11611065_10327428_lab1.ipynb

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    "# **Save this file as studentid1_studentid2_lab#.ipynb**\n",
    "(Your student-id is the number shown on your student card.)\n",
    "\n",
    "E.g. if you work with 3 people, the notebook should be named:\n",
    "12301230_3434343_1238938934_lab1.ipynb.\n",
    "\n",
    "**This will be parsed by a regexp, so please double check your filename.**\n",
    "\n",
    "Before you turn this problem in, please make sure everything runs correctly. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
    "\n",
    "**Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your names and email adresses below.**\n",
    "\n"
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    "NAME = \"Tharangni Harsha Sivaji\"\n",
    "NAME2 = \"Mirthe van Diepen\"\n",
    "NAME3 = \"\"\n",
    "EMAIL = \"tharangni@gmail.com\"\n",
    "EMAIL2 = \"mmvandiepen@gmail.com\"\n",
    "EMAIL3 = \"\""
   ]
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   "source": [
    "---"
   ]
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    "# Lab 1: Linear Regression and Overfitting\n",
    "\n",
    "### Machine Learning 1, September 2017\n",
    "\n",
    "Notes on implementation:\n",
    "\n",
    "* You should write your code and answers in this IPython Notebook: http://ipython.org/notebook.html. If you have problems, please contact your teaching assistant.\n",
    "* Please write your answers right below the questions.\n",
    "* Among the first lines of your notebook should be \"%pylab inline\". This imports all required modules, and your plots will appear inline.\n",
    "* Refer to last week's lab notes, i.e. http://docs.scipy.org/doc/, if you are unsure about what function to use. There are different correct ways to implement each problem!\n",
    "* For this lab, your regression solutions should be in closed form, i.e., should not perform iterative gradient-based optimization but find the exact optimum directly.\n",
    "* use the provided test boxes to check if your answers are correct"
   ]
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   "source": [
    "%pylab inline\n",
    "plt.rcParams[\"figure.figsize\"] = [20,10]"
   ]
  },
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    "$\\newcommand{\\bPhi}{\\mathbf{\\Phi}}$\n",
    "$\\newcommand{\\bx}{\\mathbf{x}}$\n",
    "$\\newcommand{\\bw}{\\mathbf{w}}$\n",
    "$\\newcommand{\\bt}{\\mathbf{t}}$\n",
    "$\\newcommand{\\by}{\\mathbf{y}}$\n",
    "$\\newcommand{\\bm}{\\mathbf{m}}$\n",
    "$\\newcommand{\\bS}{\\mathbf{S}}$\n",
    "$\\newcommand{\\bI}{\\mathbf{I}}$\n",
    "\n",
    "## Part 1: Polynomial Regression"
   ]
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   "source": [
    "### 1.1. Generate periodic data (5 points)\n",
    "Write a method `gen_cosine(N)` that generates toy data like in fig 1.2 of Bishop's book. The method should have a parameter $N$, and should return $N$-dimensional vectors $\\bx$ and $\\bt$, where $\\bx$ contains evenly spaced values from 0 to (including) 2$\\pi$, and the elements $t_i$ of $\\bt$ are distributed according to:\n",
    "\n",
    "$$t_i \\sim \\mathcal{N}(\\mu_i, \\sigma^2)$$\n",
    "\n",
    "where $x_i$ is the $i$-th elements of $\\bf{x}$, the mean $\\mu_i = \\cos(x_i)$ and the standard deviation $\\sigma = 0.2$.\n"
   ]
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   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import *\n",
    "\n",
    "def gen_cosine(n):\n",
    "    x = np.linspace(0, 2.*np.pi, n)\n",
    "    t = np.random.normal(np.cos(x), 0.2, n) \n",
    "    #raise NotImplementedError()\n",
    "    \n",
    "    return x, t\n"
   ]
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   "source": [
    "### Test your function\n",
    "np.random.seed(5)\n",
    "N = 10\n",
    "x, t = gen_cosine(N)\n",
    "\n",
    "assert x.shape == (N,), \"the shape of x is incorrect\"\n",
    "assert t.shape == (N,), \"the shape of t is incorrect\"\n"
   ]
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   "source": [
    "### 1.2 Polynomial regression (10 points)\n",
    "\n",
    "Write a method `fit_polynomial(x, t, M)` that finds the maximum-likelihood solution of an _unregularized_ $M$-th order polynomial for some dataset `x`. The error function to minimize w.r.t. $\\bw$ is:\n",
    "\n",
    "$E(\\bw) = \\frac{1}{2} (\\bPhi\\bw - \\bt)^T(\\bPhi\\bw - \\bt)$\n",
    "\n",
    "where $\\bPhi$ is the _feature matrix_ (or _design matrix_) as explained in Bishop's book at section 3.1.1, $\\bt$ is the vector of target values. Your method should return a vector $\\bw$ with the maximum-likelihood parameter estimates, as well as the _feature matrix_ $\\bPhi$."
   ]
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   "source": [
    "def designmatrix(x, M): # it is highly recommended to write a helper function that computes Phi\n",
    "    if M<0:\n",
    "        return 'enter positive power'\n",
    "    M += 1 #due to basis function\n",
    "    Phi = np.zeros((len(x),M), dtype=int) #empty Phi matrix\n",
    "    \n",
    "    #entering values on the basis of general equation of Phi\n",
    "    for i in range(M):\n",
    "        for j in range(len(x)):\n",
    "            Phi[j][i] = int(math.pow(x[j],i))\n",
    "    \n",
    "    return Phi\n",
    "    #raise NotImplementedError()\n",
    "\n",
    "def fit_polynomial(x, t, M): \n",
    "    Phi = designmatrix(x, M)\n",
    "    w_ml = np.dot(pinv(Phi),t)\n",
    "    \n",
    "    \n",
    "   #raise NotImplementedError()\n",
    "    \n",
    "    return w_ml, Phi\n",
    "\n",
    "# N = 10\n",
    "# x = np.square((np.linspace(-1, 1, N)))\n",
    "# t = 0.5*x + 1.5\n",
    "# m = 2\n",
    "# w, Phi = fit_polynomial(x,t,m)"
   ]
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   "source": [
    "### Test your function\n",
    "N = 10\n",
    "x = np.square((np.linspace(-1, 1, N)))\n",
    "t = 0.5*x + 1.5\n",
    "m = 2\n",
    "w, Phi = fit_polynomial(x,t,m)\n",
    "\n",
    "assert w.shape == (m+1,), \"The shape of w is incorrect\"\n",
    "assert Phi.shape == (N, m+1), \"The shape of Phi is incorrect\"\n"
   ]
  },
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   "source": [
    "### 1.3 Plot (5 points)\n",
    "Sample a dataset with $N=10$, and fit four polynomials with $M \\in (0, 2, 4, 8)$.\n",
    "For each value of $M$, plot the prediction function, along with the data and the original cosine function. The resulting figure should look similar to fig 1.4 of the Bishop's book. Note that you can use matplotlib's `plt.pyplot(.)` functionality for creating grids of figures."
   ]
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CXQu5PP/lTGs+jZuvuNnnOUREctqc7XNoOrkpR+KPcMdVdzCp6aR/LpI5RCOT3rFVIyes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\n4VjCMQYvHWw7jkiuMmL5CA6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r3XfD7Nn2cljgbX3UyKRYZYDIUHdlrKSUJLthRHwgMTUR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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e281609898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def pred_func(x,w):\n",
    "    y=[]\n",
    "    \n",
    "    for i in x:\n",
    "        res=0\n",
    "        for j in range(len(w)):\n",
    "            res +=(math.pow(i, j) * w[j])\n",
    "        else:\n",
    "            y.append(res)\n",
    "            \n",
    "    return y\n",
    "\n",
    "N=10\n",
    "x_ , t_ = gen_cosine(N) \n",
    "M = [0,2,4,8]\n",
    "\n",
    "plt.figure(figsize=(12, 10), dpi=90)\n",
    "for i in range(len(M)):\n",
    "    w_, phi = fit_polynomial(x_, t_, M[i])\n",
    "    y_ = pred_func(x_,w_)\n",
    "    \n",
    "    plt.subplot(int(221 + i))\n",
    "    plt.plot(x_, np.cos(x_), color=\"green\")\n",
    "    plt.plot(x_, y_, color=\"red\")\n",
    "    plt.plot(x_, t_, 'bo')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    plt.title('M = ' + str(M[i]))\n",
    "\n",
    "              \n",
    "plt.show()\n",
    "\n",
    "#raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "e1dec783687fc31125cbf948151940d4",
     "grade": false,
     "grade_id": "cell-2597ee45cb3998ed",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 1.4 Regularized linear regression (10 points)\n",
    "\n",
    "Write a method `fit_polynomial_reg(x, t, M, lamb)` that fits a _regularized_ $M$-th order polynomial to the periodic data, as discussed in the lectures, where `lamb` is the regularization term _lambda_. (Note that 'lambda' cannot be used as a variable name in Python since it has a special meaning). The error function to minimize w.r.t. $\\bw$:\n",
    "\n",
    "$E(\\bw) = \\frac{1}{2} (\\bPhi\\bw - \\bt)^T(\\bPhi\\bw - \\bt) + \\frac{\\lambda}{2} \\mathbf{w}^T \\mathbf{w}$\n",
    "\n",
    "For background, see section 3.1.4 of Bishop's book.\n",
    "\n",
    "The function should return $\\bw$ and $\\bPhi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "dc76736fba956e5d9cc51a318c2507c3",
     "grade": false,
     "grade_id": "cell-9fe81fd5537daff9",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [1, 0, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 0, 0],\n",
       "       [1, 1, 1]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def fit_polynomial_reg(x, t, m, lamb):\n",
    "    \n",
    "    if m<0:\n",
    "        return 'return a positive power'\n",
    "    m += 1\n",
    "    \n",
    "    Phi = np.zeros((len(x),m), dtype=int)\n",
    "    ILambda = np.dot(np.eye(m), lamb)\n",
    "    \n",
    "    for i in range(m):\n",
    "        for j in range(len(x)):\n",
    "            Phi[j][i] = int(math.pow(x[j],i))\n",
    "            \n",
    "    w_ml = np.dot(np.dot(inv(ILambda + np.dot(Phi.transpose(), Phi)), Phi.transpose()), t)\n",
    "    \n",
    "    \n",
    "#     raise NotImplementedError()\n",
    "    \n",
    "    return w_ml, Phi\n",
    "\n",
    "### Test your function\n",
    "# N = 10\n",
    "# x = np.square((np.linspace(-1, 1, N)))\n",
    "# t = 0.5*x + 1.5\n",
    "# m = 2\n",
    "# lamb = 0.1\n",
    "# w, Phi = fit_polynomial_reg(x,t,m, lamb)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "06ed377acf8ca027242a067aafbf59b8",
     "grade": true,
     "grade_id": "cell-a2e561cbc5a4140b",
     "locked": true,
     "points": 10,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "### Test your function\n",
    "N = 10\n",
    "x = np.square((np.linspace(-1, 1, N)))\n",
    "t = 0.5*x + 1.5\n",
    "m = 2\n",
    "lamb = 0.1\n",
    "w, Phi = fit_polynomial_reg(x,t,m, lamb)\n",
    "\n",
    "assert w.shape == (m+1,), \"The shape of w is incorrect\"\n",
    "assert Phi.shape == (N, m+1), \"The shape of w is incorrect\" \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "2812b11d458a2520bacff231d56b8f4c",
     "grade": false,
     "grade_id": "cell-638bbedf69267917",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### 1.5 Model selection by cross-validation (15 points)\n",
    "Use cross-validation to find a good choice of $M$ and $\\lambda$, given a dataset of $N=10$ datapoints generated with `gen_cosine(20)`. You should write a function that tries (loops over) a reasonable range of choices of $M$ and $\\lambda$, and returns the choice with the best cross-validation error. In this case you use $K=5$ folds.\n",
    "\n",
    "You can let $M \\in (0, 1, ..., 10)$, and let $\\lambda \\in (e^{-10}, e^{-9}, ..., e^{0})$.\n",
    "\n",
    "a) (5 points) First of all, write a method `pred_error(x_train, x_valid, t_train, t_valid, M, lamb)` that compares the prediction of your method `fit_polynomial_reg` for a given set of parameters $M$ and $\\lambda$ to `t_valid`. It should return the prediction error for a single fold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "2cfb7f4cc04e4af74f4655e772e33b09",
     "grade": false,
     "grade_id": "cell-d631a845dec603be",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def pred_error(x_train, x_valid, t_train, t_valid, M, reg):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    \n",
    "    return pred_err\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "45c2bc1172798293ab8fea0a856191ce",
     "grade": true,
     "grade_id": "cell-ba7261e2eae040fd",
     "locked": true,
     "points": 5,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "### Test your function\n",
    "N = 10\n",
    "x = np.linspace(-1, 1, N)\n",
    "t = 0.5*np.square(x) + 1.5\n",
    "M = 2\n",
    "reg = 0.1\n",
    "pred_err = pred_error(x[:-2], x[-2:], t[:-2], t[-2:], M, reg)\n",
    "\n",
    "assert pred_err < 0.01, \"pred_err is too big\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "0e6aab76a18a6ef5f13d92c330d3cd5c",
     "grade": false,
     "grade_id": "cell-4c1ef9acd1f93493",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "b) (10 points) Now write a method find_best_m_and_lamb(x, t) that finds the best values for $M$ and $\\lambda$. The method should return the best $M$ and $\\lambda$. To get you started, here is a method you can use to generate indices of cross-validation folds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "d673ab5c8a9231852af04a728bf93253",
     "grade": false,
     "grade_id": "cell-9abfee773ee6f780",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "def kfold_indices(N, k):\n",
    "    all_indices = np.arange(N,dtype=int)\n",
    "    np.random.shuffle(all_indices)\n",
    "    idx = [int(i) for i in np.floor(np.linspace(0,N,k+1))]\n",
    "    train_folds = []\n",
    "    valid_folds = []\n",
    "    for fold in range(k):\n",
    "        valid_indices = all_indices[idx[fold]:idx[fold+1]]\n",
    "        valid_folds.append(valid_indices)\n",
    "        train_folds.append(np.setdiff1d(all_indices, valid_indices))\n",
    "    return train_folds, valid_folds\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "65930a94ed4b46300fcf5aef054662a0",
     "grade": false,
     "grade_id": "cell-0553f08188fbfcd6",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "def find_best_m_and_lamb(x, t):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    \n",
    "    return M_best, lamb_best\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "09809a3d53a4725b396bbe8b4526cb19",
     "grade": true,
     "grade_id": "cell-523aa38e51c8913c",
     "locked": true,
     "points": 10,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "### If you want you can write your own test here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "818d2036edbff780a450e6e1f4123eff",
     "grade": false,
     "grade_id": "cell-13e48288f0ba37af",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "### 1.7 Plot best cross-validated fit (5 points)\n",
    "\n",
    "For some dataset with $N = 10$, plot the model with the optimal $M$ and $\\lambda$ according to the cross-validation error, using the method you just wrote. In addition, the plot should show the dataset itself and the function that we try to approximate. Let the plot make clear which $M$ and $\\lambda$ were found."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": false,
    "nbgrader": {
     "checksum": "9600d75426aa084eff763220c868f3da",
     "grade": true,
     "grade_id": "cell-f59cac6f24ce02fc",
     "locked": false,
     "points": 5,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "80900f5fe1ee423cd025808ec62208bc",
     "grade": false,
     "grade_id": "cell-f471e0e0ddf7667a",
     "locked": true,
     "schema_version": 1,
     "solution": false
    }
   },
   "source": [
    "## Part 2: Bayesian Linear (Polynomial) Regression\n",
    "\n",
    "### 2.1 Cosine 2 (5 points)\n",
    "\n",
    "Write a function `gen_cosine2(N)` that behaves identically to `gen_cosine(N)` except that the generated values $x_i$ are not linearly spaced, but drawn from a uniform distribution between $0$ and $2 \\pi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "checksum": "068bef52eff2adf561b5b4c2f8f8465b",
     "grade": false,
     "grade_id": "cell-36addc88e1b3fe1d",
     "locked": false,
     "schema_version": 1,
     "solution": true
    }
   },
   "outputs": [
    {
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MmWeMsRljbFFRUR1QWtsE+vky9fJYPtxTwqkzukCcUlZanlVI/okzPHFNP0T07P9SOSMA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\nj7CBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e2813c9860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gen_cosine2(n):\n",
    "    \n",
    "    x = np.sort(np.random.uniform(0, 2.*np.pi, n))\n",
    "    t = np.random.normal(np.cos(x), 0.2)\n",
    "    \n",
    "    #raise NotImplementedError()\n",
    "    \n",
    "    return x, t\n",
    "plt.plot(x,t)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "checksum": "5f697ef0ef1b33ff50de10ff8796dce9",
     "grade": true,
     "grade_id": "cell-57a847b66fb591af",
     "locked": true,
     "points": 5,
     "schema_version": 1,
     "solution": false
    }
   },
   "outputs": [],
   "source": [
    "### Test your function\n",
    "np.random.seed(5)\n",
    "N = 10\n",
    "x, t = gen_cosine2(N)\n",
    "\n",
    "assert x.shape == (N,), \"the shape of x is incorrect\"\n",
    "assert t.shape == (N,), \"the shape of t is incorrect\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Compute Posterior (15 points)\n",
    "\n",
    "You're going to implement a Bayesian linear regression model, and fit it to the periodic data. Your regression model has a zero-mean isotropic Gaussian prior over the parameters, governed by a single (scalar) precision parameter $\\alpha$, i.e.:\n",
    "\n",
    "$$p(\\bw \\;|\\; \\alpha) = \\mathcal{N}(\\bw \\;|\\; 0, \\alpha^{-1} \\bI)$$\n",
    "\n",
    "The covariance and mean of the posterior are given by:\n",
    "\n",
    "$$\\bS_N= \\left( \\alpha \\bI + \\beta \\bPhi^T \\bPhi \\right)^{-1} $$\n",
    "$$\\bm_N = \\beta\\; \\bS_N \\bPhi^T \\bt$$\n",
    "\n",
    "where $\\alpha$ is the precision of the predictive distribution, and $\\beta$ is the noise precision. \n",
    "See MLPR chapter 3.3 for background.\n",
    "\n",
    "Write a method `fit_polynomial_bayes(x, t, M, alpha, beta)` that returns the mean $\\bm_N$ and covariance $\\bS_N$ of the posterior for a $M$-th order polynomial. In addition it should return the design matrix $\\bPhi$. The arguments `x`, `t` and `M` have the same meaning as in question 1.2."
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    "def fit_polynomial_bayes(x, t, M, alpha, beta):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    \n",
    "    return m, S, Phi\n"
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    "### Test your function\n",
    "N = 10\n",
    "x = np.linspace(-1, 1, N)\n",
    "t = 0.5*np.square(x) + 1.5\n",
    "M = 2\n",
    "alpha = 0.5\n",
    "beta = 25\n",
    "m, S, Phi = fit_polynomial_bayes(x, t, M, alpha, beta)\n",
    "\n",
    "assert m.shape == (M+1,), \"the shape of m is incorrect\" \n",
    "assert S.shape == (M+1, M+1), \"the shape of S is incorrect\"\n",
    "assert Phi.shape == (N, M+1), \"the shape of Phi is incorrect\"\n"
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    "### 2.3 Prediction (10 points)\n",
    "\n",
    "The predictive distribution of Bayesian linear regression is:\n",
    "\n",
    "$$ p(t \\;|\\; \\bx, \\bt, \\alpha, \\beta) = \\mathcal{N}(t \\;|\\; \\bm_N^T \\phi(\\bx), \\sigma_N^2(\\bx))$$\n",
    "\n",
    "$$ \\sigma_N^2 = \\frac{1}{\\beta} + \\phi(\\bx)^T \\bS_N \\phi(\\bx) $$\n",
    "\n",
    "where $\\phi(\\bx)$ are the computed features for a new datapoint $\\bx$, and $t$ is the predicted variable for datapoint $\\bx$. \n",
    "\n",
    "Write a function that `predict_polynomial_bayes(x, m, S, beta)` that returns the predictive mean, variance and design matrix $\\bPhi$ given a new datapoint `x`, posterior mean `m`, posterior variance `S` and a choice of model variance `beta`."
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    "def predict_polynomial_bayes(x, m, S, beta):\n",
    "    # YOUR CODE HERE\n",
    "    raise NotImplementedError()\n",
    "    \n",
    "    return mean, sigma, Phi\n"
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   "source": [
    "### Test your function\n",
    "np.random.seed(5)\n",
    "N = 10\n",
    "x = np.linspace(-1, 1, N)\n",
    "m = np.empty(3)\n",
    "S = np.empty((3, 3))\n",
    "beta = 25\n",
    "mean, sigma, Phi = predict_polynomial_bayes(x, m, S, beta)\n",
    "\n",
    "assert mean.shape == (N,), \"the shape of mean is incorrect\"\n",
    "assert sigma.shape == (N,), \"the shape of sigma is incorrect\"\n",
    "assert Phi.shape == (N, m.shape[0]), \"the shape of Phi is incorrect\"\n"
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    "### 2.4 Plot predictive distribution (10 points)\n",
    "\n",
    "a) (5 points) Generate 10 datapoints with `gen_cosine2(10)`. Compute the posterior mean and covariance for a Bayesian polynomial regression model with $M=4$, $\\alpha=\\frac{1}{2}$ and $\\beta=\\frac{1}{0.2^2}$.\n",
    "Plot the Bayesian predictive distribution, where you plot (for $x$ between 0 and $2 \\pi$) $t$'s predictive mean and a 1-sigma predictive variance using `plt.fill_between(..., alpha=0.1)` (the alpha argument induces transparency).\n",
    "\n",
    "Include the datapoints in your plot.\n"
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   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
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    "b) (5 points) For a second plot, draw 100 samples from the parameters' posterior distribution. Each of these samples is a certain choice of parameters for 4-th order polynomial regression. \n",
    "Display each of these 100 polynomials.\n"
   ]
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    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
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    "### 2.5 Additional questions (10 points)\n",
    "\n",
    "a) (5 points) Why is $\\beta=\\frac{1}{0.2^2}$ the best choice of $\\beta$ in section 2.4?\n",
    "\n"
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    "b) (5 points) What problems do we face when it comes to choosing basis functions in linear models?"
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