
    "#### 1.2.3 Objective:"
   ]
  },
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   "source": [
    "We seek to find the parameter vector $\\theta$ that maximizes the likelihood or posterior function of the observed data\n",
    "- No regularization\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\theta &= \\arg\\max_\\theta{P(X,Y|\\theta)}\\\\\n",
    "&=\\arg\\min_\\theta{(X\\theta - Y)^T(X\\theta - Y)}\\\\\n",
    "&= \\arg\\min_\\theta{J(\\theta)}\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "- L1 regularization\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\theta &= \\arg\\max_\\theta{P(\\theta|X,Y)}\\\\\n",
    "&=\\arg\\min_\\theta{(X\\theta - Y)^T(X\\theta - Y)}+\\frac{2\\sigma^2}{b}\\left|\\theta\\right|\\\\\n",
    "&=\\arg\\min_\\theta{(X\\theta - Y)^T(X\\theta - Y)}+\\lambda\\left|\\theta\\right|= \\arg\\min_\\theta{J(\\theta)}\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "- L2 regularization\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\theta &= \\arg\\max_\\theta{P(\\theta|X,Y)}\\\\\n",
    "&=\\arg\\min_\\theta{(X\\theta - Y)^T(X\\theta - Y)}+\\sigma^2\\theta^T\\Sigma^{-1}\\theta\\\\\n",
    "&=\\arg\\min_\\theta{(X\\theta - Y)^T(X\\theta - Y)}+\\lambda\\theta^T\\theta= \\arg\\min_\\theta{J(\\theta)}\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "Although the object function is different, the form is the same with OLS."
   ]
  },
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   "source": [
    "### 1.3. Column space Perspective"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "![](https://pic1.zhimg.com/80/v2-437c1820680c560b2a7096977ce2e3a1_1440w.webp?source=1def8aca)\n",
    "If we take $X\\theta$ as a vector from the column space of $X$, then $X\\theta - Y$ is the residual vector, and $(X\\theta - Y)^T(X\\theta - Y)$ is the square of residual vector magnitude. So Minimizing MSE is equivalent to find the shortest residual vector which is orthogonal to the column space, that is:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "& X^T(X\\theta - Y) = 0 \\\\\n",
    "& X^TX\\theta =X^TY \\\\\n",
    "& \\theta = (X^TX)^{-1}X^TY\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n"
   ]
  },
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   "execution_count": 1,
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "class LinearRegression:\n",
    "    def __init__(self, lr=0.01, epochs=1000, method='closed_form', reg=None, alpha=0.01):\n",
    "        self.lr = lr  # Learning rate\n",
    "        self.epochs = epochs  # Number of iterations\n",
    "        self.method = method  # Method: 'closed_form' for closed-form solution, 'gradient_descent' for gradient descent\n",
    "        self.theta = None  # Parameters\n",
    "        self.reg = reg  # Regularization method: None (no penalty), 'l1' (L1 regularization), 'l2' (L2 regularization)\n",
    "        self.alpha = alpha  # Regularization parameter\n",
    "        self.loss_history = [] # Loss record\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        # Add bias term\n",
    "        X_b = np.c_[np.ones((X.shape[0], 1)), X]\n",
    "\n",
    "        if self.method == 'closed_form':\n",
    "            # Closed-form solution\n",
    "            if self.reg is None:\n",
    "                # No regularization\n",
    "                self.theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)\n",
    "            elif self.reg == 'l1':\n",
    "                # L1 regularization (Lasso)\n",
    "                L = np.eye(X_b.shape[1])\n",
    "                L[0, 0] = 0  # No penalty for the bias term\n",
    "                self.theta = np.linalg.inv(X_b.T.dot(X_b) + self.alpha * L).dot(X_b.T).dot(y)\n",
    "            elif self.reg == 'l2':\n",
    "                # L2 regularization (Ridge)\n",
    "                self.theta = np.linalg.inv(X_b.T.dot(X_b) + self.alpha * np.eye(X_b.shape[1])).dot(X_b.T).dot(y)\n",
    "        elif self.method == 'gradient_descent':\n",
    "            # Initialize parameters\n",
    "            self.theta = np.random.randn(X_b.shape[1], 1)\n",
    "            # Gradient descent\n",
    "            for _ in range(self.epochs):\n",
    "                gradients = 2 / len(X_b) * X_b.T.dot(X_b.dot(self.theta) - y)\n",
    "                if self.reg == 'l1':\n",
    "                    # L1 regularization (Lasso)\n",
    "                    gradients[1:] += self.alpha * np.sign(self.theta[1:])\n",
    "                elif self.reg == 'l2':\n",
    "                    # L2 regularization (Ridge)\n",
    "                    gradients[1:] += 2 * self.alpha * self.theta[1:]\n",
    "                self.theta -= self.lr * gradients\n",
    "                loss = np.mean((X_b.dot(self.theta) - y) ** 2)\n",
    "                self.loss_history.append(loss)\n",
    "        else:\n",
    "            raise ValueError(\"Unsupported method. Choose 'closed_form' or 'gradient_descent'.\")\n",
    "\n",
    "    def predict(self, X):\n",
    "        # Add bias term\n",
    "        X_b = np.c_[np.ones((X.shape[0], 1)), X]\n",
    "        return X_b.dot(self.theta)\n"
   ]
  },
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>solution</th>\n",
       "      <th>w</th>\n",
       "      <th>b</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>closed_form_None</td>\n",
       "      <td>1.301655</td>\n",
       "      <td>11.848666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>closed_form_l1</td>\n",
       "      <td>4.199940</td>\n",
       "      <td>6.070421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>closed_form_l2</td>\n",
       "      <td>3.450970</td>\n",
       "      <td>6.914557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>gradient_descent_None</td>\n",
       "      <td>2.157985</td>\n",
       "      <td>10.274356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>gradient_descent_l1</td>\n",
       "      <td>7.233404</td>\n",
       "      <td>0.119167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>gradient_descent_l2</td>\n",
       "      <td>7.186451</td>\n",
       "      <td>0.116280</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "                solution         w          b\n",
       "0       closed_form_None  1.301655  11.848666\n",
       "1         closed_form_l1  4.199940   6.070421\n",
       "2         closed_form_l2  3.450970   6.914557\n",
       "3  gradient_descent_None  2.157985  10.274356\n",
       "4    gradient_descent_l1  7.233404   0.119167\n",
       "5    gradient_descent_l2  7.186451   0.116280"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate some random data\n",
    "np.random.seed(42)\n",
    "X_org = np.random.rand(100, 1)\n",
    "# Introduce outliers\n",
    "# X = np.linspace(0,100,100)\n",
    "y_org = 4 + 3 * X_org + np.random.randn(100, 1)\n",
    "X_outliers = np.array([[1], [1.01], [1.02],[1.03], [1.04], [1.05]])\n",
    "y_outliers = np.array([[30], [35], [39],[40], [41], [42]])\n",
    "X = np.vstack((X_org, X_outliers))\n",
    "y = np.vstack((y_org, y_outliers))\n",
    "methods = ['closed_form','gradient_descent']\n",
    "regs = [None,'l1','l2']\n",
    "# Instantiate and fit the models\n",
    "# No penalty (ordinary linear regression)\n",
    "models = {}\n",
    "for m in methods:\n",
    "    for r in regs:\n",
    "        models['{}_{}'.format(m,r)] = LinearRegression(method=m,reg=r,alpha=10)\n",
    "        models['{}_{}'.format(m,r)].fit(X,y)\n",
    "w, b = [], []\n",
    "for k in models:\n",
    "    p = models[k].theta.ravel()\n",
    "    w.append(p[0])\n",
    "    b.append(p[1])\n",
    "df = pd.DataFrame({'solution':list(models.keys()),'w':w,'b':b})\n",
    "df"
   ]
  },
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    {
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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize data and fitted models\n",
    "plt.figure(figsize=(10, 5))\n",
    "\n",
    "# Scatter plot of original data\n",
    "plt.scatter(X, y, color='blue', label='Original data')\n",
    "\n",
    "# Fitted lines for closed-form solution and gradient descent\n",
    "for m in methods:\n",
    "    for r in regs:\n",
    "        plt.plot(X, models['{}_{}'.format(m,r)].predict(X), label='{}_{}'.format(m,r))\n",
    "# plt.plot(X, lin_reg_no_penalty_gd.predict(X), color='red', label='Gradient descent')\n",
    "\n",
    "plt.title('Linear Regression')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a4671845-8188-46d5-8b72-8dd530a0de23",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot loss change during gradient descent\n",
    "plt.figure(figsize=(8, 5))\n",
    "for r in regs:\n",
    "    # plt.plot(X, models['{}_{}'.format(m,r)].predict(X), label='{}_{}'.format(m,r))\n",
    "    plt.plot(range(len(models['{}_{}'.format(methods[1],r)].loss_history)), \n",
    "             models['{}_{}'.format(methods[1],r)].loss_history, \n",
    "             label='{}_{}'.format(methods[1],r))\n",
    "plt.title('Gradient Descent Loss')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel('Loss')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3822b77c-3585-46c6-ae63-c6bc234c457e",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 2. Bayesian Line regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17268b35-5184-4804-bdeb-f3a27afb97e0",
   "metadata": {},
   "source": [
    "Bayesian regression is a probabilistic approach to regression analysis that incorporates prior knowledge about the model parameters into the modeling process. Unlike classical regression methods, Bayesian regression provides a framework for modeling uncertainty in the parameters and making probabilistic predictions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ec0b9b7-53c2-453c-a194-b774448c5f53",
   "metadata": {
    "tags": []
   },
   "source": [
    "### 2.1 Model Representation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b611619f-0d06-4962-a816-ace584bae084",
   "metadata": {},
   "source": [
    "In Bayesian regression, we model the relationship between the independent variables $X$ and the dependent variable $Y$ using a probabilistic model. The key components of the model are:\n",
    "\n",
    "- **Likelihood**: This represents the conditional distribution of the dependent variable $y$ given the independent variables $X$ and the model parameters $\\theta$. It is typically assumed to be Gaussian:\n",
    "\n",
    "$$\n",
    "p(Y|X, \\theta) = \\mathcal{N}(X\\theta, \\sigma^2 I)\n",
    "$$\n",
    "\n",
    "- **Prior**: This represents our beliefs about the distribution of the model parameters $\\theta$ before observing any data. It is specified as a probability distribution, often chosen to be a Gaussian distribution:\n",
    "\n",
    "$$\n",
    "p(\\theta) = \\mathcal{N}(\\mu, \\Sigma)\n",
    "$$\n",
    "\n",
    "3. **Posterior**: This represents the updated beliefs about the parameters after observing the data $X$ and $Y$. According to Bayes' theorem, the posterior is proportional to the likelihood times the prior:\n",
    "\n",
    "$$\n",
    "p(\\theta|X, Y) \\propto p(Y|X, \\theta) \\cdot p(\\theta)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7de51603-5ce1-43aa-9693-31e44cedb3bd",
   "metadata": {
    "tags": []
   },
   "source": [
    "### 2.2 Model Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66a2ae14-f24a-44dd-81d0-72a73495cd7f",
   "metadata": {},
   "source": [
    "The goal of learning in Bayesian regression is to estimate the posterior distribution of the model parameters $\\theta$ given the observed data $X$ and $Y$. This involves updating the prior distribution using Bayes' theorem to obtain the posterior distribution.\n",
    "\n",
    "According to the problem description, assuming the prior distribution is a multivariate Gaussian distribution $N(\\mu, \\Sigma)$, hence:\n",
    "\n",
    "$$\n",
    "p(\\theta) = \\frac{1}{\\sqrt{(2\\pi)^p \\lvert \\Sigma \\rvert}} \\exp\\left(-\\frac{1}{2}(\\theta - \\mu)^T \\Sigma^{-1} (\\theta - \\mu)\\right)\n",
    "$$\n",
    "\n",
    "The likelihood function is given by:\n",
    "\n",
    "$$\n",
    "p(Y|X, \\theta) = \\frac{1}{\\sqrt{(2\\pi)^n\\sigma^2}} \\exp\\left(-\\frac{1}{2\\sigma^2}(Y - X\\theta)^T(Y - X\\theta)\\right)\n",
    "$$\n",
    "\n",
    "Therefore, the expression for the posterior probability is:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "p(\\theta|X, Y) & \\propto \\exp\\left(-\\frac{1}{2}\\left[\\sigma^{-2}(Y - X\\theta)^T(Y - X\\theta) + (\\theta - \\mu)^T \\Sigma^{-1} (\\theta - \\mu)\\right]\\right) \\\\\n",
    "& \\propto \\exp(-\\frac{1}{2}[\\theta^T(\\frac{X^TX}{\\sigma^2}+\\Sigma^{-1})\\theta-2\\theta^T(\\frac{X^TY}{\\sigma^2}+\\Sigma^{-1}\\mu)])\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "As both the prior distribution $p(\\theta)$ and the likelihood function $p(Y|X, \\theta)$ are Gaussian distributions, then the posterior probability will be a Gaussian distribution. In this case, we can calculate the mean and variance of the posterior probability. If we assume posterior probability is a multivariate Gaussian distribution $N(\\mu_{\\text{post}}, \\Sigma_{\\text{post}})$, hence:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "p(\\theta|X, Y) &= \\frac{1}{\\sqrt{(2\\pi)^p \\lvert \\Sigma_{\\text{post}} \\rvert}} \\exp\\left(-\\frac{1}{2}(\\theta - \\mu_{\\text{post}})^T \\Sigma_{\\text{post}}^{-1} (\\theta - \\mu_{\\text{post}})\\right) \\\\\n",
    "&= \\frac{1}{\\sqrt{(2\\pi)^p \\lvert \\Sigma_{\\text{post}} \\rvert}} \\exp\\left(-\\frac{1}{2}[\\theta^T\\Sigma_{\\text{post}}^{-1}\\theta-2\\theta^T\\Sigma_{\\text{post}}^{-1}\\mu_{\\text{post}}+\\mu_{\\text{post}}^T\\Sigma_{\\text{post}}^{-1}\\mu_{\\text{post}}]\\right) \\\\\n",
    "& \\propto \\exp(-\\frac{1}{2}[\\theta^T(\\frac{X^TX}{\\sigma^2}+\\Sigma^{-1})\\theta-2\\theta^T(\\frac{X^TY}{\\sigma^2}+\\Sigma^{-1}\\mu)])\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "So the covariance matrix $\\Sigma_{\\text{post}}$ of the posterior distribution:\n",
    "\n",
    "$$\n",
    "\\Sigma_{\\text{post}} = (\\frac{X^TX}{\\sigma^2}+\\Sigma^{-1})^{-1}\n",
    "$$\n",
    "\n",
    "The mean vector $\\mu_{\\text{post}}$ of the posterior distribution:\n",
    "\n",
    "$$\n",
    "\\mu_{\\text{post}} = \\Sigma_{\\text{post}}(\\frac{X^TY}{\\sigma^2}+\\Sigma^{-1}\\mu)\n",
    "$$\n",
    "\n",
    "That is\n",
    "\n",
    "$$\n",
    "p(\\theta|X, Y) \\sim N(\\Sigma_{\\text{post}}(\\frac{X^TY}{\\sigma^2}+\\Sigma^{-1}\\mu),(\\frac{X^TX}{\\sigma^2}+\\Sigma^{-1})^{-1})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "facfa84a-eb60-4a2f-95fd-f14c580458f0",
   "metadata": {},
   "source": [
    "### 2.3 Model Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77283a5a-482f-4f00-8a0b-6703be055707",
   "metadata": {},
   "source": [
    "The prediction of Bayesian linear regression is to get the predictive distribution of target value $\\mathbf{y_*}$ when given input feature vector $\\mathbf{x_*}$ which can be obtained from the posterior probability distribution. As the predictive distribution can be represented as a Gaussian distribution, it can be written as:\n",
    "\n",
    "$$\n",
    "p(\\mathbf{y_*} | \\mathbf{x_*}, X, Y, \\alpha) = \\mathcal{N}(\\mu_*, \\sigma_*^2)\n",
    "$$\n",
    "\n",
    "$\\mu_*$ is the mean of the predicted target value $y_*$, and $\\sigma_*^2$ is the variance of the predicted target value $\\mathbf{y_*}$, which can be calculated using the following formulas:\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\mu_* &= \\mathbb{E}[\\mathbf{y_*}] \\\\\n",
    "&= \\mathbb{E}[\\mathbf{x_*}^T\\theta_{\\text{post}} + \\epsilon] \\\\\n",
    "&=\\mathbf{x_*}^T \\mathbb{E}[\\theta_{\\text{post}}] \\\\\n",
    "&=\\mathbf{x_*}^T\\mu_{\\text{post}}\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\sigma_*^2 &= \\text{Var}[\\mathbf{y_*}] \\\\\n",
    "&= \\text{Var}[\\mathbf{x_*}^T\\theta_{\\text{post}} + \\epsilon] \\\\\n",
    "&= \\text{Var}[\\mathbf{x_*}^T\\theta_{\\text{post}}] + \\text{Var}[\\epsilon] \\\\\n",
    "&= \\mathbf{x_*}^T\\text{Var}[\\theta_{\\text{post}}]\\mathbf{x_*} + \\sigma^2  \\\\\n",
    "&= \\sigma^2  + \\mathbf{x_*}^T \\Sigma_{\\text{post}} \\mathbf{x_*} \n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "where:\n",
    "\n",
    "- $\\mathbf{x_*}$ is the new input feature vector.\n",
    "- $\\mu_{\\text{post}}$ is the expected value of the posterior probability distribution of the parameter vector.\n",
    "- $\\Sigma_{\\text{post}}$ is the variance-covariance matrix of the posterior probability distribution of the parameter vector.\n",
    "- $\\epsilon $ is the error term assumed to be normally distributed with mean zero and variance $ \\sigma^2 $, that is  $\\epsilon\\sim{N(0,\\sigma^2)}$.\n",
    "\n",
    "Thus, we obtain the mean $\\mu_*$ and variance $\\sigma_*^2$ of the predictive distribution, and consequently, the probability density function of the predictive distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c0023a4-4f34-4a28-bdff-ed4495d6f239",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "19222054-70b8-4843-ae5c-569a961dc7fc",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_line(w, c, label=None):\n",
    "    # Generate evenly spaced points between 0 and 1\n",
    "    x = np.linspace(0, 1, 100).reshape(-1, 1)\n",
    "    # Add bias term to the input features\n",
    "    x_b = np.c_[np.ones((x.shape[0], 1)), x]\n",
    "    # Calculate predicted values\n",
    "    y = x_b.dot(w)\n",
    "    # Plot the line\n",
    "    plt.plot(x, y, c=c, label=label)\n",
    "\n",
    "def bayes_pred(sigma,mean_posterior,theta_sigma_posterior,x):\n",
    "    x_b = np.c_[np.ones((x.shape[0], 1)), x]\n",
    "    y_pred_mean = x_b.dot(mean_posterior)\n",
    "    y_pred_std = np.sqrt([sigma + x_b[i].dot(theta_sigma_posterior).dot(x_b[i].T) for i in range(len(x_b))]).reshape(-1, 1)\n",
    "    return y_pred_mean,y_pred_std\n",
    "    \n",
    "def bayes_lr(sigma, X_b, y, theta_mu, theta_sigma_prior):\n",
    "    # Compute posterior covariance matrix\n",
    "    theta_sigma_posterior = np.linalg.inv(np.linalg.inv(theta_sigma_prior) + np.dot(X_b.T, X_b) / sigma**2)\n",
    "    # Compute posterior mean\n",
    "    mean_posterior = theta_sigma_posterior.dot(np.dot(X_b.T, y) / sigma**2 + np.linalg.inv(theta_sigma_prior).dot(theta_mu))\n",
    "    return mean_posterior, theta_sigma_posterior\n",
    "\n",
    "# Define parameters\n",
    "sigma = 1\n",
    "X_b = np.c_[np.ones((X.shape[0], 1)), X]\n",
    "theta_mu = np.zeros(X_b.shape[1]).reshape(-1, 1)\n",
    "theta_sigma_prior = 1 * np.eye(X_b.shape[1])  # Prior covariance matrix\n",
    "plot_x = np.linspace(0, 1.05, 100).reshape(-1, 1)\n",
    "# Compute posterior parameters\n",
    "mean_posterior, theta_sigma_posterior = bayes_lr(sigma, X_b[:100], y[:100], theta_mu, theta_sigma_prior)\n",
    "outlier_posterior, outlier_sigma_posterior = bayes_lr(sigma, X_b[100:], y[100:], mean_posterior, theta_sigma_posterior)\n",
    "\n",
    "# Compute posterior predictive distribution\n",
    "y_pred_mean,y_pred_std = bayes_pred(sigma,mean_posterior,theta_sigma_posterior,plot_x)\n",
    "y_outlier_mean,y_outlier_std = bayes_pred(sigma,outlier_posterior,outlier_sigma_posterior,plot_x)\n",
    "# y_outlier_mean = X_b.dot(outlier_posterior)\n",
    "# y_outlier_std = np.sqrt([sigma + X_b[i].dot(outlier_sigma_posterior).dot(X_b[i].T) for i in range(len(X_b))]).reshape(-1, 1)\n",
    "\n",
    "# Plot results\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "# Fill 3σ intervals without outliers\n",
    "plt.fill_between(plot_x.ravel(), (y_pred_mean - 3 * y_pred_std).ravel(), (y_pred_mean + 3 * y_pred_std).ravel(), color='orange', alpha=0.3, label='3σ Interval without outliers')\n",
    "\n",
    "# Fill 3σ intervals with outliers as new data\n",
    "plt.fill_between(plot_x.ravel(), (y_outlier_mean - 3 * y_outlier_std).ravel(), (y_outlier_mean + 3 * y_outlier_std).ravel(), color='green', alpha=0.3, label='3σ Interval with outliers as new data')\n",
    "\n",
    "# Plot training data\n",
    "plt.scatter(X, y, color='blue', label='Training Data')\n",
    "\n",
    "# Plot model predictions\n",
    "for m in methods:\n",
    "    for r in regs:\n",
    "        plt.plot(X, models['{}_{}'.format(m, r)].predict(X), label='{}_{}'.format(m, r))\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')\n",
    "plt.title('Bayesian Linear Regression Prediction with 3σ Interval')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e848d463-2f65-4b01-a48a-fda00a8f8937",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 3. Gaussian Process Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14eec8e8-7e4c-4b38-952a-3f9067ad1787",
   "metadata": {
    "tags": []
   },
   "source": [
    "### 3.1 Weight Space Perspective"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77db2a83-4d5b-4378-b6c7-84a666e22146",
   "metadata": {},
   "source": [
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "900f1aa3-46ed-43cb-a4da-e40a030d6c07",
   "metadata": {},
   "source": [
    "In Gaussian Process Regression (GPR), we start by considering a bayesian linear regression model whose input data $\\mathbf{x}$ maps the to a high-dimensional feature space by a feature mapping function $\\phi(\\mathbf{x})$, the model can be expressed as follows:\n",
    "\n",
    "$$ \\mathbf{y} = \\phi(\\mathbf{x})^T\\theta + \\epsilon $$\n",
    "\n",
    "where:\n",
    "- $\\phi(\\mathbf{x})$ is the feature mapping function\n",
    "- $\\epsilon$ is assumed to be Gaussian noise with mean 0 and variance $\\sigma^2$.\n",
    "- $p(\\theta)\\sim N(0, \\Sigma)$\n",
    "\n",
    "So the covariance matrix $\\Sigma_{\\text{post}}$ of the posterior distribution is:\n",
    "\n",
    "$$\n",
    "\\Sigma_{\\text{post}} = (\\frac{\\phi(X)^T\\phi(X)}{\\sigma^2}+\\Sigma^{-1})^{-1}\n",
    "$$\n",
    "\n",
    "The mean vector $\\mu_{\\text{post}}$ of the posterior distribution is:\n",
    "\n",
    "$$\n",
    "\\mu_{\\text{post}} = \\Sigma_{\\text{post}}\\frac{\\phi(X)^TY}{\\sigma^2}\n",
    "$$\n",
    "\n",
    "As the Woodbury Formula is:\n",
    "$$\n",
    "(A + UCV)^{-1} = A^{-1} - A^{-1}U(C^{-1} + VA^{-1}U)^{-1}VA^{-1}\n",
    "$$\n",
    "So\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\Sigma_{\\text{post}} &= (\\Sigma^{-1}+\\phi(X)^T\\sigma^{-2}\\phi(X))^{-1} \\\\\n",
    "&=\\Sigma -\\Sigma\\phi(X)^T(\\sigma^2I+\\phi(X)\\Sigma\\phi(X)^T)^{-1}\\phi(X)\\Sigma\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\mu_{\\text{post}} &= \\Sigma_{\\text{post}}\\frac{\\phi(X)^TY}{\\sigma^2} \\\\\n",
    "&= \\Sigma\\frac{\\phi(X)^TY}{\\sigma^2} - \\Sigma\\phi(X)^T(\\sigma^2I+\\phi(X)\\Sigma\\phi(X)^T)^{-1}\\phi(X)\\Sigma\\frac{\\phi(X)^TY}{\\sigma^2} \\\\\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "So the mean and variance of the predicted target value $\\mathbf{y_*}$ when given a new input feature vector $\\mathbf{x_*}$ can be calculated using the following formulas:\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\mu_* &= \\phi(\\mathbf{x_*})^T\\mu_{\\text{post}} \\\\\n",
    "&= \\phi(\\mathbf{x_*})^T\\Sigma\\frac{\\phi(X)^TY}{\\sigma^2} -\\phi(\\mathbf{x_*})^T\\Sigma\\phi(X)^T(\\sigma^2I+\\phi(X)\\Sigma\\phi(X)^T)^{-1}\\phi(X)\\Sigma\\frac{\\phi(X)^TY}{\\sigma^2} \n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\sigma_*^2 &= \\sigma^2  + \\phi(\\mathbf{x_*})^T \\Sigma_{\\text{post}}\\phi(\\mathbf{x_*}) \\\\\n",
    "&= \\sigma^2 + \\phi(\\mathbf{x_*})^T\\Sigma\\phi(\\mathbf{x_*}) - \\phi(\\mathbf{x_*})^T\\Sigma\\phi(X)^T(\\sigma^2I+\\phi(X)\\Sigma\\phi(X)^T)^{-1}\\phi(X)\\Sigma\\phi(\\mathbf{x_*})\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "As $\\phi(\\mathbf{x})^T\\Sigma\\phi(\\mathbf{x'}) = \\phi(\\mathbf{x})^T\\Sigma^\\frac{1}{2}\\Sigma^\\frac{1}{2}\\phi(\\mathbf{x'})$ and $\\Sigma$ is a symmetric matrix, $\\phi(\\mathbf{x})^T\\Sigma\\phi(\\mathbf{x'})$ can be wrote as \n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\\phi(\\mathbf{x})^T\\Sigma\\phi(\\mathbf{x'}) &=(\\Sigma^\\frac{1}{2}\\phi(\\mathbf{x}))^T(\\Sigma^\\frac{1}{2}\\phi(\\mathbf{x'})) \\\\\n",
    "&= \\Psi(\\mathbf{x})^T\\Psi(\\mathbf{x'}) \\\\\n",
    "&= K(\\mathbf{x},\\mathbf{x'})\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "where\n",
    "- $\\Psi(\\mathbf{x})$ is a linear transformation that $\\Psi(\\mathbf{x}) = \\Sigma^\\frac{1}{2}\\phi(\\mathbf{x})$\n",
    "- $K(\\mathbf{x}, \\mathbf{x}')$ is the covariance function (kernel).\n",
    "\n",
    "The mean and variance of $\\mathbf{y_*}$ can be simplificated as\n",
    "\n",
    "$$ \n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\mu_* &= \\phi(\\mathbf{x_*})^T\\Sigma\\frac{\\phi(X)^TY}{\\sigma^2} -\\phi(\\mathbf{x_*})^T\\Sigma\\phi(X)^T(\\sigma^2I+\\phi(X)\\Sigma\\phi(X)^T)^{-1}\\phi(X)\\Sigma\\frac{\\phi(X)^TY}{\\sigma^2} \\\\\n",
    "&= \\sigma^{-2}K(\\mathbf{x_*},X)(I-(\\sigma^2I+K(X,X))^{-1}K(X,X))Y\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\sigma_*^2 &= \\sigma^2 + \\phi(\\mathbf{x_*})^T\\Sigma\\phi(\\mathbf{x_*}) - \\phi(\\mathbf{x_*})^T\\Sigma\\phi(X)^T(\\sigma^2I+\\phi(X)\\Sigma\\phi(X)^T)^{-1}\\phi(X)\\Sigma\\phi(\\mathbf{x_*}) \\\\\n",
    "&= \\sigma^2 + K(\\mathbf{x_*},\\mathbf{x_*}) - K(\\mathbf{x_*},X)(\\sigma^2I+K(X,X))^{-1}K(X,\\mathbf{x_*})\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "Another method to get $\\mu_*$ is below,\n",
    "As\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "& \\Sigma_{\\text{post}} = (\\frac{\\phi(X)^T\\phi(X)}{\\sigma^2}+\\Sigma^{-1})^{-1}\\\\\n",
    "& \\Sigma_{\\text{post}}^{-1} = \\frac{\\phi(X)^T\\phi(X)}{\\sigma^2}+\\Sigma^{-1} \\\\\n",
    "& \\Sigma_{\\text{post}}^{-1}\\Sigma = \\frac{\\phi(X)^T\\phi(X)\\Sigma}{\\sigma^2}+I \\\\\n",
    "& \\Sigma_{\\text{post}}^{-1}\\Sigma\\phi(X)^T = \\frac{\\phi(X)^T\\phi(X)\\Sigma\\phi(X)^T}{\\sigma^2}+\\phi(X)^T \\\\\n",
    "& \\Sigma\\phi(X)^T = \\sigma^{-2}\\Sigma_{\\text{post}}\\phi(X)^T[\\phi(X)\\Sigma\\phi(X)^T+\\sigma^2I] \\\\\n",
    "& \\sigma^{-2}\\Sigma_{\\text{post}}\\phi(X)^T = \\Sigma\\phi(X)^T[\\phi(X)\\Sigma\\phi(X)^T+\\sigma^2I]^{-1}  \\\\\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "So the mean vector $\\mu_*$ is:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\mu_* &= \\phi(\\mathbf{x_*})^T\\mu_{\\text{post}} \\\\\n",
    "&= \\phi(\\mathbf{x_*})^T\\Sigma_{\\text{post}}\\frac{\\phi(X)^TY}{\\sigma^2} \\\\\n",
    "&= \\phi(\\mathbf{x_*})^T\\Sigma\\phi(X)^T[\\phi(X)\\Sigma\\phi(X)^T+\\sigma^2I]^{-1}Y \\\\\n",
    "&= K(\\mathbf{x_*},X)[K(X,X)+\\sigma^2I]^{-1}Y\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fda087db-f3a1-4a77-83d9-34ea54631bc2",
   "metadata": {},
   "source": [
    "### 3.2 Function Space Perspective"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9e23eab-d85a-41af-9bd5-20392809ffd5",
   "metadata": {},
   "source": [
    "In GPR, we are interested in modeling the underlying function $f(\\mathbf{x})$ directly rather than the weights $\\mathbf{w}$. We assume that the function $f(\\mathbf{x})$ itself follows a Gaussian process:\n",
    "\n",
    "$$\n",
    "f(\\mathbf{x}) \\sim \\mathcal{GP}(m(\\mathbf{x}), k(\\mathbf{x}, \\mathbf{x}'))\n",
    "$$\n",
    "\n",
    "where:\n",
    "- $m(\\mathbf{x})$ is the mean function,\n",
    "- $k(\\mathbf{x}, \\mathbf{x}')$ is the covariance function (kernel).\n",
    "\n",
    "We can treat the observed data and the output values of the point to be predicted as a joint Gaussian distribution and utilize the properties of joint probability for inference.\n",
    "\n",
    "Assuming we have a set of observed data $\\{(\\mathbf{x_i}, \\mathbf{y_i})\\}_{i=1}^n$, where $\\mathbf{x_i}$ is the input and $\\mathbf{y_i}$ is the corresponding output. Our goal is to predict the unknown function $f(\\mathbf{x_i})$, and given a new input $\\mathbf{x_*}$, we want to predict the corresponding output $\\mathbf{x_*}$).\n",
    "\n",
    "Firstly, we assume that the output values of the observed data $\\mathbf{y_i}$ are composed of the unknown function $f(\\mathbf{x_i})$ and independent identically distributed Gaussian noise terms $\\epsilon_i$:\n",
    "\n",
    "$$\n",
    "\\mathbf{y_i} = f(\\mathbf{x_i}) + \\epsilon, \\quad \\epsilon \\sim \\mathcal{N}(0, \\sigma^2)\n",
    "$$\n",
    "\n",
    "We construct a joint Gaussian distribution for the observed data and the output values of the point to be predicted:\n",
    "\n",
    "$$\n",
    "Y_\\text{joint} = \\begin{bmatrix} Y \\\\ \\mathbf{y_*} \\end{bmatrix} \\sim \\mathcal{N}\\left(\\begin{bmatrix}m(X) \\\\ m(\\mathbf{x_*})\\end{bmatrix}, \\begin{bmatrix} K+\\sigma^2 & k_* \\\\ k_*^T & k(\\mathbf{x_*}, \\mathbf{x_*}) \\end{bmatrix}\\right)\n",
    "$$\n",
    "\n",
    "Here\n",
    "- $K$ is the covariance matrix of the observed data\n",
    "- $k_*$ is the covariance vector between the observed data and the point to be predicted,\n",
    "- $k(\\mathbf{x_*}, \\mathbf{x_*})$ is the self-covariance of the point to be predicted.\n",
    "- $\\sigma^2$ is the variance of the noise.\n",
    "\n",
    "We can then utilize the properties of joint Gaussian distribution, given the observed data $Y$, to compute the conditional probability distribution of the point to be predicted $\\mathbf{y_*}$:\n",
    "\n",
    "$$\n",
    "p(y_* | Y) = \\mathcal{N}(\\mu_*, \\sigma_*^2)\n",
    "$$\n",
    "\n",
    "where $\\mu_*$ and $\\sigma_*^2$ are the mean and variance of the point to be predicted\n",
    "\n",
    "Let $A=\\begin{bmatrix}p & I\\end{bmatrix}$, $B = AY_\\text{joint}$ is also a normal distribution with variance as below:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\text{Var}B &= \\text{Var}(AY_\\text{joint}) \\\\\n",
    "&= A\\text{Var}(Y_\\text{joint})A^T \\\\\n",
    "&= \\begin{bmatrix}p & I\\end{bmatrix}\\begin{bmatrix} K+\\sigma^2 & k_* \\\\ k_*^T & k(\\mathbf{x_*}, \\mathbf{x_*}) \\end{bmatrix}\\begin{bmatrix}p^T \\\\ I\\end{bmatrix} \\\\\n",
    "&= \\begin{bmatrix}p(K+\\sigma^2I)+k_*^T & pk_*+k(\\mathbf{x_*}, \\mathbf{x_*})\\end{bmatrix}\\begin{bmatrix}p^T \\\\ I\\end{bmatrix} \\\\\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "And let $p(K+\\sigma^2I)+k_*^T=0$ to get a $p$ to make calculations simple, that is $p=-k_*^T(K+\\sigma^2I)^{-1}$, so\n",
    "\n",
    "$$\n",
    "A=\\begin{bmatrix}-k_*^T(K+\\sigma^2I)^{-1} & I\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\text{Var}(B) = \\text{Var}(AY_\\text{joint}) \\\\\n",
    "&= A\\text{Var}(Y_\\text{joint})A^T \\\\\n",
    "&= \\begin{bmatrix}0 & -k_*^T(K+\\sigma^2I)^{-1}k_*+k(\\mathbf{x_*}, \\mathbf{x_*})\\end{bmatrix}\\begin{bmatrix}p^T \\\\ I\\end{bmatrix} \\\\\n",
    "&= -k_*^T(K+\\sigma^2I)^{-1}k_*+k(\\mathbf{x_*}, \\mathbf{x_*})\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\mathbb{E}[B] &= \\mathbb{E}[AY_\\text{joint}] \\\\\n",
    "&= A\\mathbb{E}[Y_\\text{joint}] \\\\\n",
    "&=\\begin{bmatrix}-k_*^T(K+\\sigma^2I)^{-1} & I\\end{bmatrix} \\begin{bmatrix}m(X) \\\\ m(\\mathbf{x_*})\\end{bmatrix} \\\\\n",
    "&=-k_*^T(K+\\sigma^2I)^{-1}m(X) + m(\\mathbf{x_*})\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "B &=AY \\\\\n",
    "&= \\begin{bmatrix}-k_*^T(K+\\sigma^2I)^{-1} & I\\end{bmatrix} \\begin{bmatrix}Y \\\\ y_*\\end{bmatrix} \\\\\n",
    "&=-k_*^T(K+\\sigma^2I)^{-1}Y + y_*\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "y_*|Y &= B + k_*^T(K+\\sigma^2I)^{-1}Y \\\\\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\mathbb{E}[y_*|Y] &= \\mathbb{E}[B + k_*^T(K+\\sigma^2I)^{-1}Y] \\\\\n",
    "&= \\mathbb{E}[B] + k_*^T(K+\\sigma^2I)^{-1}Y \\\\\n",
    "&= -k_*^T(K+\\sigma^2I)^{-1}m(X) + m(\\mathbf{x_*}) + k_*^T(K+\\sigma^2I)^{-1}Y \\\\\n",
    "&= m(\\mathbf{x_*}) + k_*^T(K+\\sigma^2I)^{-1}[Y-m(X)]\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\text{Var}(y_*|Y) &= \\text{Var}(B + k_*^T(K+\\sigma^2I)^{-1}Y) \\\\\n",
    "&= \\text{Var}(B) \\\\\n",
    "&= -k_*^T(K+\\sigma^2I)^{-1}k_*+k(\\mathbf{x_*}, \\mathbf{x_*})\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "So the mean and variance of the point to be predicted is:\n",
    "\n",
    "- $\\mu_* = m(\\mathbf{x_*}) + k_*^T(K+\\sigma^2I)^{-1}[Y-m(X)]$\n",
    "- $\\sigma_*^2 = -k_*^T(K+\\sigma^2I)^{-1}k_*+k(\\mathbf{x_*}, \\mathbf{x_*})$\n",
    "\n",
    "**This is the same with weight space !**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1cabe219-5bfa-4817-9367-24d0b193b7ac",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.gaussian_process import GaussianProcessRegressor\n",
    "from sklearn.gaussian_process.kernels import RBF, WhiteKernel\n",
    "\n",
    "# 生成带有噪声的合成数据\n",
    "np.random.seed(0)\n",
    "X = np.random.uniform(0, 10, 20)[:, np.newaxis]\n",
    "y = np.sin(X) + np.random.normal(0, 0.1, size=X.shape)\n",
    "\n",
    "# 定义高斯过程回归模型\n",
    "kernel = RBF(length_scale=1.0, length_scale_bounds=(1e-1, 10.0)) + WhiteKernel(noise_level=1, noise_level_bounds=(1e-3, 1e3))\n",
    "gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=10)\n",
    "\n",
    "# 拟合模型\n",
    "gp.fit(X, y)\n",
    "\n",
    "# 生成测试数据\n",
    "x_test = np.linspace(0, 10, 100)[:, np.newaxis]\n",
    "\n",
    "# 进行预测\n",
    "y_pred_gp, gp_sigma = gp.predict(x_test, return_std=True)\n",
    "# Define parameters\n",
    "sigma = 1\n",
    "X_b = np.c_[np.ones((X.shape[0], 1)), X]\n",
    "theta_mu = np.zeros(X_b.shape[1]).reshape(-1, 1)\n",
    "theta_sigma_prior = 1 * np.eye(X_b.shape[1])  # Prior covariance matrix\n",
    "\n",
    "# Compute posterior parameters\n",
    "mean_posterior, theta_sigma_posterior = bayes_lr(sigma, X_b[:100], y[:100], theta_mu, theta_sigma_prior)\n",
    "y_pred_mean,y_pred_std = bayes_pred(sigma,mean_posterior,theta_sigma_posterior,x_test)\n",
    "\n",
    "# 绘制结果\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X, y, color='blue', label='Training Data')\n",
    "plt.plot(x_test, y_pred_mean, c='orange', label='Bayes Line Regression Mean')\n",
    "plt.plot(x_test, y_pred_gp, c='blue', label='GP Mean')\n",
    "plt.fill_between(x_test.ravel(), (y_pred_mean - y_pred_std).ravel(), (y_pred_mean + y_pred_std).ravel(), color='orange', alpha=0.3, label='95% Confidence Interval of Bayes Line Regression')\n",
    "plt.fill_between(x_test.ravel(), y_pred_gp - 2 * gp_sigma, y_pred_gp + 2 * gp_sigma, color='blue', alpha=0.2, label='95% Confidence Interval of GP')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')\n",
    "plt.title('Gaussian Process Regression')\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()\n"
   ]
  },
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   "id": "b171e7f0-8283-4a77-a8c6-5ba33f8b3222",
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   "source": [
    "## Reference\n",
    "- [1] [OLS](https://www.bilibili.com/video/BV1aE411o7qd/?p=9)\n",
    "- [2] [OLS-likelihood](https://www.bilibili.com/video/BV1aE411o7qd/?p=10)\n",
    "- [3] [Ridge Regression-Frequentist](https://www.bilibili.com/video/BV1aE411o7qd/?p=11)\n",
    "- [4] [Ridge Regression-Bayesian](https://www.bilibili.com/video/BV1aE411o7qd/?p=12)\n",
    "- [5] [\n",
    "Bayesian linear regression1](https://www.bilibili.com/video/BV1aE411o7qd/?p=108)\n",
    "- [6] [\n",
    "Bayesian linear regression2](https://www.bilibili.com/video/BV1aE411o7qd/?p=109)\n",
    "- [7] [\n",
    "Bayesian linear regression3](https://www.bilibili.com/video/BV1aE411o7qd/?p=110)\n",
    "- [8] [\n",
    "Bayesian linear regression4](https://www.bilibili.com/video/BV1aE411o7qd/?p=111)\n",
    "- [9] [\n",
    "Bayesian linear regression5](https://www.bilibili.com/video/BV1aE411o7qd/?p=112)\n",
    "- [10] [Gaussian process regression](https://www.bilibili.com/video/BV1aE411o7qd/?p=113)\n",
    "- [11] [GP-weight space](https://www.bilibili.com/video/BV1aE411o7qd/?p=114)\n",
    "- [12] [GP-weight space to function space](https://www.bilibili.com/video/BV1aE411o7qd/?p=115)\n",
    "- [13] [GP-function space](https://www.bilibili.com/video/BV1aE411o7qd/?p=116)\n",
    "- [14] [\n",
    "Gaussian distribution-marginal probability](https://www.bilibili.com/video/BV1aE411o7qd/?p=7)\n",
    "- [15] [\n",
    "Gaussian distribution joint probability](https://www.bilibili.com/video/BV1aE411o7qd/?p=8)\n",
    "- [16] [GP](https://www.cs.cmu.edu/~epxing/Class/10715/lectures/GP.pdf)"
   ]
  }
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