Liangjie_Lu hw1.ipynb

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   "source": [
    "# STA 208: Homework 1 (Do not distribute)\n",
    "\n",
    "## Due 04/28/2023 midnight (11:59pm)\n",
    "\n",
    "__Instructions:__ \n",
    "\n",
    "1. Submit your homework using one file name ”LastName_FirstName hw1.html” on canvas. \n",
    "2. The written portions can be either done in markdown and TeX in new cells or written by hand and scanned. Using TeX is strongly preferred. However, if you have scanned solutions for handwriting, you can submit a zip file. Please make sure your handwriting is clear and readable and your scanned files are displayed properly in your jupyter notebook. \n",
    "3. Your code should be readable; writing a piece of code should be compared to writing a page of a book. Adopt the one-statement-per-line rule. Consider splitting a lengthy statement into multiple lines to improve readability. (You will lose one point for each line that does not follow the one-statementper-line rule)\n",
    "4. To help understand and maintain code, you should always add comments to explain your code. (homework with no comments will receive 0 points). For a very long comment, please break it into multiple lines.\n",
    "5. In your Jupyter Notebook, put your answers in new cells after each exercise. You can make as many new cells as you like. Use code cells for code and Markdown cells for text.\n",
    "6. Please make sure to print out the necessary results to avoid losing points. We should not run your code to figure out your answers. \n",
    "7. However, also make sure we are able to open this notebook and run everything here by running the cells in sequence; in case that the TA wants to check the details.\n",
    "8. You will be graded on correctness of your math, code efficiency and succinctness, and conclusions and modelling decisions\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6de66a11",
   "metadata": {},
   "source": [
    "**Author:** Liangjie Lu\n",
    "\n",
    "**Note:** Most of the codes and even the conclusions of Exercise 4 are directly copied from our TA's discussion presentation. But I also have my modification for that part. I truly learnt a lot and truly took time to think it over.I am so grateful for that! "
   ]
  },
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   "cell_type": "markdown",
   "id": "43772f97",
   "metadata": {},
   "source": [
    "### Exercise 1 (Empirical risk minimization) (20 pts, 5 pts each)\n",
    "\n",
    "Consider Poisson model with rate parameter $\\lambda$ which has PMF,\n",
    "$$\n",
    "p(y|\\lambda) = \\frac{\\lambda^y}{y!} e^{-\\lambda},\n",
    "$$\n",
    "where $y = 0,1,\\ldots$ is some count variable.\n",
    "In Poison regression, we model $\\lambda = e^{\\beta^\\top x}$ to obtain $p(y | x,\\beta)$.\n",
    "\n",
    "1. Let the loss function for Poisson regression be $\\ell_i(\\beta) = - \\log p(y_i | x_i, \\beta)$ for a dataset consisting of predictor variables and count values $\\{x_i,y_i\\}_{i=1}^n$.  Here $\\propto$ means that we disregard any additive terms that are not dependent on $\\beta$.  Write an expression for $\\ell_i$ and derive its gradient. \n",
    "2. Show that the empirical risk $R_n(\\beta)$ is a convex function of $\\beta$.\n",
    "3. Consider the mapping $F_\\eta(\\beta) = \\beta - \\eta \\nabla R_n(\\beta)$ which is the iteration of gradient descent ($\\eta>0$ is called the learning parameter).  Show that at the minimizer of $R_n$, $\\hat \\beta$, we have that $F(\\hat \\beta) = \\hat \\beta$.\n",
    "4. I have a script to simulate from this model below.  Implement the gradient descent algorithm above and show that with enough data ($n$ large enough) the estimated $\\hat \\beta$ approaches the true $\\beta$ (you can look at the sum of square error between these two vectors)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56e0544a",
   "metadata": {},
   "source": [
    "**Ans 1.**\n",
    "\n",
    "$$p(y|x,\\beta)=\\frac{1}{y!}\\exp\\{\\beta'xy-\\exp\\{\\beta'x\\}\\}$$\n",
    "\n",
    "$$l_i(\\beta)=\\log\\bigg((y_i)!\\bigg)-\\beta'x_iy_i + \\exp\\{\\beta'x_i\\}\\ \\ \\forall i$$\n",
    "\n",
    "$$\\frac{\\partial l_i(\\beta)}{\\partial \\beta}=x_i(\\exp\\{\\beta'x_i\\}-y_i)\\ \\ \\forall i$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6764169",
   "metadata": {},
   "source": [
    "**Ans 2.**\n",
    "\n",
    "*Proof.*\n",
    "\n",
    "$$R_n(\\beta)=\\frac{1}{n}\\sum_i^n\\log((y_i)!)   +   \\frac{-1}{n}\\beta'\\sum_i^n x_iy_i + \\frac{1}{n}\\sum_i^n \\exp\\{\\beta'x_i\\}$$\n",
    "\n",
    "Since $$H_{R_n(\\beta)}=\\nabla^2 R_n(\\beta)  = \\frac{\\partial}{\\partial \\beta'} (0   +   \\frac{-1}{n}\\sum_i^n x_iy_i + \\frac{1}{n}\\sum_i^n x_i\\exp\\{\\beta'x_i\\})=\\frac{1}{n}\\sum_i x_ix_i'\\exp\\{\\beta'x_i\\},$$\n",
    "\n",
    "then $z'H_{R_n(\\beta)}z=\\frac{1}{n}\\sum_i (x_i'z)^2\\exp\\{\\beta'x_i\\}\\ge 0\\ \\  \\forall z\\in\\mathbf{R}$, which means $H_{R_n(\\beta)}\\succeq 0$. Moreover, Dom$(R_n(\\beta))=\\mathbf{R}^{dim(\\beta)}$ is a convex domain. \n",
    "\n",
    "So $R_n(\\beta)$ is a convex function. $\\square$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0df8969",
   "metadata": {},
   "source": [
    "**Ans 3.**\n",
    "\n",
    "*Proof.*\n",
    "\n",
    "For the convex function $R_n(\\beta)$, it gets minimized when \n",
    "\n",
    "$$\\nabla R_n(\\widehat{\\beta})=0,$$\n",
    "\n",
    "Suppose the minimizer is $\\widehat{\\beta}$. Then $F(\\widehat{\\beta})= \\widehat{\\beta} - \\eta \\nabla R_n(\\widehat{\\beta})=\\widehat{\\beta}$. $\\square$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58a0281e",
   "metadata": {},
   "source": [
    "**Ans 4.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ff3ad3c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "adb9d5f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Simulate from the Poisson regression model (use y,X)\n",
    "np.random.seed(2022)\n",
    "n, p = 1000,20\n",
    "X = np.random.normal(0,1,size = (n,p))\n",
    "beta = np.random.normal(0,.2,size = (p))\n",
    "lamb = np.exp(X @ beta)\n",
    "y = np.random.poisson(lamb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81d5ed65",
   "metadata": {},
   "outputs": [],
   "source": [
    "def GD_poisson(X, y, ita, maxiter, eps):\n",
    "    from copy import deepcopy\n",
    "    beta_0 = np.linalg.inv(X.T @ X) @ (X.T @ np.log(y + 0.01)) # Trivial initial guess\n",
    "    n = len(X)\n",
    "    epoch = 1\n",
    "    beta_hat = deepcopy(beta_0)\n",
    "    while epoch <= maxiter:\n",
    "        d_loss = 1/n * (X.T @ (-y + np.exp( X @ beta_hat)))\n",
    "        beta_pre = deepcopy(beta_hat)\n",
    "        # Find best ita, Amijo backtracking line search\n",
    "        ita_hat = ita # Initialization of ita_hat\n",
    "        loss_pre = - 1/n * ((beta_pre.T @ X.T) @ y) + 1/n * sum(np.exp( X @ beta_pre ) ) # Ignore useless part\n",
    "        c = 0.01\n",
    "        while ita_hat >= ita/4096:\n",
    "            beta_hat_tmp = beta_hat - ita_hat * d_loss\n",
    "            loss_hat_tmp = - 1/n * ((beta_hat_tmp.T @ X.T) @ y) + 1/n * sum(np.exp( X @ beta_hat_tmp ) ) # Ignore useless part\n",
    "            if loss_hat_tmp <= loss_pre - c * np.linalg.norm(d_loss) ** 2:\n",
    "                break\n",
    "            ita_hat /= 2\n",
    "        else:\n",
    "            return beta_pre\n",
    "        beta_hat = deepcopy(beta_hat_tmp)\n",
    "        ss_err = np.linalg.norm(beta_hat-beta_pre) ** 2\n",
    "        if ss_err <= eps:\n",
    "            break\n",
    "        epoch += 1\n",
    "    return beta_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1f1fcfa7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1588004469619665"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ita, maxiter, eps = 10, 10000, 0.001\n",
    "beta_hat = GD_poisson(X, y, ita, maxiter, eps)\n",
    "np.linalg.norm(beta_hat - beta)/np.linalg.norm(beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91b4a26f",
   "metadata": {},
   "source": [
    "This result shows that I might have implement right GD algorithm for this problem. Below are some simulations to prove the second half of the question."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6dc8c7c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Simulate from the Poisson regression model (use y,X)\n",
    "np.random.seed(2022)\n",
    "n, p = 5000,20\n",
    "X = np.random.normal(0,1,size = (n,p))\n",
    "beta = np.random.normal(0,.2,size = (p))\n",
    "lamb = np.exp(X @ beta)\n",
    "y = np.random.poisson(lamb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b1287e1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "ita, maxiter, eps = 10, 10000, 0.001\n",
    "n_list = list(range(500,5000+1,500))\n",
    "beta_hat_list = []\n",
    "err_rate_list = []\n",
    "for idx, n_chosen in enumerate(n_list):\n",
    "    beta_hat = GD_poisson(X[0:n_chosen+1,:], y[0:n_chosen+1], ita, maxiter, eps)\n",
    "    beta_hat_list.append(beta_hat)\n",
    "    err_rate_list.append(np.linalg.norm(beta_hat - beta)/np.linalg.norm(beta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5ea49391",
   "metadata": {},
   "outputs": [
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# assuming n_list and err_list are already defined\n",
    "plt.plot(n_list, err_rate_list)\n",
    "plt.xlabel('# of data')\n",
    "plt.ylabel('Error rates: ||beta_hat-beta||/||beta||')\n",
    "plt.title('Error plot')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab5e5055",
   "metadata": {},
   "source": [
    "According to this plot, the relative error rate tends to converge to zero as $n$ (the number of data) goes large.So there is some clue that with enough data ($n$ large enough) the estimated $\\hat \\beta$ approaches the true $\\beta$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "360cc371",
   "metadata": {},
   "source": [
    "### Exercise 2 (Regression and OLS) (35 pts, 5 pts each)\n",
    "\n",
    "Consider the regression setting in which $x_i \\in \\mathbb R^p$ and $y_i \\in \\mathbb R$, for $i=1,\\ldots,n$ and $p < n$.\n",
    "\n",
    "1. For a given regressor, let $\\hat y_i$ be prediction given $x_i$, and $\\hat y$ be the vector form.  Show that linear regression can be written in the form\n",
    "$$\n",
    "\\hat y = H y,\n",
    "$$\n",
    "where $H$ is dependent on $X$ (the matrix of where each row is $x_i$), assuming that $p < n$ and $X$ is full rank.  Give an expression for $H$ or an algorithm for computing $H$. \n",
    "2. Assuming $p < n$ and $X$ is full rank, let $X = U D V^\\top$ be the thin singular value decomposition where $U$ is $n \\times p$, and $V, D$ is $p \\times p$ ($D$ is diagonal). \n",
    "    - a) Derive an expression for the OLS coefficients $\\hat\\beta = A b$ such that $A$ is $p \\times p$ and depends on $V$ and $D$, and $b$ is a $p$ vector and does not depend on $D$.   \n",
    "    - b) Describe a fit method that precomputes these quantities separately\n",
    "    - c) Use the simulated data $y$ and $X$ in below to find $\\hat \\beta$ using SVD.\n",
    "    - d) Call a new data $\\tilde X \\in \\mathbb{R}^{m \\times p}$, derive an expression for the predicted $y$ with $\\tilde X$ using SVD. \n",
    "3. Consider a regressor that performs OLS using the SVD above, but every instance of D will only use the largest $r$ values on the diagonal, the remainder will be set to 0.  Call this new $p \\times p$ matrix $D_r$ ($r < p$).  Then the new coefficient vector is the OLS computed as if the design matrix is modified by $X \\gets U D_r V^\\top$.  \n",
    "    - a) Given that you have computed $b$ already, how could you make a method `change_rank` that recomputes $A$ with $D_r$ instead of $D$? \n",
    "    - b) Choose $r = 10$, recompute $\\hat\\beta$ (call it $\\hat\\beta_{\\text{LowRank}}$) in Question 2-c."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f99a157f",
   "metadata": {},
   "source": [
    "**Ans 1.**\n",
    "\n",
    "*Proof.*\n",
    "\n",
    "The OLS problem:\n",
    "$$\\min_\\beta||Y-X\\beta||_2^2$$\n",
    "\n",
    "$$\\Rightarrow\\frac{\\partial}{\\partial \\beta}||Y-X\\beta||_2^2=\\frac{\\partial}{\\partial \\beta}(Y-X\\beta)'(Y-X\\beta)=-2X'(Y-X\\beta)\\overset{\\text{Let}}=\\bf {0}$$\n",
    "\n",
    "$$\\Rightarrow X'Y=(X'X)\\widehat \\beta_{OLS}\\Rightarrow \\widehat \\beta_{OLS}=(X'X)^{-1}X'Y$$\n",
    "\n",
    "$$\\Rightarrow \\widehat Y=X\\widehat \\beta_{OLS}=X(X'X)^{-1}X'Y=HY$$\n",
    "\n",
    "where $H\\triangleq X(X'X)^{-1}X'$.\n",
    "\n",
    "Here is the code to compute **H**:\n",
    "\n",
    "> H = X @ np.linalg(X.T @ X) @ X.T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c2af8b8",
   "metadata": {},
   "source": [
    "**Ans 2.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "101e0083",
   "metadata": {},
   "source": [
    "*a)* $$\\widehat \\beta = (X'X)^{-1}X'Y=(VDU'UDV')^{-1}VDU'Y=(VD^2V')^{-1}VDU'Y=Ab$$\n",
    "\n",
    "where $A\\triangleq (VD^2V')^{-1}VD$, $b\\triangleq U'Y\\perp \\!\\!\\! \\perp V,D$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff4f870c",
   "metadata": {},
   "source": [
    "*b)*  **And** *c)*\n",
    "\n",
    "Honestly, I get confused with what exactly I need to do in these parts. Pardon me for merging them together. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ced8a4c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Simulate from the linear regression model (use y,X)\n",
    "np.random.seed(2022)\n",
    "n, p = 100,20\n",
    "X = np.random.normal(0,1,size = (n,p))\n",
    "beta = np.random.normal(0,.2,size = (p))\n",
    "sigma = 1\n",
    "y = np.random.normal(X @ beta, sigma**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "882a747b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_rank(X) # X is full rank"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5adca8b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Precompute according to the above formula\n",
    "u, s, vh = np.linalg.svd(X, full_matrices=True)\n",
    "U, D, V = u[:,0:X.shape[1]], np.diag(s), vh.T\n",
    "# Trivial version\n",
    "A = np.linalg.inv(V @ D ** 2 @ V.T ) @ V @ D\n",
    "b = U.T @ y\n",
    "beta_hat = A @ b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b7115ace",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Faster way to precompute these things\n",
    "VD = V * s\n",
    "A = np.linalg.inv(VD @ VD.T) @ VD\n",
    "b = U.T @ y\n",
    "beta_hat = A @ b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1cf0656",
   "metadata": {},
   "source": [
    "d) $$\\widehat Y=\\tilde X\\widehat\\beta=\\tilde XAb$$\n",
    "\n",
    "where $A\\triangleq (VD^2V')^{-1}VD$, $b\\triangleq U'Y$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8b4c138",
   "metadata": {},
   "source": [
    "**Ans 3.**\n",
    "\n",
    "*a)*\n",
    "\n",
    "$$\\tilde A=((VD_r)(VD_r)')^{-1}VD_r$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "388431a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def change_rank(V, s, r):\n",
    "    \"\"\"\n",
    "    Input:\n",
    "        V: np.array [nxn]\n",
    "        s: np.array [nx1]\n",
    "        r: int\n",
    "        \n",
    "    Output:\n",
    "        Ar: (VDr**2V')^-1VDr\n",
    "            where Dr = diag(s[:r] 0...0)\n",
    "    \"\"\"\n",
    "    import numpy as np\n",
    "    from copy import deepcopy\n",
    "    s_r = deepcopy(s)\n",
    "    s_r[r:] = 0\n",
    "    VDr = V * s_r\n",
    "    Ar = np.linalg.inv(VDr @ VDr.T) @ VDr\n",
    "    return Ar, s_r"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42424a78",
   "metadata": {},
   "source": [
    "*b)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "23f0d097",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ar, s_r = change_rank(V, s, r=10)\n",
    "beta_hat_lowrank = Ar @ b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "634fe776",
   "metadata": {},
   "source": [
    "### Exercise 3 (Subset selection)  (20 pts, 5 each)\n",
    "\n",
    "Recall the subset selection problem with tuning parameter $k$,\n",
    "$$\n",
    "\\min_{\\beta : \\| \\beta \\|_0 \\le k}\\| y - X \\beta \\|_2^2,\n",
    "$$\n",
    "where $\\|\\beta\\|_0 = \\#\\{j = 1\\,\\ldots,p : \\beta_j \\ne 0 \\}$.\n",
    "\n",
    "Notice that we can write this as \n",
    "$$\n",
    "\\min_{\\beta : |{\\rm supp}(\\beta)| \\le k}\\| y - X \\beta \\|_2^2,\n",
    "$$\n",
    "where \n",
    "${\\rm supp}(\\beta) = \\{j = 1\\,\\ldots,p : \\beta_j \\ne 0 \\}$ (${\\rm supp}(\\beta)$ is the support of $\\beta$).\n",
    "\n",
    "1. Write the subset selection problem in the following form\n",
    "$$\n",
    "\\min_{S \\subseteq \\{1,\\ldots,p\\}, |S|\\le k} y^\\top P_S y,\n",
    "$$\n",
    "where $P_S$ is a projection.  \n",
    "2. Suppose that we have a nested sequence of models $S_1\\subset S_2 \\subset \\ldots \\subset S_p$ such that $|S_k| = k$ ($|S_k|$ is the cardinality of $S_k$, meaning that it contains $k$ variables).  Prove that $$y^\\top P_{S_k} y \\ge y^\\top P_{S_{k+1}}\\ \\ y$$ for $k=1,\\ldots,p-1$.  What does this tell us about the solution to the subset selection problem and the constraint $|S| \\le k$?\n",
    "\n",
    "    (Hint: using the fact that $X^TX$ is positive definite, write $X^TX= VD^2V^T$)\n",
    "\n",
    "3. Suppose that $X$ is orthogonal, then write a computationally efficient pseudocode to solve the subset selection problem.  Prove that it is correct (your algorithm actually solves subset selection under othogonal design).\n",
    "4. (Challenge) Suppose that we have that $n = p$ and $y_i = \\beta_i + \\epsilon_i$ (identity design matrix) where $\\epsilon_i$ satisfies \n",
    "$$\n",
    "\\mathbb P \\left\\{ |\\epsilon_i| \\ge t \\right\\} \\le 2 e^{-t^2 / 2\\sigma^2}\n",
    "$$\n",
    "for any $t > 0$ (this is true for central Normal RVs) for some $\\sigma > 0$.\n",
    "Suppose that there is some true $S_0 \\subset\\{1,\\ldots,p\\}$ such that $|S_0| = k < p$ and ${\\rm supp}(\\beta) = S_0$.\n",
    "Prove the following.\n",
    "\n",
    "__Proposition__\n",
    "Define $\\mu = \\min_{j \\in S_0} |\\beta_j|$ and call $\\mu / \\sigma$ the signal-to-noise ratio.  Then if \n",
    "$$\n",
    "\\frac{\\mu}{\\sigma} > 2 \\sqrt{2 \\log \\left( \\frac{2n}{\\delta}\\right)},\n",
    "$$\n",
    "then the true $S$ is selected by subset selection with probability at least $1 - \\delta$.\n",
    "\n",
    "Hint: rewrite the subset selection problem with $X = I$ and compare the objective at $S_0$ to any other $S$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9832af7",
   "metadata": {},
   "source": [
    "**Ans 1.** \n",
    "\n",
    "$$\n",
    "\\min_{\\beta : \\| \\beta \\|_0 \\le k}\\| y - X \\beta \\|_2^2\n",
    "\\Leftrightarrow\n",
    "\\min_{S \\subseteq \\{1,\\ldots,p\\}, |S|\\le k,\\beta_S\\in \\mathbb{R}^k} ||y - X_{\\cdot,S}\\ \\beta_S \\|_2^2\n",
    "$$\n",
    "\n",
    "where $(X_{\\cdot,S})_i=X_{\\cdot,S_i} \\ \\forall i\\in\\{k\\}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a060d6e",
   "metadata": {},
   "source": [
    "For fixed support set $S$, $\\widehat\\beta_S=\\arg\\min_{\\beta_S\\in \\mathbb{R}^k} ||y - X_{\\cdot,S}\\ \\beta_S \\|_2^2=X_{\\cdot,S}(X_{\\cdot,S}'X_{\\cdot,S})^{-1}X_{\\cdot,S}y=H_S y$, where $H_S\\triangleq X_{\\cdot,S}(X_{\\cdot,S}'X_{\\cdot,S})^{-1}X_{\\cdot,S}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ad0c5a1",
   "metadata": {},
   "source": [
    "It is easy to see that:\n",
    "\n",
    "* $(I-H_S)'=I-H_S$,\n",
    "\n",
    "* $(I-H_S)^2=I+H_S^2-2H_S=I+H_S-2H_S=I-H_S$.\n",
    "\n",
    "So $P_S\\triangleq (I-H_S)$ is a projection matrix. Obviously, $y'P_S'P_Sy=y'P_Sy$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8633f81",
   "metadata": {},
   "source": [
    "So $$\n",
    "\\min_{\\beta : \\| \\beta \\|_0 \\le k}\\| y - X \\beta \\|_2^2\n",
    "\\Leftrightarrow \n",
    "\\min_{S \\subseteq \\{1,\\ldots,p\\}, |S|\\le k} ||(I-H_S)y||_2^2\n",
    "\\Leftrightarrow\n",
    "\\min_{S \\subseteq \\{1,\\ldots,p\\}, |S|\\le k} y'P_Sy\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae6153cd",
   "metadata": {},
   "source": [
    "where $P_S=I-H_S=I-X_{\\cdot,S}(X_{\\cdot,S}'X_{\\cdot,S})^{-1}X_{\\cdot,S}$, and $(X_{\\cdot,S})_i=X_{\\cdot,S_i} \\ \\forall i\\in\\{k\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2f21027",
   "metadata": {},
   "source": [
    "**Ans 2.** **My provement is a little bit long. Thanks for your patience!**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efc69c6a",
   "metadata": {},
   "source": [
    "Denote $H_{i}\\triangleq X_{S_{i}}\\ (X_{S_{i}}'\\ X_{S_{i}}\\ )^{-1}X_{S_{i}}'$, $P_{i}\\triangleq 1 - H_{i}\\ \\ \\forall i=1,2,\\cdots,p$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8889b8b",
   "metadata": {},
   "source": [
    "$\\forall k\\in\\{p-1\\}$, WLOG, I can suppose $X_{S_{k+1}}=\\begin{pmatrix} X_{S_k}&x \\end{pmatrix}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17525a32",
   "metadata": {},
   "source": [
    "Denote $H_x\\triangleq x(x'x)^{-1}x'$, $P_x\\triangleq 1-H_x$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db96fda1",
   "metadata": {},
   "source": [
    "So \n",
    "$$\n",
    "\\begin{aligned}\n",
    "&H_{k+1}\n",
    "\\\\=&\n",
    "    \\begin{pmatrix} X_{S_k}&x\\end{pmatrix}\n",
    "    \\begin{pmatrix}\n",
    "        X_{S_k}'X_{S_k}      & X_{S_k}'x\\\\\n",
    "        x'X_{S_k}          & x'x\n",
    "    \\end{pmatrix}^{-1}\n",
    "    \\begin{pmatrix}\n",
    "        X_{S_k}'\\\\\n",
    "        x'\n",
    "    \\end{pmatrix}\n",
    "\\\\=&\n",
    "    \\begin{pmatrix} \n",
    "        X_{S_k}     &    x\n",
    "    \\end{pmatrix}\n",
    "    \\begin{pmatrix}\n",
    "       ( X_{S_k}'X_{S_k} -   X_{S_k}'x   (x'x)^{-1}   x'X_{S_k}   )^{-1}        &     0\\\\\n",
    "       0  &     (     x'x    -   x'X_{S_k}  (X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x     )^{-1}\n",
    "    \\end{pmatrix}\n",
    "        \\begin{pmatrix}\n",
    "            I    &   -  X_{S_k}'x  (x'x)^{-1}\\\\\n",
    "            -  x'X_{S_k} (  X_{S_k}'X_{S_k}  )^{-1}   &   I\n",
    "        \\end{pmatrix}\n",
    "    \\begin{pmatrix}\n",
    "    X_{S_k}'\\\\\n",
    "    x'\n",
    "    \\end{pmatrix}\n",
    "\\end{aligned}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afbc1d63",
   "metadata": {},
   "source": [
    "So \n",
    "$$\n",
    "\\begin{aligned}\n",
    "&H_{k+1}\n",
    "\\\\=&\n",
    "    \\begin{pmatrix} \n",
    "        X_{S_k}  &    x\n",
    "    \\end{pmatrix}\n",
    "    \\begin{pmatrix}\n",
    "       ( X_{S_k}'X_{S_k} -   X_{S_k}'x   (x'x)^{-1}   x'X_{S_k}   )^{-1}        &     0\\\\\n",
    "       0  &     (     x'x    -   x'X_{S_k}  (X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x     )^{-1}\n",
    "    \\end{pmatrix}\n",
    "    \\begin{pmatrix}\n",
    "        X_{S_k}'    +   -  X_{S_k}'x  (x'x)^{-1}x'\\\\\n",
    "        -  x'X_{S_k} (  X_{S_k}'X_{S_k}  )^{-1} X_{S_k}'  +   x'\n",
    "    \\end{pmatrix}\n",
    "\\\\=&\n",
    "    \\begin{pmatrix} \n",
    "        X_{S_k}  &    x\n",
    "    \\end{pmatrix}\n",
    "    \\begin{pmatrix}\n",
    "       ( X_{S_k}'X_{S_k} -   X_{S_k}'x   (x'x)^{-1}   x'X_{S_k}   )^{-1}        &     0\\\\\n",
    "       0  &     (     x'x    -   x'X_{S_k}  (X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x     )^{-1}\n",
    "    \\end{pmatrix}\n",
    "    \\begin{pmatrix}\n",
    "        X_{S_k}' (I      -  x  (x'x)^{-1}x')\\\\\n",
    "        x' (I-  X_{S_k} (  X_{S_k}'X_{S_k}  )^{-1} X_{S_k}')   \n",
    "    \\end{pmatrix}\n",
    "\\\\=&\n",
    "    \\begin{pmatrix}\n",
    "       X_{S_k}\\bigg( X_{S_k}'X_{S_k} -   X_{S_k}'x   (x'x)^{-1}   x'X_{S_k}   \\bigg)^{-1}        & x\\bigg(     x'x    -   x'X_{S_k}  (X_{S_k}'X_{S_k} \\bigg)^{-1}   X_{S_k}'x     )^{-1}\n",
    "    \\end{pmatrix}\n",
    "    \\begin{pmatrix}\n",
    "        X_{S_k}' (I      -  x  (x'x)^{-1}x')\\\\\n",
    "        x' (I-  X_{S_k} (  X_{S_k}'X_{S_k}  )^{-1} X_{S_k}')   \n",
    "    \\end{pmatrix}\n",
    "\\\\=&\n",
    "       X_{S_k}\\bigg( X_{S_k}'X_{S_k} -   X_{S_k}'x   (x'x)^{-1}   x'X_{S_k}   \\bigg)^{-1}X_{S_k}' (I      -  x  (x'x)^{-1}x')     \n",
    "\\\\&+        \n",
    "\\\\& \n",
    "       x\\bigg(     x'x    -   x'X_{S_k}  (X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x     \\bigg)^{-1}x' (I-  X_{S_k} (  X_{S_k}'X_{S_k}  )^{-1} X_{S_k}')\n",
    "\\end{aligned}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78b9aaca",
   "metadata": {},
   "source": [
    "So \n",
    "\n",
    "\\begin{aligned}\n",
    "&H_{k+1}\n",
    "\\\\=&\n",
    "       X_{S_k}\\bigg( X_{S_k}'X_{S_k} -   X_{S_k}'x   (x'x)^{-1}   x'X_{S_k}   \\bigg)^{-1}X_{S_k}' (I      -  x  (x'x)^{-1}x')     \n",
    "    \\\\&+        \n",
    "    \\\\& \n",
    "       x\\bigg(     x'x    -   x'X_{S_k}  (X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x     \\bigg)^{-1}x' (I-  X_{S_k} (  X_{S_k}'X_{S_k}  )^{-1} X_{S_k}')\n",
    "\\\\=&\n",
    "       X_{S_k}\n",
    "       \\bigg[\n",
    "           ( X_{S_k}'X_{S_k} )^{-1}   \n",
    "           +   \n",
    "           ( X_{S_k}'X_{S_k} )^{-1}   \n",
    "               X_{S_k}'x   \\bigg(  x'x    -  x'X_{S_k}   ( X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x )^{-1}  x'X_{S_k} \n",
    "           ( X_{S_k}'X_{S_k} \\bigg)^{-1}\n",
    "       \\bigg]\n",
    "       X_{S_k}' (I      -  x  (x'x)^{-1}x')     \n",
    "    \\\\&+        \n",
    "    \\\\& \n",
    "       x\\bigg(     x'x    -   x'X_{S_k}  (X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x     \\bigg)^{-1}x' (I-  X_{S_k} (  X_{S_k}'X_{S_k}  )^{-1} X_{S_k}')\n",
    "\\\\=&\n",
    "           X_{S_k}  ( X_{S_k}'X_{S_k} )^{-1}   X_{S_k}' (I      -  x  (x'x)^{-1}x') \n",
    "    \\\\&+  \n",
    "           X_{S_k}  ( X_{S_k}'X_{S_k} )^{-1}   \n",
    "               X_{S_k}'x   \\bigg(  x'x    -  x'X_{S_k}   ( X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x \\bigg)^{-1}  x'X_{S_k} \n",
    "           ( X_{S_k}'X_{S_k} )^{-1}  X_{S_k}' (I      -  x  (x'x)^{-1}x')   \n",
    "    \\\\&+        \n",
    "    \\\\& \n",
    "       x\n",
    "       \\bigg(     x'x    -   x'X_{S_k}  (X_{S_k}'X_{S_k} )^{-1}   X_{S_k}'x     \\bigg)^{-1}\n",
    "       x' (I-  X_{S_k} (  X_{S_k}'X_{S_k}  )^{-1} X_{S_k}')\n",
    "\\\\=&\n",
    "       [\n",
    "           H_k (I      -  H_x) \n",
    "    \\\\&+  \n",
    "           H_k  x(  x'x    -  x'  H_k   x )^{-1}  x'  H_k (I      -  H_x)   \n",
    "       ] \n",
    "    \\\\&+        \n",
    "    \\\\& \n",
    "       x\n",
    "       (     x'x    -   x'  H_k  x     )^{-1}\n",
    "       x' (I-  H_k)\n",
    "\\\\=&\n",
    "    H_k+(I-H_k)x(x'(I-H_k)x)^{-1}(I-H_k)\n",
    "    \\\\&+\n",
    "        H_k x(x'x-x'H_k x)^{-1}x'\n",
    "    \\\\&-\n",
    "        H_k x(x'x)^{-1}x'    \n",
    "    \\\\&-\n",
    "        H_k x(x'x-x'H_k x)^{-1}x'H_k x(x'x)^{-1}x'\n",
    "\\\\=&\n",
    "    H_k+(I-H_k)x(x'(I-H_k)x)^{-1}(I-H_k)\n",
    "\\\\=&\n",
    "    H_k+P\\{P_k x\\}\n",
    "\\end{aligned}\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "448e1e5e",
   "metadata": {},
   "source": [
    "where $P\\{M\\}\\triangleq M(M'M)^{-1}M^{-1}$ is the projection matrix onto the column space of matrix $M$ $\\forall$ full rank matrix $M$. So $P\\{M\\}\\succeq 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "748fbd18",
   "metadata": {},
   "source": [
    "Here hides the fact that $(A'A-A'BA)((A'A)^{-1}+(A'A-A'BA)^{-1}A'BA(A'A)^{-1})=I-A'BA(A'A)^{-1}+A'BA(A'A)^{-1}=I \\ \\ \\forall$ full rank matrices $ A, B$, so $(A'A-A'BA)^{-1}=((A'A)^{-1}+(A'A-A'BA)^{-1}A'BA(A'A)^{-1})$, and therefore I have \n",
    "    $$\n",
    "        H_k x(x'x-x'H_k x)^{-1}x'\n",
    "    -\n",
    "        H_k x(x'x)^{-1}x'    \n",
    "    -\n",
    "        H_k x(x'x-x'H_k x)^{-1}x'H_k x(x'x)^{-1}x'=        H_k x[(x'x-x'H_k x)^{-1}-(x'x)^{-1}-(x'x-x'H_k x)^{-1}x'H_k x(x'x)^{-1}]x'\n",
    "    =0$$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92207765",
   "metadata": {},
   "source": [
    "You'll see that throughout my whole proof, I treated every component as a matrix rather than making use of the fact that $x'x$ and $x'H_k x$ are scale values. So the conclusion could be naturly generalized to matrix form:\n",
    "$$P\\{X\\}=P\\{A\\}+P\\{(I-P\\{A\\})B\\}\\ \\ \\forall \\text{full rank matrix}\\  X$$\n",
    "\n",
    "where $X\\triangleq\\begin{pmatrix}A & B \\end{pmatrix}$, $P\\{X\\}\\triangleq X(X'X)^{-1}X'$ is the projection matrix onto the column space of matrix $X$.\n",
    "\n",
    "So $P\\{X\\}-P\\{A\\}=P\\{(I-P\\{A\\})B\\}\\succeq 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70ebada9",
   "metadata": {},
   "source": [
    "Thus, we have a more convenient way to prove the whole thing at the cost of some more innocent assuptions WLOG, but let us get back to the normal track:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4ee9775",
   "metadata": {},
   "source": [
    "$$y'P_{S_k}y-y'P_{S_{k+1}\\ \\ }y=y'(P_{S_k}-P_{S_{k+1}}\\ \\ )y=y'(H_{k+1}-H_{k})y=y'(P\\{P_k x\\})y\\ge 0\\ \\ \\forall y\\in \\mathbf{R}^n$$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12d1388f",
   "metadata": {},
   "source": [
    "This result tells us that for any subset sequence, the more columns of the data matrix $X$ we selected, the no larger the loss function could be."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e18ecad4",
   "metadata": {},
   "source": [
    "Here is the second way to prove this result: \n",
    "\n",
    "WLOG, define $X_{S_{k+1}}\\triangleq(X_{S_k}\\ \\ x)$ and $H_\\Delta\\triangleq H_{S_{k+1}}\\ -H_{S_{k}}$. Notice that $H_{S_{k+1}}\\ X_{S_{k}}\n",
    "=H_{S_{k+1}}\\ X_{S_{k+1}}\\begin{pmatrix}I_{|S_k|}\\\\\\textbf{0}\\end{pmatrix}\n",
    "=X_{S_{k+1}}\\begin{pmatrix}I_{|S_k|}\\\\\\textbf{0}\\end{pmatrix}\n",
    "=X_{S_k}\\Rightarrow H_{S_{k+1}}\\ H_{S_k}=H_{S_k}$. \n",
    "\n",
    "Therefore, it is easy to prove that \n",
    "$H_\\Delta=H_\\Delta'$ and \n",
    "$\n",
    "H_\\Delta^2\n",
    "=H_{S_{k+1}}^2+H_{S_k}^2-H_{S_{k+1}}\\ H_{S_k}-H_{S_{k}}H_{S_{k+1}}\\ \n",
    "=H_{S_{k+1}}\\ +H_{S_k}-2H_{S_k}\n",
    "=H_\\Delta\n",
    "$. \n",
    "It means $H_\\Delta$ is a projection matrix. \n",
    "So $H_\\Delta\\succeq 0$, \n",
    "and $y'P_{S_k}y-y'P_{S_{k+1}}\\ y'H_{\\Delta}y\\ge 0\\ \\forall y\\in\\mathbf{R}^n$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea124a14",
   "metadata": {},
   "source": [
    "**Ans 3.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d18668f5",
   "metadata": {},
   "source": [
    "Since $X_{\\cdot,i}'X_{\\cdot,j}=\\delta_{ij}\\triangleq \\textbf{1}\\{i=j\\}\\ \\ \\forall i,j\\in\\{p\\}\\triangleq\\{1,2,\\cdots,p\\}$, $p$ is the number of columns of $X$,\n",
    "\n",
    "then $X_S'X_S=I_{|S|}\\Rightarrow H_S\\triangleq X_S(X_S'X_S)^{-1}X_S'=X_SX_S'\\Rightarrow y'H_Sy=||X_S'y||_2^2=\\sum_{i\\in S}(X'y)_i^2\\le \\sum_{l\\in\\{|S|\\}}(X'y)_{i_l}^2$ , \n",
    "\n",
    "where $z_{i_1}^2\\ge z_{i_2}^2\\ge\\cdots\\ge z_{i_p}^2$, $\\{i_l\\}_{l=1}^p=\\{p\\}$, $z_i\\triangleq (X'y)_i \\forall i\\in\\{p\\}$.\n",
    "\n",
    "So $\\min_{|S|\\le k}y'P_Sy=\\min_{|S|\\le k}(y'y-y'H_Sy)=\\max_{|S|\\le k}(y'H_Sy)=\\max_{|S|\\le k}\\sum_{l\\in\\{|S|\\}}(X'y)_{i_l}^2=\\sum_{l\\in\\{k\\}}(X'y)_{i_l}^2$ ,\n",
    "\n",
    "where $z_{i_1}^2\\ge z_{i_2}^2\\ge\\cdots\\ge z_{i_p}^2$, $\\{i_l\\}_{l=1}^p=\\{p\\}$, $z_i\\triangleq (X'y)_i \\forall i\\in\\{p\\}$.\n",
    "\n",
    "Therefore, $S$ is the index set comprising the subindices that correspond to the $k$ largest values of $|X'y|$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12b2d755",
   "metadata": {},
   "source": [
    "Here is the corresponding pseudocode code:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa6a7a37",
   "metadata": {},
   "source": [
    "---\n",
    "**Algorithm** subset_select_on_orthogonal:\n",
    "\n",
    "**Input**: orthogonal matrix $X\\in\\mathbf{R}^{n\\times p}$, vector $y\\in \\mathbf{R}$, and a constant scale $k$, the maximum size of index set $S$.\n",
    "\n",
    "**Output**: the optimal index set $S$ that satifies $|S|\\le k$.\n",
    "\n",
    "1. $z = |X'y|$\n",
    "\n",
    "2. $S = \\{ i| z_i $ is the largest $i$-th entry of $ z, i\\le k  \\}$\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e84696c9",
   "metadata": {},
   "source": [
    "Here is the Python code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e5b702c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def subset_select_on_orthogonal(X_orthogonal, y, set_size):\n",
    "    k = set_size\n",
    "    z = X_orthogonal.T @ y\n",
    "    z_abs = abs(z)# z_abs = |X'y| now\n",
    "    S = np.argsort(z_abs)[-k:] # np.argsort returns the indices that would sort an array. \n",
    "    # [-k:] is to take the subindices that correspond to the  𝑘 largest values of  |𝑋′𝑦|\n",
    "    return S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "dbf019da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 1, 5, 2, 4], dtype=int64)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import ortho_group\n",
    "\n",
    "# Set the random seed to 2023\n",
    "np.random.seed(2023)\n",
    "\n",
    "row_length = 9\n",
    "# Generate a random orthogonal matrix\n",
    "X = ortho_group.rvs(dim=row_length)\n",
    "\n",
    "# Generate a random vector\n",
    "y = np.random.rand(row_length)\n",
    "\n",
    "# Set maximum size of the subindice set\n",
    "set_size = 5\n",
    "\n",
    "# Calculate the best subindice set\n",
    "S = subset_select_on_orthogonal(X,y,set_size)\n",
    "\n",
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "30b37d19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.23849965, 0.83877248, 0.84763553, 0.81091195, 0.91112095,\n",
       "       0.84241894, 0.02617022, 0.09571838, 0.0585945 ])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify the correctness of the result\n",
    "z = abs(X.T @ y)\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "20c6f671",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 8, 7, 0, 3, 1, 5, 2, 4], dtype=int64)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argsort(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "aae4ae06",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02617022, 0.0585945 , 0.09571838, 0.23849965, 0.81091195,\n",
       "       0.83877248, 0.84241894, 0.84763553, 0.91112095])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z[np.argsort(z)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0652d1ce",
   "metadata": {},
   "source": [
    "**Ans 4.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e184232",
   "metadata": {},
   "source": [
    "We know that $\n",
    "\\frac{\\mu}{\\sigma} > 2 \\sqrt{2 \\log \\left( \\frac{2n}{\\delta}\\right)}\n",
    "\\\\\\Leftrightarrow\n",
    "\\frac{1}{\\sqrt{2}}\\frac{\\mu / 2}{\\sigma}>\n",
    "\\sqrt{\\log(\\frac{2n}{\\delta})}\n",
    "\\\\\\Leftrightarrow\n",
    "\\frac{1}{2}(\\frac{\\mu / 2}{\\sigma})^2 >\n",
    "\\log (\\frac{2n}{\\delta})\n",
    "\\\\\\Leftrightarrow\n",
    "\\exp\\{\\frac{1}{2}(\\frac{\\mu / 2}{\\sigma})^2 \\}>\n",
    "\\frac{2n}{\\delta}\n",
    "\\\\\n",
    "\\Leftrightarrow\n",
    "\\exp\\{\\frac{-1}{2}(\\frac{\\mu / 2}{\\sigma})^2 \\}\\le\n",
    "\\frac{\\delta}{2n}\n",
    "\\\\\n",
    "\\Leftrightarrow\n",
    "2n \\exp\\{\\frac{-1}{2}(\\frac{\\mu / 2}{\\sigma})^2 \\}\\le\n",
    "\\delta\n",
    "\\\\\n",
    "\\Leftrightarrow\n",
    "1-2n \\exp\\{\\frac{-1}{2}(\\frac{\\mu / 2}{\\sigma})^2 \\}>\n",
    "1-\\delta\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e479d842",
   "metadata": {},
   "source": [
    "And that $\n",
    "P\\{|\\epsilon_i| \\ge t,\\exists i\\in\\{p\\}\\}\n",
    "\\\\=\n",
    "\\mathbb P\\{\\cup_{i=1}^p\\{|\\epsilon_i| \\ge t\\}\\}\n",
    "\\\\\\le\n",
    "\\mathbb P \\left\\{ |\\epsilon_1| \\ge t \\right\\}+\n",
    "\\mathbb P \\left\\{ |\\epsilon_2| \\ge t \\right\\}+\n",
    "\\cdots+\n",
    "\\mathbb P \\left\\{ |\\epsilon_p| \\ge t \\right\\}\n",
    "\\le 2p e^{-t^2 / 2\\sigma^2}\n",
    "=2n e^{-t^2 / 2\\sigma^2}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06f9ca4b",
   "metadata": {},
   "source": [
    "So $\n",
    "P\\{|\\epsilon_i|<\\mu/2\\ \\forall i\\in\\{p\\}\\}\n",
    "\\\\=1-P\\{|\\epsilon_i| \\ge \\mu/2,\\exists i\\in\\{p\\}\\}\n",
    "> 1- 2n e^{-(\\mu/2)^2 / 2\\sigma^2}\n",
    "\\\\>1-\\delta$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2acdd106",
   "metadata": {},
   "source": [
    "WLOG, suppose $\\beta_i\\not=0,$ $i=1,2,\\cdots,k$, i.e. $S_0=\\{k\\}\\triangleq\\{1,2,\\cdots,k\\}$. Define $S$ to be the set chosen by subset selection algorithm.\n",
    "\n",
    "Therefore, \n",
    "$\n",
    "P(S=S_0)\n",
    "=\n",
    "P\\{|(\\beta_S)_i|=|(X_S'y)_i|=|(y_S)_i|=|(y_{S_0})_i|>|(y_{ \\{p\\}\\text{\\ } S_0})_j|, i\\in \\{k\\},\\ \\ j\\in\\{|S\\text{\\ } S_0|\\}\\}\n",
    "\\\\=\n",
    "P\\{|\\beta_i+\\epsilon_i|>|\\epsilon_j|, i=1,2,\\cdots,k,\\ \\ j=k+1,k+2,\\cdots,p\\}\n",
    "\\\\\\ge\n",
    "P\\{\\beta_i+\\epsilon_i>|\\epsilon_j|, i=1,2,\\cdots,k,\\ \\ j=k+1,k+2,\\cdots,p\\}\\text{[This is a sufficient condition for the above one]}\n",
    "\\\\\\ge\n",
    "P\\{\\beta_i-|\\epsilon_i|>|\\epsilon_j|, i=1,2,\\cdots,k,\\ \\ j=k+1,k+2,\\cdots,p\\}\\text{[This is a sufficient condition for the above one]}\n",
    "\\\\\\ge\n",
    "P\\{\\beta_i>2|\\epsilon_j|, i=1,2,\\cdots,k,\\ \\ j=1,2,\\cdots,p\\}\\text{[This is a sufficient condition for the above one]}\n",
    "\\\\=\n",
    "P\\{\\mu=\\min_{i\\in\\{k\\}} |\\beta_i|=\\min_{i\\in\\{k\\}} \\beta_i>2|\\epsilon_j|,\\ j=1,2,\\cdots,p\\}\n",
    "\\\\=\n",
    "P\\{|\\epsilon_i|<\\mu/2\\ \\forall i\\in\\{p\\}\\}\n",
    "\\\\>\n",
    "1-\\delta.\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1e8672a",
   "metadata": {},
   "source": [
    "### Exercise 4 (Ridge, lasso and adaptive lasso) (35 pts, 5 pts each)\n",
    "\n",
    "For this exercise, it may be helpful to use the `sklearn.linear_model` module.  I have also included a plotting tool for making the lasso path in ESL.\n",
    "\n",
    "1. Load the training and test data using the script below.  Fit OLS on the training dataset and compute the test error.  Throughout you do not need to compute an intercept but you should normalize the $X$ (divide by the column norms).\n",
    "2. Ridge regression: Train and tune ridge regression using a validation set (choose LOOCV) and compute the test error (square error loss).\n",
    "3. Fit the lasso path with lars to the data and compute the test error for each returned lasso coefficient.\n",
    "4. Perform 3 without the lasso modification generating the lars path.  Compare and contrast the lars path to the lasso path, what is the key difference.  Comment on when the active sets differ and how, if they do at all.\n",
    "5. Fit the lasso path with coordinate descent to the data. Compare the lasso path using coordinate descent with the path using lars. Comment on what you found.\n",
    "6. Extract each active set from the lasso path and recompute the restricted OLS for each.  Compute and compare the test error for each model.\n",
    "7. Read this website [click here](https://towardsdatascience.com/an-adaptive-lasso-63afca54b80d). Fit the adaptive lasso method to the data. Compare the test error between the adaptive lasso and lasso for each returned coefficient. Comment on what you found."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "423d6da2",
   "metadata": {},
   "source": [
    "**Ans 1.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5b0b5814",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression, Ridge, Lasso, LassoCV, LassoLarsCV\n",
    "from sklearn.preprocessing import StandardScaler, normalize\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.linear_model import RidgeCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c4717250",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_lars(coefs, lines=False, title=\"Lars Path\"):\n",
    "    \"\"\"\n",
    "    Plot the lasso path where coefs is a matrix - the columns are beta vectors\n",
    "    \"\"\"\n",
    "    xx = np.sum(np.abs(coefs.T), axis=1)\n",
    "    xx /= xx[-1]\n",
    "    plt.plot(xx, coefs.T)\n",
    "    ymin, ymax = plt.ylim()\n",
    "    if lines:\n",
    "        plt.vlines(xx, ymin, ymax, linestyle='dashed')\n",
    "    plt.xlabel('|coef| / max|coef|')\n",
    "    plt.ylabel('Coefficients')\n",
    "    plt.title(title)\n",
    "    plt.axis('tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "85814dce",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "with open('hw1.data','rb') as f:\n",
    "    y_tr,X_tr,y_te,X_te = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f32cf98e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test error for OLS: 1.0396\n"
     ]
    }
   ],
   "source": [
    "# Normalize X\n",
    "X = np.concatenate((X_tr, X_te))\n",
    "y = np.concatenate((y_tr, y_te))\n",
    "X = normalize(X, axis=0)\n",
    "\n",
    "X_tr = X[:1000, :]\n",
    "X_te = X[1000:, :]\n",
    "\n",
    "# Fit OLS\n",
    "lm = LinearRegression(fit_intercept=False)\n",
    "lm.fit(X_tr, y_tr)\n",
    "\n",
    "# Compute test error\n",
    "y_hat = lm.predict(X_te)\n",
    "test_error_ols = np.sum((y_te-y_hat)**2)/len(y_hat)\n",
    "print(\"Test error for OLS: {:.4f}\".format(test_error_ols))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8da50fbd",
   "metadata": {},
   "source": [
    "**Ans 2.** \n",
    "\n",
    "Train and tune ridge regression using a validation set (choose LOOCV) and compute the test error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "3cdb41cc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda:  0.00024623190954773874\n",
      "min validation error:  1.139043321613451\n"
     ]
    }
   ],
   "source": [
    "lamdas = np.linspace(0.001**3,0.001,200)\n",
    "model_ridge = RidgeCV(alphas = lamdas, store_cv_values=True)\n",
    "model_ridge.fit(X_tr, y_tr)\n",
    "cv_vals = model_ridge.cv_values_\n",
    "LOOridge = cv_vals.mean(axis=0)\n",
    "lamda = lamdas[np.argmin(LOOridge)]\n",
    "print('lambda: ', lamda)\n",
    "print('min validation error: ', np.min(LOOridge))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "78bd5577",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test error for Ridge: 1.0381\n"
     ]
    }
   ],
   "source": [
    "# Compute test error\n",
    "y_te_pred_ridge = model_ridge.predict(X_te)\n",
    "test_error_ridge = mean_squared_error(y_te, y_te_pred_ridge)\n",
    "print(\"Test error for Ridge: {:.4f}\".format(test_error_ridge))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1176af2",
   "metadata": {},
   "source": [
    "**Ans 3.** Fit the lasso path with lars to the data and compute the test error for each returned lasso coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d554e009",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import lars_path, lasso_path, Lasso\n",
    "plot_range = range(40,60)\n",
    "# Lasso with LARS\n",
    "larlasso_path = lars_path(X_tr, y_tr, method='lasso')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0b0154ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test error for Lasso coefficient 40: 1.0185\n",
      "Test error for Lasso coefficient 41: 1.0147\n",
      "Test error for Lasso coefficient 42: 1.0145\n",
      "Test error for Lasso coefficient 43: 1.0121\n",
      "Test error for Lasso coefficient 44: 1.0103\n",
      "Test error for Lasso coefficient 45: 1.0076\n",
      "Test error for Lasso coefficient 46: 1.0060\n",
      "Test error for Lasso coefficient 47: 1.0060\n",
      "Test error for Lasso coefficient 48: 1.0053\n",
      "Test error for Lasso coefficient 49: 1.0036\n",
      "Test error for Lasso coefficient 50: 1.0034\n",
      "Test error for Lasso coefficient 51: 1.0033\n",
      "Test error for Lasso coefficient 52: 1.0031\n",
      "Test error for Lasso coefficient 53: 1.0017\n",
      "Test error for Lasso coefficient 54: 1.0016\n",
      "Test error for Lasso coefficient 55: 1.0012\n",
      "Test error for Lasso coefficient 56: 1.0009\n",
      "Test error for Lasso coefficient 57: 0.9988\n",
      "Test error for Lasso coefficient 58: 0.9988\n",
      "Test error for Lasso coefficient 59: 0.9986\n"
     ]
    }
   ],
   "source": [
    "# Compute test error for each Lasso coefficient\n",
    "for i in plot_range:\n",
    "    coef = larlasso_path[2][:,i]\n",
    "    y_te_pred_lasso = X_te.dot(coef)\n",
    "    test_error_lasso = mean_squared_error(y_te, y_te_pred_lasso)\n",
    "    print(\"Test error for Lasso coefficient {}: {:.4f}\".format(i, test_error_lasso))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c642e960",
   "metadata": {},
   "source": [
    "**Ans 4.** Perform 3 without the lasso modification generating the lars path. Compare and contrast the lars path to the lasso path, what is the key difference. Comment on when the active sets differ and how, if they do at all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "b93087e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Perform 3 without the lasso modification generating the lars path.\n",
    "lars_path = lars_path(X_tr, y_tr, method='lar')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ac6c0671",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test error for LARS path without the lasso modification 40: 1.0185\n",
      "Test error for LARS path without the lasso modification 41: 1.0147\n",
      "Test error for LARS path without the lasso modification 42: 1.0145\n",
      "Test error for LARS path without the lasso modification 43: 1.0121\n",
      "Test error for LARS path without the lasso modification 44: 1.0103\n",
      "Test error for LARS path without the lasso modification 45: 1.0076\n",
      "Test error for LARS path without the lasso modification 46: 1.0060\n",
      "Test error for LARS path without the lasso modification 47: 1.0060\n",
      "Test error for LARS path without the lasso modification 48: 1.0053\n",
      "Test error for LARS path without the lasso modification 49: 1.0036\n",
      "Test error for LARS path without the lasso modification 50: 1.0034\n",
      "Test error for LARS path without the lasso modification 51: 1.0033\n",
      "Test error for LARS path without the lasso modification 52: 1.0031\n",
      "Test error for LARS path without the lasso modification 53: 1.0017\n",
      "Test error for LARS path without the lasso modification 54: 1.0016\n",
      "Test error for LARS path without the lasso modification 55: 1.0012\n",
      "Test error for LARS path without the lasso modification 56: 1.0009\n",
      "Test error for LARS path without the lasso modification 57: 0.9988\n",
      "Test error for LARS path without the lasso modification 58: 0.9988\n",
      "Test error for LARS path without the lasso modification 59: 0.9986\n"
     ]
    }
   ],
   "source": [
    "# Compute test error for each Lasso coefficient\n",
    "for i in plot_range:\n",
    "    coef = lars_path[2][:,i]\n",
    "    y_te_pred_lars = X_te.dot(coef)\n",
    "    test_error_lars = mean_squared_error(y_te, y_te_pred_lars)\n",
    "    print(\"Test error for LARS path without the lasso modification {}: {:.4f}\".format(i, test_error_lars))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a2f615df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare and contrast the lars path to the lasso path\n",
    "plot_lars(larlasso_path[2][plot_range,:], lines=False, title=\"Lasso Path\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4bb17492",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare and contrast the lars path to the lasso path\n",
    "plot_lars(lars_path[2][plot_range,:], lines=False, title=\"LARS without Lasso modification\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db721792",
   "metadata": {},
   "source": [
    "Lasso path and the lars path are quite similar. They get slightly different after `|coef|/max|coef|` gets larger than 0.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d5438d05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 103), (100, 102))"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index_lars = (lars_path[2]!=0) * 1\n",
    "index_lasso = (larlasso_path[2]!=0) * 1\n",
    "index_lasso.shape, index_lars.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "b9a6673f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "70\n"
     ]
    }
   ],
   "source": [
    "for k in range(102):\n",
    "    if np.sum(index_lasso[:, k] != index_lars[:, k]) > 0:\n",
    "        print(k)\n",
    "        break\n",
    "# this tells us that the lasso path and lars path differs in the 71th path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "a5ade8d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index_lars[:, 70] != index_lasso[:, 70]\n",
    "# this tells us that lasso drops the 4-th coefficient but lars doesn't drop it"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b04ed74",
   "metadata": {},
   "source": [
    "**Ans 5.** Fit the lasso path with coordinate descent to the data. Compare the lasso path using coordinate descent with the path using lars. Comment on what you found."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "4ba20719",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lasso_path = lasso_path(X_tr, y_tr)\n",
    "plot_lars(lasso_path[1][plot_range,:], lines=False, title='Lasso Path with Coordinate Descent')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5125e606",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lars(lars_path[2][plot_range,:], lines=False, title=\"LARS without Lasso modification\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "8d14a680",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 100), (100, 102))"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index_lars = (lars_path[2]!=0) * 1\n",
    "index_lasso_2 = (lasso_path[1]!=0) * 1\n",
    "index_lasso_2.shape, index_lars.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "4ee14e8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "for k in range(100):\n",
    "    if np.sum(index_lasso_2[:, k] != index_lars[:, k]) > 0:\n",
    "        print(k)\n",
    "        break\n",
    "# this tells us that the lasso path and lars path differs in the 71th path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "0a93d2b7",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index_lars[:, 70] != index_lasso_2[:, 70]\n",
    "# this tells us that lasso drops the 4-th coefficient but lars doesn't drop it"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b2d4152",
   "metadata": {},
   "source": [
    "The lasso path using coordinate descent and the path using lars are also very silimar with eath other."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15834cd5",
   "metadata": {},
   "source": [
    "**Ans 6.** Extract each active set from the lasso path and recompute the restricted OLS for each. Compute and compare the test error for each model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f98033c1",
   "metadata": {},
   "source": [
    "Below is the figure for test errors. The test error drops first but then increases drastically. When $\\lambda$ is greater, more coefficients are to be dropped and the model could not predict well. The minimum test error happens when $\\lambda=0.000949$ and $\\widehat{err}=0.9844$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d135c4a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "error_resols = []\n",
    "active_sets = lars_path[2]\n",
    "for i in range(len(lars_path[0])):\n",
    "    active_set = active_sets[:, i]\n",
    "    X_restr = X_tr[:, np.where(active_set!=0)[0]]\n",
    "    X_reste = X_te[:, np.where(active_set!=0)[0]]\n",
    "    if np.sum(active_set!=0)==0:\n",
    "        y_reshat = 0\n",
    "    else:\n",
    "        ols = LinearRegression(fit_intercept=False)\n",
    "        ols.fit(X_restr, y_tr)\n",
    "        y_reshat = ols.predict(X_reste)\n",
    "    error_resols += [np.mean((y_reshat-y_te)**2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "a307557b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0009490267003594619, 0.9844499297178834)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lars_path[0][np.argmin(error_resols)], min(error_resols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "a1a8fa59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  5,  8, 27, 38, 50, 52, 53, 68, 69, 76, 77, 78, 80,\n",
       "       91, 96, 97], dtype=int64)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(index_lasso[:, np.argmin(error_resols)]==1)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5c6698e1",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Restricted OLS Test Error for Lasso')"
      ]
     },
     "execution_count": 42,
     "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": [
    "plt.plot(lars_path[0],error_resols, 'r', label='Test Error for Lasso')\n",
    "plt.xlabel('lambdas')\n",
    "plt.ylabel('Test error')\n",
    "plt.title('Restricted OLS Test Error for Lasso')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "330f0bcb",
   "metadata": {},
   "source": [
    "### Exercise 4 (Ridge, lasso and adaptive lasso) (35 pts, 5 pts each)\n",
    "\n",
    "For this exercise, it may be helpful to use the `sklearn.linear_model` module.  I have also included a plotting tool for making the lasso path in ESL.\n",
    "\n",
    "6. Extract each active set from the lasso path and recompute the restricted OLS for each.  Compute and compare the test error for each model.\n",
    "7. Read this website [click here](https://towardsdatascience.com/an-adaptive-lasso-63afca54b80d). Fit the adaptive lasso method to the data. Compare the test error between the adaptive lasso and lasso for each returned coefficient. Comment on what you found."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16bac027",
   "metadata": {},
   "source": [
    "**Ans 7.** Read this website [click here](https://towardsdatascience.com/an-adaptive-lasso-63afca54b80d). Fit the adaptive lasso method to the data. Compare the test error between the adaptive lasso and lasso for each returned coefficient. Comment on what you found."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "85cdf54a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load packages\n",
    "import numpy as np\n",
    "import asgl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "22c783a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda1 = np.linspace(0.001**3,0.001,1800)\n",
    "tvt_lasso = asgl.TVT(model='lm', penalization='lasso', lambda1=lambda1, parallel=True,\n",
    "                     error_type='MSE', random_state=1, train_size=50, validate_size=25)\n",
    "lasso_result = tvt_lasso.train_validate_test(x=X_tr, y=y_tr)\n",
    "\n",
    "lasso_prediction_error = lasso_result['test_error']\n",
    "lasso_betas = lasso_result['optimal_betas'][1:] # Remove intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "fec5dfd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "tvt_alasso = asgl.TVT(model='lm', penalization='alasso', lambda1=lambda1, parallel=True,\n",
    "                      weight_technique='lasso', \n",
    "                      error_type='MSE', random_state=1, \n",
    "                      train_size=50, validate_size=25)\n",
    "alasso_result = tvt_alasso.train_validate_test(x=X_tr, y=y_tr)\n",
    "\n",
    "alasso_prediction_error = alasso_result['test_error']\n",
    "alasso_betas = alasso_result['optimal_betas'][1:] # Remove intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "65268613",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lasso error:1.996\n",
      "Adaptive lasso error:1.634\n"
     ]
    }
   ],
   "source": [
    "# Prediction error\n",
    "print(f'Lasso error:{np.round(lasso_prediction_error, 3)}\\nAdaptive lasso error:{np.round(alasso_prediction_error, 3)}')\n",
    "\n",
    "#Lasso error:1.996\n",
    "#Adaptive lasso error:1.634"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54ac1840",
   "metadata": {},
   "source": [
    "The adaptive lasso method has a smaller error than the original one. But this result is not so stable. Try these different initial settings `lambda1 = np.linspace(0.001**3,0.001,3000)` and `lambda1 = np.linspace(0.001**3,0.001,300)`\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78146704",
   "metadata": {},
   "source": [
    "For `lambda1 = np.linspace(0.001**3,0.001,3000)`, the result is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "2cd923db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lasso error:1.996\n",
      "Adaptive lasso error:2.01\n"
     ]
    }
   ],
   "source": [
    "lambda1 = np.linspace(0.001**3,0.001,3000)\n",
    "tvt_lasso = asgl.TVT(model='lm', penalization='lasso', lambda1=lambda1, parallel=True,\n",
    "                     error_type='MSE', random_state=1, train_size=50, validate_size=25)\n",
    "lasso_result = tvt_lasso.train_validate_test(x=X_tr, y=y_tr)\n",
    "\n",
    "lasso_prediction_error = lasso_result['test_error']\n",
    "lasso_betas = lasso_result['optimal_betas'][1:] # Remove intercept\n",
    "\n",
    "tvt_alasso = asgl.TVT(model='lm', penalization='alasso', lambda1=lambda1, parallel=True,\n",
    "                      weight_technique='lasso', \n",
    "                      error_type='MSE', random_state=1, \n",
    "                      train_size=50, validate_size=25)\n",
    "alasso_result = tvt_alasso.train_validate_test(x=X_tr, y=y_tr)\n",
    "\n",
    "alasso_prediction_error = alasso_result['test_error']\n",
    "alasso_betas = alasso_result['optimal_betas'][1:] # Remove intercept\n",
    "\n",
    "# Prediction error\n",
    "print(f'Lasso error:{np.round(lasso_prediction_error, 3)}\\nAdaptive lasso error:{np.round(alasso_prediction_error, 3)}')\n",
    "\n",
    "#Lasso error:1.996\n",
    "#Adaptive lasso error:2.01"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d693f0b",
   "metadata": {},
   "source": [
    "For `lambda1 = np.linspace(0.001**3,0.001,300)`, the result is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "75395938",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lasso error:1.996\n",
      "Adaptive lasso error:3.37\n"
     ]
    }
   ],
   "source": [
    "lambda1 = np.linspace(0.001**3,0.001,300)\n",
    "tvt_lasso = asgl.TVT(model='lm', penalization='lasso', lambda1=lambda1, parallel=True,\n",
    "                     error_type='MSE', random_state=1, train_size=50, validate_size=25)\n",
    "lasso_result = tvt_lasso.train_validate_test(x=X_tr, y=y_tr)\n",
    "\n",
    "lasso_prediction_error = lasso_result['test_error']\n",
    "lasso_betas = lasso_result['optimal_betas'][1:] # Remove intercept\n",
    "\n",
    "tvt_alasso = asgl.TVT(model='lm', penalization='alasso', lambda1=lambda1, parallel=True,\n",
    "                      weight_technique='lasso', \n",
    "                      error_type='MSE', random_state=1, \n",
    "                      train_size=50, validate_size=25)\n",
    "alasso_result = tvt_alasso.train_validate_test(x=X_tr, y=y_tr)\n",
    "\n",
    "alasso_prediction_error = alasso_result['test_error']\n",
    "alasso_betas = alasso_result['optimal_betas'][1:] # Remove intercept\n",
    "\n",
    "# Prediction error\n",
    "print(f'Lasso error:{np.round(lasso_prediction_error, 3)}\\nAdaptive lasso error:{np.round(alasso_prediction_error, 3)}')\n",
    "\n",
    "#Lasso error:1.996\n",
    "#Adaptive lasso error:3.37"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1972948b",
   "metadata": {},
   "source": [
    "Without further investigation on these result, I could find that\n",
    "\n",
    "* Adaptive lasso method could have a smaller error than the original lasso method as long as it starts with well-chosen $\\lambda$s\n",
    "\n",
    "* Too smaller or to large $\\lambda$s are all bad for adaptive lasso method. The performance of adaptive lasso method is sensitive to the initial setting.\n",
    "\n",
    "* When compared with adaptive lasso method, the performance of Lasso method is much less sensitive to the initial settings."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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