{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas\n",
    "import scipy\n",
    "import scipy.linalg as linalg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions(precision=5,suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example for Regression with p>n\n",
    "We consider our toy example with three data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>D</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   D  y\n",
       "0  5  2\n",
       "1  3  5\n",
       "2  1  3"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = np.array([5,3,1])\n",
    "y = np.array([2,5,3])\n",
    "pandas.DataFrame({\"D\":D,\"y\":y})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We fit a polynomial of degree $k=3$. For polynomial regression functions $f:\\mathbb{R}\\rightarrow\\mathbb{R}$ we have\n",
    "$$f(x) = \\beta_0 +\\beta_1 x+ \\beta_2x^2 + \\beta_3x^3 = \\phi(x)^\\top\\beta,$$\n",
    "where \n",
    "$$\\phi(x)=\\begin{pmatrix}1\\\\ x\\\\ x^2\\\\ x^3\\end{pmatrix}.$$\n",
    "We implement $\\phi$ and create the design matrix. Note that the following definition of $\\phi$ for polynomials is only correct if the dimensionality of the feature space is equal to one, as it is in this example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ϕ(x):\n",
    "    return np.row_stack((np.ones(x.shape[0]),x, x**2, x**3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The design matrix gathers the transposed feature vectors of the data matrix:\n",
    "$$X = \\begin{pmatrix} \\phi^\\top(5)\\\\ \\phi^\\top(3)\\\\ \\phi^\\top(1)\\end{pmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   5.,  25., 125.],\n",
       "       [  1.,   3.,   9.,  27.],\n",
       "       [  1.,   1.,   1.,   1.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=ϕ(D).T\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(n,p)=(3,4)\n"
     ]
    }
   ],
   "source": [
    "n,p = X.shape\n",
    "print(\"(n,p)=({},{})\".format(n,p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We try to solve the system of linear equations which returns the global minimizers $\\beta$ of the regression objective\n",
    "$$\\{\\beta\\in\\mathbb{R}^p\\mid X^\\top X\\beta = X^\\top y\\}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:1: LinAlgWarning: Ill-conditioned matrix (rcond=2.30128e-19): result may not be accurate.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 1.82422,  0.89453,  0.39453, -0.11328])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "β = linalg.solve(X.T@X,X.T@y)\n",
    "β"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives a warning because $X^\\top X$ is not invertible. So let's try to implement the formula for non-invertible $X^\\top X$ from the lecture. Therefore, we need the SVD of $X$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 3) (3,) (4, 4)\n"
     ]
    }
   ],
   "source": [
    "U,σs,Vt = linalg.svd(X)\n",
    "print(U.shape, σs.shape, Vt.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "V=Vt.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We calculate $r$, the number of nonzero singular values. If $r<p$, then the matrix $X^\\top X$ is not invertible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r=(σs>0).sum()\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We construct the $n\\times p$ matrix $\\Sigma$ from the denoted $n<p$ singular values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[130.69682,   0.     ,   0.     ,   0.     ],\n",
       "       [  0.     ,   4.19889,   0.     ,   0.     ],\n",
       "       [  0.     ,   0.     ,   0.84299,   0.     ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Σ = np.column_stack((np.diag(σs),np.zeros(3)))\n",
    "Σ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[17081.65872,     0.     ,     0.     ,     0.     ],\n",
       "       [    0.     ,    17.63064,     0.     ,     0.     ],\n",
       "       [    0.     ,     0.     ,     0.71064,     0.     ],\n",
       "       [    0.     ,     0.     ,     0.     ,     0.     ]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ΣtΣ = Σ.T@Σ\n",
    "ΣtΣ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we did everything right, then we should get $X=U\\Sigma V^\\top$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   5.,  25., 125.],\n",
       "       [  1.,   3.,   9.,  27.],\n",
       "       [  1.,   1.,   1.,   1.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U@Σ@Vt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   5.,  25., 125.],\n",
       "       [  1.,   3.,   9.,  27.],\n",
       "       [  1.,   1.,   1.,   1.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now calculate a $\\beta$ in the set of global minimizers. If ```random=True``` then a random matrix replaces the zero rows in the pseudo inverse of $\\Sigma^\\top\\Sigma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_beta(random =True):\n",
    "    ΣtΣ_p = Σ.T@Σ\n",
    "    ΣtΣ_p[ΣtΣ_p>0] = 1/ΣtΣ_p[ΣtΣ_p>0]\n",
    "    A=ΣtΣ_p\n",
    "    if random:\n",
    "        A[r:p,:]=np.random.rand(p-r,p)\n",
    "    return V@A@Σ.T@U.T@y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot it! The function resulting from setting ```random=False``` is the one in blue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 5))\n",
    "x = np.linspace(0, 6, 100)\n",
    "β = get_beta(random = False)\n",
    "f_x = ϕ(x).T@β\n",
    "plt.plot(x, f_x, label=\"f_0\")\n",
    "for i in range(1,5):\n",
    "    β = get_beta()\n",
    "    f_x = ϕ(x).T@β\n",
    "    plt.plot(x, f_x, label=\"f_\"+str(i))\n",
    "plt.scatter(D, y, edgecolor='b', s=50)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.ylim((-2, 10))\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.63666,  1.18212,  0.282  , -0.10078])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_beta(random = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-45.6257 ,  73.65107, -28.07542,   3.05005])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_beta(random = True)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}