Notebooks/Symbolic regression classification generator.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate a polynomial string"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def symbolize(s):\n",
    "    \"\"\"\n",
    "    Converts a a string (equation) to a SymPy symbol object\n",
    "    \"\"\"\n",
    "    from sympy import sympify\n",
    "    s1=s.replace('.','*')\n",
    "    s2=s1.replace('^','**')\n",
    "    s3=sympify(s2)\n",
    "    \n",
    "    return(s3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eval_multinomial(s,vals=None,symbolic_eval=False):\n",
    "    \"\"\"\n",
    "    Evaluates polynomial at vals.\n",
    "    vals can be simple list, dictionary, or tuple of values.\n",
    "    vals can also contain symbols instead of real values provided those symbols have been declared before using SymPy\n",
    "    \"\"\"\n",
    "    from sympy import Symbol\n",
    "    sym_s=symbolize(s)\n",
    "    sym_set=sym_s.atoms(Symbol)\n",
    "    sym_lst=[]\n",
    "    for s in sym_set:\n",
    "        sym_lst.append(str(s))\n",
    "    sym_lst.sort()\n",
    "    if symbolic_eval==False and len(sym_set)!=len(vals):\n",
    "        print(\"Length of the input values did not match number of variables and symbolic evaluation is not selected\")\n",
    "        return None\n",
    "    else:\n",
    "        if type(vals)==list:\n",
    "            sub=list(zip(sym_lst,vals))\n",
    "        elif type(vals)==dict:\n",
    "            l=list(vals.keys())\n",
    "            l.sort()\n",
    "            lst=[]\n",
    "            for i in l:\n",
    "                lst.append(vals[i])\n",
    "            sub=list(zip(sym_lst,lst))\n",
    "        elif type(vals)==tuple:\n",
    "            sub=list(zip(sym_lst,list(vals)))\n",
    "        result=sym_s.subs(sub)\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper function for flipping binary values of a _ndarray_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def flip(y,p):\n",
    "    import numpy as np\n",
    "    lst=[]\n",
    "    for i in range(len(y)):\n",
    "        f=np.random.choice([1,0],p=[p,1-p])\n",
    "        lst.append(f)\n",
    "    lst=np.array(lst)\n",
    "    return np.array(np.logical_xor(y,lst),dtype=int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classification sample generation based on a symbolic expression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_classification_symbolic(m=None,n_samples=100,n_features=2,flip_y=0.0):\n",
    "    \"\"\"\n",
    "    Generates classification sample based on a symbolic expression.\n",
    "    Calculates the output of the symbolic expression at randomly generated (Gaussian distribution) points and\n",
    "    assigns binary classification based on sign.\n",
    "    m: The symbolic expression. Needs x1, x2, etc as variables and regular python arithmatic symbols to be used.\n",
    "    n_samples: Number of samples to be generated\n",
    "    n_features: Number of variables. This is automatically inferred from the symbolic expression. So this is ignored \n",
    "                in case a symbolic expression is supplied. However if no symbolic expression is supplied then a \n",
    "                default simple polynomial can be invoked to generate classification samples with n_features.\n",
    "    flip_y: Probability of flipping the classification labels randomly. A higher value introduces more noise and make\n",
    "            the classification problem harder.\n",
    "    Returns a numpy ndarray with dimension (n_samples,n_features+1). Last column is the response vector.\n",
    "    \"\"\"\n",
    "    \n",
    "    import numpy as np\n",
    "    from sympy import Symbol,sympify\n",
    "    \n",
    "    if m==None:\n",
    "        m=''\n",
    "        for i in range(1,n_features+1):\n",
    "            c='x'+str(i)\n",
    "            c+=np.random.choice(['+','-'],p=[0.5,0.5])\n",
    "            m+=c\n",
    "        m=m[:-1]\n",
    "    sym_m=sympify(m)\n",
    "    n_features=len(sym_m.atoms(Symbol))\n",
    "    evals=[]\n",
    "    lst_features=[]\n",
    "    for i in range(n_features):\n",
    "        lst_features.append(np.random.normal(scale=5,size=n_samples))\n",
    "    lst_features=np.array(lst_features)\n",
    "    lst_features=lst_features.T\n",
    "    for i in range(n_samples):\n",
    "        evals.append(eval_multinomial(m,vals=list(lst_features[i])))\n",
    "    \n",
    "    evals=np.array(evals)\n",
    "    evals_binary=evals>0\n",
    "    evals_binary=evals_binary.flatten()\n",
    "    evals_binary=np.array(evals_binary,dtype=int)\n",
    "    evals_binary=flip(evals_binary,p=flip_y)\n",
    "    evals_binary=evals_binary.reshape(n_samples,1)\n",
    "    \n",
    "    lst_features=lst_features.reshape(n_samples,n_features)\n",
    "    x=np.hstack((lst_features,evals_binary))\n",
    "    \n",
    "    return (x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "x=gen_classification_symbolic(m='2*x1+3*x2+5*x3',n_samples=10,flip_y=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "df=pd.DataFrame(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.442614</td>\n",
       "      <td>-0.523797</td>\n",
       "      <td>2.300378</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.463687</td>\n",
       "      <td>3.200522</td>\n",
       "      <td>4.309449</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.580825</td>\n",
       "      <td>-2.606877</td>\n",
       "      <td>5.845246</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.888534</td>\n",
       "      <td>3.727563</td>\n",
       "      <td>-3.174944</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.120233</td>\n",
       "      <td>-2.737827</td>\n",
       "      <td>-8.308171</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-4.832498</td>\n",
       "      <td>-6.591497</td>\n",
       "      <td>5.565251</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-2.326688</td>\n",
       "      <td>4.751803</td>\n",
       "      <td>3.309559</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-1.213919</td>\n",
       "      <td>-10.209268</td>\n",
       "      <td>2.447471</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-1.320891</td>\n",
       "      <td>0.770222</td>\n",
       "      <td>-8.735817</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2.150437</td>\n",
       "      <td>6.061752</td>\n",
       "      <td>-6.733177</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0          1         2    3\n",
       "0 -0.442614  -0.523797  2.300378  1.0\n",
       "1 -0.463687   3.200522  4.309449  1.0\n",
       "2 -2.580825  -2.606877  5.845246  1.0\n",
       "3  0.888534   3.727563 -3.174944  0.0\n",
       "4 -1.120233  -2.737827 -8.308171  0.0\n",
       "5 -4.832498  -6.591497  5.565251  0.0\n",
       "6 -2.326688   4.751803  3.309559  1.0\n",
       "7 -1.213919 -10.209268  2.447471  0.0\n",
       "8 -1.320891   0.770222 -8.735817  0.0\n",
       "9  2.150437   6.061752 -6.733177  0.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.566707</td>\n",
       "      <td>7.645691</td>\n",
       "      <td>0.559811</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-10.528796</td>\n",
       "      <td>2.241197</td>\n",
       "      <td>-4.216359</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.000866</td>\n",
       "      <td>0.615997</td>\n",
       "      <td>2.021055</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.919458</td>\n",
       "      <td>3.593280</td>\n",
       "      <td>0.498438</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.671159</td>\n",
       "      <td>-0.679506</td>\n",
       "      <td>-5.125242</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-4.484902</td>\n",
       "      <td>-12.881067</td>\n",
       "      <td>2.340985</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.302499</td>\n",
       "      <td>-5.054502</td>\n",
       "      <td>-1.396578</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-2.321861</td>\n",
       "      <td>-2.548314</td>\n",
       "      <td>2.881654</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-7.021660</td>\n",
       "      <td>4.530175</td>\n",
       "      <td>2.701544</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-9.778964</td>\n",
       "      <td>-0.132642</td>\n",
       "      <td>4.021956</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0          1         2    3\n",
       "0   5.566707   7.645691  0.559811  1.0\n",
       "1 -10.528796   2.241197 -4.216359  0.0\n",
       "2   5.000866   0.615997  2.021055  1.0\n",
       "3   2.919458   3.593280  0.498438  1.0\n",
       "4   4.671159  -0.679506 -5.125242  1.0\n",
       "5  -4.484902 -12.881067  2.340985  1.0\n",
       "6   1.302499  -5.054502 -1.396578  0.0\n",
       "7  -2.321861  -2.548314  2.881654  0.0\n",
       "8  -7.021660   4.530175  2.701544  0.0\n",
       "9  -9.778964  -0.132642  4.021956  0.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=gen_classification_symbolic(m='12*x1/(x2+5*x3)',n_samples=10,flip_y=0.2)\n",
    "df=pd.DataFrame(x)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression sample generation based on a symbolic expression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen_regression_symbolic(m=None,n_samples=100,n_features=2,noise=0.0,noise_dist='normal'):\n",
    "    \"\"\"\n",
    "    Generates regression sample based on a symbolic expression. Calculates the output of the symbolic expression \n",
    "    at randomly generated (drawn from a Gaussian distribution) points\n",
    "    m: The symbolic expression. Needs x1, x2, etc as variables and regular python arithmatic symbols to be used.\n",
    "    n_samples: Number of samples to be generated\n",
    "    n_features: Number of variables. This is automatically inferred from the symbolic expression. So this is ignored \n",
    "                in case a symbolic expression is supplied. However if no symbolic expression is supplied then a \n",
    "                default simple polynomial can be invoked to generate regression samples with n_features.\n",
    "    noise: Magnitude of Gaussian noise to be introduced (added to the output).\n",
    "    noise_dist: Type of the probability distribution of the noise signal. \n",
    "    Currently supports: Normal, Uniform, t, Beta, Gamma, Poission, Laplace\n",
    "\n",
    "    Returns a numpy ndarray with dimension (n_samples,n_features+1). Last column is the response vector.\n",
    "    \"\"\"\n",
    "    \n",
    "    import numpy as np\n",
    "    from sympy import Symbol,sympify\n",
    "    \n",
    "    if m==None:\n",
    "        m=''\n",
    "        for i in range(1,n_features+1):\n",
    "            c='x'+str(i)\n",
    "            c+=np.random.choice(['+','-'],p=[0.5,0.5])\n",
    "            m+=c\n",
    "        m=m[:-1]\n",
    "    \n",
    "    sym_m=sympify(m)\n",
    "    n_features=len(sym_m.atoms(Symbol))\n",
    "    evals=[]\n",
    "    lst_features=[]\n",
    "    \n",
    "    for i in range(n_features):\n",
    "        lst_features.append(np.random.normal(scale=5,size=n_samples))\n",
    "    lst_features=np.array(lst_features)\n",
    "    lst_features=lst_features.T\n",
    "    lst_features=lst_features.reshape(n_samples,n_features)\n",
    "    \n",
    "    for i in range(n_samples):\n",
    "        evals.append(eval_multinomial(m,vals=list(lst_features[i])))\n",
    "    \n",
    "    evals=np.array(evals)\n",
    "    evals=evals.reshape(n_samples,1)\n",
    "    \n",
    "    if noise_dist=='normal':\n",
    "        noise_sample=noise*np.random.normal(loc=0,scale=1.0,size=n_samples)\n",
    "    elif noise_dist=='uniform':\n",
    "        noise_sample=noise*np.random.uniform(low=0,high=1.0,size=n_samples)\n",
    "    elif noise_dist=='beta':\n",
    "        noise_sample=noise*np.random.beta(a=0.5,b=1.0,size=n_samples)\n",
    "    elif noise_dist=='Gamma':\n",
    "        noise_sample=noise*np.random.gamma(shape=1.0,scale=1.0,size=n_samples)\n",
    "    elif noise_dist=='laplace':\n",
    "        noise_sample=noise*np.random.laplace(loc=0.0,scale=1.0,size=n_samples)\n",
    "        \n",
    "    noise_sample=noise_sample.reshape(n_samples,1)\n",
    "    evals=evals+noise_sample\n",
    "        \n",
    "    x=np.hstack((lst_features,evals))\n",
    "    \n",
    "    return (x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate samples with a rational function as input \n",
    "### $$\\frac{10x_1}{(3x_2+4x_3)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-7.08499</td>\n",
       "      <td>-4.35839</td>\n",
       "      <td>8.10732</td>\n",
       "      <td>-3.67783156896633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-10.6684</td>\n",
       "      <td>0.779056</td>\n",
       "      <td>-6.64651</td>\n",
       "      <td>4.45796155973331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-6.69542</td>\n",
       "      <td>-5.307</td>\n",
       "      <td>1.17935</td>\n",
       "      <td>5.95108211351032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-3.83581</td>\n",
       "      <td>6.46401</td>\n",
       "      <td>-5.99678</td>\n",
       "      <td>8.28104884665168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.50995</td>\n",
       "      <td>-1.46056</td>\n",
       "      <td>-4.10213</td>\n",
       "      <td>0.493224249022704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2.22995</td>\n",
       "      <td>-1.12163</td>\n",
       "      <td>4.41009</td>\n",
       "      <td>1.51213441402200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.26261</td>\n",
       "      <td>0.982687</td>\n",
       "      <td>7.0676</td>\n",
       "      <td>1.31581579041464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.787195</td>\n",
       "      <td>2.20071</td>\n",
       "      <td>-4.68889</td>\n",
       "      <td>-0.724650906335961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.720728</td>\n",
       "      <td>-2.32469</td>\n",
       "      <td>-0.468637</td>\n",
       "      <td>-0.917106940761226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-3.04485</td>\n",
       "      <td>-3.26701</td>\n",
       "      <td>-3.19083</td>\n",
       "      <td>1.40239700700260</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2                   3\n",
       "0  -7.08499  -4.35839   8.10732   -3.67783156896633\n",
       "1  -10.6684  0.779056  -6.64651    4.45796155973331\n",
       "2  -6.69542    -5.307   1.17935    5.95108211351032\n",
       "3  -3.83581   6.46401  -5.99678    8.28104884665168\n",
       "4  -1.50995  -1.46056  -4.10213   0.493224249022704\n",
       "5   2.22995  -1.12163   4.41009    1.51213441402200\n",
       "6   4.26261  0.982687    7.0676    1.31581579041464\n",
       "7  0.787195   2.20071  -4.68889  -0.724650906335961\n",
       "8  0.720728  -2.32469 -0.468637  -0.917106940761226\n",
       "9  -3.04485  -3.26701  -3.19083    1.40239700700260"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=gen_regression_symbolic(m='10*x1/(3*x2+4*x3)',n_samples=10,noise=0.1)\n",
    "df=pd.DataFrame(x)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate samples with no symbolic input and with 10 features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-3.55302</td>\n",
       "      <td>-3.60695</td>\n",
       "      <td>-10.0729</td>\n",
       "      <td>7.85252</td>\n",
       "      <td>-3.76276</td>\n",
       "      <td>7.78251</td>\n",
       "      <td>-0.638193</td>\n",
       "      <td>-4.75034</td>\n",
       "      <td>-0.989603</td>\n",
       "      <td>0.181414</td>\n",
       "      <td>-10.2675547899900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-6.34778</td>\n",
       "      <td>-2.74753</td>\n",
       "      <td>-4.75187</td>\n",
       "      <td>4.70489</td>\n",
       "      <td>2.70014</td>\n",
       "      <td>5.29475</td>\n",
       "      <td>-0.190095</td>\n",
       "      <td>4.85289</td>\n",
       "      <td>-4.50207</td>\n",
       "      <td>-1.22839</td>\n",
       "      <td>-1.93507315813350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.15057</td>\n",
       "      <td>-0.43572</td>\n",
       "      <td>-5.47805</td>\n",
       "      <td>6.96074</td>\n",
       "      <td>3.10096</td>\n",
       "      <td>-1.50898</td>\n",
       "      <td>1.09913</td>\n",
       "      <td>4.73097</td>\n",
       "      <td>-0.216513</td>\n",
       "      <td>-3.25629</td>\n",
       "      <td>4.91632094325713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.11181</td>\n",
       "      <td>5.62156</td>\n",
       "      <td>0.0660036</td>\n",
       "      <td>6.66565</td>\n",
       "      <td>1.88656</td>\n",
       "      <td>-4.57167</td>\n",
       "      <td>-0.84389</td>\n",
       "      <td>-2.44545</td>\n",
       "      <td>1.66649</td>\n",
       "      <td>7.36169</td>\n",
       "      <td>18.0607243993836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-3.27857</td>\n",
       "      <td>-4.13545</td>\n",
       "      <td>4.36299</td>\n",
       "      <td>-3.73405</td>\n",
       "      <td>-1.3958</td>\n",
       "      <td>-6.39237</td>\n",
       "      <td>1.99202</td>\n",
       "      <td>-0.216661</td>\n",
       "      <td>-10.3905</td>\n",
       "      <td>3.43896</td>\n",
       "      <td>-23.7181534803553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-6.78726</td>\n",
       "      <td>-7.76895</td>\n",
       "      <td>-2.2653</td>\n",
       "      <td>-3.4326</td>\n",
       "      <td>-16.8937</td>\n",
       "      <td>-1.79111</td>\n",
       "      <td>4.79866</td>\n",
       "      <td>-4.43692</td>\n",
       "      <td>2.01342</td>\n",
       "      <td>-3.46766</td>\n",
       "      <td>-49.7886776301048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.66157</td>\n",
       "      <td>-4.34424</td>\n",
       "      <td>6.69391</td>\n",
       "      <td>-3.42321</td>\n",
       "      <td>-8.63976</td>\n",
       "      <td>0.862722</td>\n",
       "      <td>2.70897</td>\n",
       "      <td>-13.5047</td>\n",
       "      <td>-7.14555</td>\n",
       "      <td>-3.16143</td>\n",
       "      <td>-33.7432854958296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.46949</td>\n",
       "      <td>7.11633</td>\n",
       "      <td>-1.08523</td>\n",
       "      <td>6.41709</td>\n",
       "      <td>-1.23161</td>\n",
       "      <td>7.07956</td>\n",
       "      <td>6.6377</td>\n",
       "      <td>6.06688</td>\n",
       "      <td>-4.99262</td>\n",
       "      <td>3.85005</td>\n",
       "      <td>19.9862211512126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.13155</td>\n",
       "      <td>4.02597</td>\n",
       "      <td>-3.05607</td>\n",
       "      <td>4.9271</td>\n",
       "      <td>-3.60454</td>\n",
       "      <td>6.06252</td>\n",
       "      <td>0.936673</td>\n",
       "      <td>4.07096</td>\n",
       "      <td>-2.04052</td>\n",
       "      <td>5.11093</td>\n",
       "      <td>15.8002295267657</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-1.6051</td>\n",
       "      <td>4.97768</td>\n",
       "      <td>-7.69743</td>\n",
       "      <td>-0.65865</td>\n",
       "      <td>4.07053</td>\n",
       "      <td>2.98333</td>\n",
       "      <td>-10.9341</td>\n",
       "      <td>4.9402</td>\n",
       "      <td>2.9771</td>\n",
       "      <td>0.68357</td>\n",
       "      <td>21.5880195549236</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        0        1          2        3        4         5         6   \\\n",
       "0 -3.55302 -3.60695   -10.0729  7.85252 -3.76276   7.78251 -0.638193   \n",
       "1 -6.34778 -2.74753   -4.75187  4.70489  2.70014   5.29475 -0.190095   \n",
       "2  2.15057 -0.43572   -5.47805  6.96074  3.10096  -1.50898   1.09913   \n",
       "3  1.11181  5.62156  0.0660036  6.66565  1.88656  -4.57167  -0.84389   \n",
       "4 -3.27857 -4.13545    4.36299 -3.73405  -1.3958  -6.39237   1.99202   \n",
       "5 -6.78726 -7.76895    -2.2653  -3.4326 -16.8937  -1.79111   4.79866   \n",
       "6  1.66157 -4.34424    6.69391 -3.42321 -8.63976  0.862722   2.70897   \n",
       "7  3.46949  7.11633   -1.08523  6.41709 -1.23161   7.07956    6.6377   \n",
       "8  1.13155  4.02597   -3.05607   4.9271 -3.60454   6.06252  0.936673   \n",
       "9  -1.6051  4.97768   -7.69743 -0.65865  4.07053   2.98333  -10.9341   \n",
       "\n",
       "         7         8         9                  10  \n",
       "0  -4.75034 -0.989603  0.181414  -10.2675547899900  \n",
       "1   4.85289  -4.50207  -1.22839  -1.93507315813350  \n",
       "2   4.73097 -0.216513  -3.25629   4.91632094325713  \n",
       "3  -2.44545   1.66649   7.36169   18.0607243993836  \n",
       "4 -0.216661  -10.3905   3.43896  -23.7181534803553  \n",
       "5  -4.43692   2.01342  -3.46766  -49.7886776301048  \n",
       "6  -13.5047  -7.14555  -3.16143  -33.7432854958296  \n",
       "7   6.06688  -4.99262   3.85005   19.9862211512126  \n",
       "8   4.07096  -2.04052   5.11093   15.8002295267657  \n",
       "9    4.9402    2.9771   0.68357   21.5880195549236  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=gen_regression_symbolic(n_features=10,n_samples=10,noise=0.1)\n",
    "df=pd.DataFrame(x)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate samples with less noise and plot: $0.2x^2+1.2x+6+f_{noise}(x\\mid{N=0.1})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAFQZJREFUeJzt3X+MHPV5x/HP482Srmmls4Xj2AcXo9R1heMEqydwlfyRQBLTH8GHlSAISK4a1a2UVEqDrrUDEqYhMuopraI0reo0KK7iQkxqFpOkvYKVKi0CknPXznGBK26IgTXBTsP1RziF4/z0j5016/P+mP0xuzv7fb8ky7uzezvf5ZIPwzPPPGPuLgDA4FvW6wUAALqDwAeAQBD4ABAIAh8AAkHgA0AgCHwACASBDwCBIPABIBAEPgAE4k29XkClSy65xNetW9frZQBAqhw9evQn7r6q0fv6KvDXrVunqampXi8DAFLFzE7GeR8lHQAIBIEPAIFoO/DN7BfM7LtmdtzMZszsrmj7SjN7xMyejf5e0f5yAQCt6sQR/s8lXePu75J0paTrzGyLpF2Sjrj7eklHoucAgB5pO/C95P+ip9noj0vaJml/tH2/pLF29wUAaF1HunTMLCPpqKRflvRFd3/SzFa7+0vRW34saXUn9gUAgyRfKGpiclan5ua1diin8a0bNLZ5OJF9deSkrbsvuvuVki6VdJWZvWPJ667SUf8FzGynmU2Z2dSZM2c6sRwASIV8oajdh6ZVnJuXSyrOzWv3oWnlC8VE9tfRLh13n5P0bUnXSXrZzNZIUvT36Ro/s8/dR919dNWqhtcNAMDAmJic1fzC4nnb5hcWNTE5m8j+OtGls8rMhqLHOUkfkPSMpMOSdkRv2yHpoXb3BQCD5NTcfFPb29WJGv4aSfujOv4ySQfd/Rtm9rikg2b2MUknJd3YgX0BwMBYO5RTsUq4rx3KJbK/tgPf3b8vaXOV7f8l6dp2Px8ABtX41g3afWj6vLJOLpvR+NYNieyvr2bpAEBIyt043erSIfABoIfGNg8nFvBLMUsHAAJB4ANAIAh8AAgEgQ8AgSDwASAQBD4ABILAB4BAEPgAEAguvAKAOro5rz5pBD4A1FCeV1+edVOeVy8plaFPSQcAauj2vPqkcYQPABUqSzhVb9On5ObVJ43ABwCVgn7P4RnNzS80fG9S8+qTRuADCN7SWn09Sc6rTxqBDyB41Wr1S5lElw4ApF2jmvzwUE6P7bqmS6tJDoEPIBi1eupr3VtWSncJZynaMgEEoVynL0bdN+We+nyhqPGtG5TLZi74mRXLs9q7fVNqSzhLcYQPIAj1eurL5ZpBuaK2FgIfQBBq1enL27t5b9leoaQDIAi1eufT2lPfCgIfQBCq1ekH6YRsHJR0AAyERlMty48HvU5fD4EPIPXiTrUMoU5fDyUdAKk3aFMtk0LgA0i9Rh04KCHwAaQeHTjxEPgAUo8OnHg4aQsg9ejAiYfABzAQQu/AiaPtwDezyyT9naTVklzSPnf/vJmtlPQ1Sesk/UjSje7+Srv7AzD4GvXUozWdqOG/Luk2d79C0hZJHzezKyTtknTE3ddLOhI9B4C66k21RHvaDnx3f8nd/z16/L+SnpY0LGmbpP3R2/ZLGmt3XwAGHz31yelol46ZrZO0WdKTkla7+0vRSz9WqeQDAHXRU5+cjgW+mf2ipH+Q9El3/5/K19zdVarvV/u5nWY2ZWZTZ86c6dRyAKQUPfXJ6Ujgm1lWpbA/4O6Hos0vm9ma6PU1kk5X+1l33+fuo+4+umrVqk4sB0CK0VOfnLYD38xM0pclPe3uf17x0mFJO6LHOyQ91O6+AAy+sc3D2rt9k4aHcjKVbiA+SLcZ7CUrVVva+ACz90j6V0nTks5Gmz+tUh3/oKQRSSdVasv8ab3PGh0d9ampqbbWA6A/5QtF3fXwjF55dUGSNJTLas/1GwnyDjCzo+4+2uh9bffhu/u/SbIaL1/b7ucDSL98oajxrx/XwuIbB5hz8wsaf+C4JBH6XcIsHQCJyheKuu3g+WFftnDWabfsIgIfQGLKF1Et1ikd027ZPczSAdBRlWMRlpnVDXuJdstuIvABdMzSWw02CvvsMqPdsosIfAAdcUd+Wl994vnY76dLp/sIfABtu+VLj+ux/6zbdX1OLpuhr75HCHwAbckXig3DPmOms+6MOu4xAh9A08onZosxOmw4ou8fBD6A2PKFom5/cFo/e22x8ZsjhH3/IPABxNLsSVlJunXLCGHfR7jwCkBDrYT9u9++UnePbUpoRWgFR/gAqlo67CyujJk+d+O7OLLvQwQ+gAvkC0Xd9sBxLZ5tbpouJ2j7G4EP4AJ3PTzTdNgP03LZ9wh8ABeIW8bJZZdp7/Z3EvIpQeADaJpJumXLCCdlU4bAB3CBoVxWc/PVj/JXLM/qzg8xAyeNCHwgQJUjjKuNO9hz/UaNP3BcC0vq+LdyVJ9qBD4QmKUjjItz89p9aFrSG7caLP9d718KSB8CHwjMnsMz58K+bH5hUROTs+cF+tjmYQJ+wBD4QADyhaI+fej7enXhbM33cKvBwUfgAwOsmWFn3Gpw8BH4wIDKF4r6o68dU9zLp7jV4OAj8IEBlC8U9cmvHYv9/hXLs9TrA0DgAwOm2cmWuWxGd35oY4IrQr8g8IEBkS8UtefwTM0Lpqq5+KKMPnsDw85CQeADKVZ5q0GTYtfrGY0QJgIfSKk78tM68MTz50I+bti/++0rdeD3fj2pZaGPEfhACuULxabvQCUR9qEj8IEUaaVOL1GrRwmBD6REK/eVZbIlKhH4QArkC0UdaCLsufsUqiHwgRSYmJyNdVL24osymvnT6xJfD9JpWSc+xMzuNbPTZvZUxbaVZvaImT0b/b2iE/sCQhRnsFk2Y/rsDbRZoraOBL6kr0haelixS9IRd18v6Uj0HEALGg02G8plNfHhd1HCQV0dKem4+3fMbN2SzdskvTd6vF/Sv0j6k07sDxhElRdRZcy06H6uFj++dcN5Ny0po/sGzTD3uJdrNPigUuB/w93fET2fc/eh6LFJeqX8fMnP7ZS0U5JGRkZ+7eTJkx1ZD5AW+UJR4w8cU61R9blsRnu3l0o13IEK1ZjZUXcfbfi+bgR+9PwVd69bxx8dHfWpqamOrAdIg7hTLYeHcnps1zVdWBHSKG7gJ9ml87KZrXH3l8xsjaTTCe4LSJV8oai7Hp7RK6/Gu4CKu1GhEzp10raaw5J2RI93SHoowX0BqZEvFDX+9eOxw17iblTojE61Zd4n6XFJG8zsRTP7mKR7JH3AzJ6V9P7oORC8iclZLSzGL6XmshnuRoWO6FSXzs01Xrq2E58PpF2zJZwyrphFJ3GlLZCQVgedSdL6t1ysRz713s4vCkEj8IEElFotj2vhbHNdcMtM+ujV3JgEySDwgQRMTM42FfZDuaz2XM9USySLwAc65I78tA48+byaubSF/np0E4EPdEArs+qzy4zuG3RVkn34QDCamVUvRcPOPsKwM3QXR/hAi8rDzk7NzceaVc/dp9BrBD7QgnyhWHV6ZS3U6tEPKOkALZiYnI0d9tTq0S8IfKAFcYeZ5bLLqNWjb1DSAeqodVOSoeXZqmMSMmY66868evQlAh+o4Y78tA488fy5E7KLUYN9cW5e2WWmbMbOG4JWvlEJIY9+RUkHqKLcV1+r+2bhrOvii96k4aGcTKWTsoQ9+h1H+ECFZqZa/vf8go7d+cEurAroDAIfiDTbaslNSZA2BD6CV3liNi5uSoI0IvARtGaP6iVuSoL0IvARtLgXUJmkW7Ywpx7pRuAjKJXzb9YO5WKVcZhVj0FB4CMYS/vqi3PzMqlm6yWlGwwaAh9ByBeK54V9mUsXhD4XUGFQceEVgjAxOVvzSN4lLqBCEDjCx0BqplbP6GKEgsDHwMkXihr/+vFzc27qhb1J9NMjGJR0MHDuenjmvKFmtZRbLSnfIBQc4WPg1JuDMzyUO1fmoQMHoSHwkVq1ZtXXQ60eISPwkUpLRyJUzqqvZSiX7cragH5F4CN18oWiPnXwmM42LtOfk11m2nP9xuQWBaQAJ22RKuUOnDhhX9lbz31lAY7wkTITk7OxOnDorQcuROCj7+ULRe05PKO5+cZ3oZKYVQ/Uknjgm9l1kj4vKSPpb939nqT3ifRr5aYkEgPPgHoSDXwzy0j6oqQPSHpR0vfM7LC7/yDJ/SK98oWibn9wWj97Lf4NSaTSSVnq9EB9SZ+0vUrSCXf/obu/Jul+SdsS3idSqtx902zYD+WyhD0QQ9IlnWFJL1Q8f1HS1QnvEynTTvmGE7NAfD0/aWtmOyXtlKSRkZEerwbd1so9ZSUpmzFOzAJNSrqkU5R0WcXzS6Nt57j7PncfdffRVatWJbwc9JN8oajbDh5vOuxXLM9q4sOUcIBmJX2E/z1J683scpWC/iZJH014n0iB8pF9eSRCHLdyE3GgLYkGvru/bmafkDSpUlvmve4+k+Q+0b+a7aevRNgD7Uu8hu/u35L0raT3g/6WLxQ1/sBxLTQxACdjppuvvoygBzqk5ydtEYaJydlYYZ8x0+dupD4PJIHAR2Iq7ysb57g+l81wA3EgQQQ+Oq6VWj0jEYDkEfjoqGb76rMZo8US6BICHx01MTkbO+xXLM/qzg9tJOyBLiHw0VGnYoxHMEnP3fNbyS8GwHkIfLSs8qTs2qgGv3Yo13AmztoGNxoHkAxucYiWlGv1xagDpzg3r92HpvW+X10lq/Nz3JwE6B0CHy2pVqufX1jUt585o1u2jFQN/RXLs7RdAj1ESQctqVWrPzU3r7vHNmn0bSsvKPcQ9EBvEfhoSa1afbk+P7Z5mIAH+gyBj4aqnZwd37rhgn576vNAf6OGj7pqnZyVpL3bN2l4KCdT6UpZ6vNAf+MIH3XVOjk7MTmrx3ZdQ8ADKcIRPuqqd3IWQLoQ+Kir1kVSXDwFpA+Bj7rGt25QLps5bxsnZ4F0ooaPuso1enrqgfQj8NEQPfXAYKCkAwCBIPABIBAEPgAEgsAHgEAQ+AAQCAIfAAJB4ANAIOjDHwB35Kd135MvaNFdGTPdfPVluntsU6+XBaDPEPgpd0d+Wl994vlzzxfdzz0n9AFUoqSTcvc9+UJT2wGEi8BPuUX3prYDCBeBn3IZs6a2AwgXgZ9yN199WVPbAYSrrcA3s4+Y2YyZnTWz0SWv7TazE2Y2a2Zb21smarl7bJNu3TJy7og+Y6Zbt4xwwhbABdrt0nlK0nZJf1O50cyukHSTpI2S1kp61Mx+xd0XL/wItOvusU0EPICG2jrCd/en3X22ykvbJN3v7j939+cknZB0VTv7AgC0J6ka/rCkyr7AF6NtAIAeaVjSMbNHJb21yku3u/tD7S7AzHZK2ilJIyMj7X4cAKCGhoHv7u9v4XOLkirbRC6NtlX7/H2S9knS6OgozeMAkJCkSjqHJd1kZm82s8slrZf03YT2BQCIoa0uHTO7QdIXJK2S9E0zO+buW919xswOSvqBpNclfZwOnTfkC0VNTM7q1Ny81g7lNL51AzcJB5A48z66BH90dNSnpqZ6vYxE5QtF7T40rfmFN/79l8tmtHf7JkIfQEvM7Ki7jzZ6H1fadtnE5Ox5YS9J8wuLmpis1t0KAJ1D4HfZqbn5prYDQKcQ+F22dijX1HYA6BQCv8vGt25QLps5b1sum9H41g09WhGAUHDHqy4rn5ilSwdAtxH4PTC2eZiAB9B1lHQAIBAEPgAEgsAHgEAQ+AAQCAIfAAJBl05MDDwDkHYEfgxLB54V5+a1+9C0JBH6AFKDkk4MDDwDMAgI/BgYeAZgEBD4MTDwDMAgIPBjYOAZgEHASdsYGHgGYBAQ+DEx8AxA2gUX+PTTAwhVUIFPPz2AkAV10pZ+egAhCyrw6acHELKgAp9+egAhCyrw6acHELKgTtrSTw8gZEEFvkQ/PYBwDUTg01sPAI2lPvDprQeAeFJ/0pbeegCIJ/WBT289AMST+sCntx4A4mkr8M1swsyeMbPvm9mDZjZU8dpuMzthZrNmtrX9pVZHbz0AxNPuEf4jkt7h7u+U9B+SdkuSmV0h6SZJGyVdJ+mvzCxT81PaMLZ5WHu3b9LwUE4maXgop73bN3HCFgCWaKtLx93/ueLpE5I+HD3eJul+d/+5pOfM7ISkqyQ93s7+aqG3HgAa62QN/3cl/WP0eFjSCxWvvRhtAwD0SMMjfDN7VNJbq7x0u7s/FL3ndkmvSzrQ7ALMbKeknZI0MjLS7I8DAGJqGPju/v56r5vZ70j6bUnXurtHm4uSLqt426XRtmqfv0/SPkkaHR31au8BALSv3S6d6yT9saTr3f3VipcOS7rJzN5sZpdLWi/pu+3sCwDQnnZHK/ylpDdLesTMJOkJd/8Dd58xs4OSfqBSqefj7r5Y53MAAAmzN6owvWdmZySd7PU6mnCJpJ/0ehE9FPL3D/m7S3z/fvv+b3P3VY3e1FeBnzZmNuXuo71eR6+E/P1D/u4S3z+t3z/1oxUAAPEQ+AAQCAK/Pft6vYAeC/n7h/zdJb5/Kr8/NXwACARH+AAQCAK/BWb2ETObMbOzZja65LWujIXuB2a2x8yKZnYs+vObvV5TN5jZddHv94SZ7er1errNzH5kZtPR73yq1+tJkpnda2anzeypim0rzewRM3s2+ntFL9fYDAK/NU9J2i7pO5UbuzkWuo/8hbtfGf35Vq8Xk7To9/lFSb8h6QpJN0e/99C8L/qdp641sUlfUen/y5V2STri7uslHYmepwKB3wJ3f9rdq90099xYaHd/TlJ5LDQGx1WSTrj7D939NUn3q/R7xwBy9+9I+umSzdsk7Y8e75c01tVFtYHA76wQx0L/YXTHs3vT9J+2bQjxd7yUS3rUzI5G025Ds9rdX4oe/1jS6l4uphntztIZWHHGQoeg3j8HSX8t6TMqBcBnJH1OpfsiYLC9x92LZvYWleZoPRMdCQfH3d3MUtPqSODX0GgsdA2xx0KnRdx/Dmb2JUnfSHg5/WDgfsfNcvdi9PdpM3tQpTJXSIH/spmtcfeXzGyNpNO9XlBclHQ6K6ix0NH/2MtuUOlk9qD7nqT1Zna5mV2k0kn6wz1eU9eY2cVm9kvlx5I+qDB+75UOS9oRPd4hKTX/xc8RfgvM7AZJX5C0StI3zeyYu28NcCz0n5nZlSqVdH4k6fd7u5zkufvrZvYJSZOSMpLudfeZHi+rm1ZLejAah/4mSX/v7v/U2yUlx8zuk/ReSZeY2YuS7pR0j6SDZvYxlab73ti7FTaHK20BIBCUdAAgEAQ+AASCwAeAQBD4ABAIAh8AAkHgA0AgCHwACASBDwCB+H/0CnQH9nV5lgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fce05fba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=gen_regression_symbolic(m='0.2*x**2+1.2*x+6',n_samples=100,noise=0.1)\n",
    "df=pd.DataFrame(x)\n",
    "plt.scatter(df[0],df[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate samples with more noise and plo: $0.2x^2+1.2x+6+f_{noise}(x\\mid{N=10})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fce36c19e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=gen_regression_symbolic(m='0.2*x**2+1.2*x+6',n_samples=100,noise=10)\n",
    "df=pd.DataFrame(x)\n",
    "plt.scatter(df[0],df[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Generate samples with larger coefficent for the quadratic term and plot: $1.3x^2+1.2x+6+f_{noise}(x\\mid{N=10})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fce36cde10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=gen_regression_symbolic(m='1.3*x**2+1.2*x+6',n_samples=100,noise=10)\n",
    "df=pd.DataFrame(x)\n",
    "plt.scatter(df[0],df[1])\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.2"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}