kerreg-MPSKICB/kernel_regression.ipynb

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    "<h1><center>Regresja jądrowa</center></h1>\n",
    "\n",
    "#### <center>Karolina Oparczyk, Tomasz Grzybowski, Jan Nowak</center>\n"
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    "Regresja jądrowa używana jest jako funkcja wagi do opracowania modelu regresji nieparametrycznej. Nadaje ona niektórym elementom zbioru większą \"wagę\", która ma wpływ na ostateczny wynik. \n",
    "\n",
    "Można ją porównać do rysowania krzywej na wykresie punktowym tak, aby była jak najlepiej do nich dopasowana."
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    "Właściwości regresji jądrowej:\n",
    "* symetryczna - wartość maksymalna leży pośrodku krzywej\n",
    "<img src=\"files/symmetric.PNG\">\n",
    "* powierzchnia pod krzywą funkcji wynosi 1\n",
    "* wartość funkcji jądrowej nie jest ujemna"
   ]
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   "source": [
    "Do implementacji regresji jądrowej można użyć wielu różnych jąder. Przykłady użyte w projekcie:\n",
    "* jądro Gaussa\n",
    "\\begin{equation}\n",
    "K(x) = \\frac1{h\\sqrt{2\\pi}}e^{-\\frac12(\\frac{x - x_i}h)^2}\n",
    "\\end{equation}"
   ]
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       "/*!\n",
       " * @overview es6-promise - a tiny implementation of Promises/A+.\n",
       " * @copyright Copyright (c) 2014 Yehuda Katz, Tom Dale, Stefan Penner and contributors (Conversion to ES6 API by Jake Archibald)\n",
       " * @license   Licensed under MIT license\n",
       " *            See https://raw.githubusercontent.com/stefanpenner/es6-promise/master/LICENSE\n",
       " * @version   v4.2.8+1e68dce6\n",
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       "/*!\n",
       " * Determine if an object is a Buffer\n",
       " *\n",
       " * @author   Feross Aboukhadijeh <https://feross.org>\n",
       " * @license  MIT\n",
       " */\n",
       "e.exports=function(t){return null!=t&&(n(t)||function(t){return\"function\"==typeof t.readFloatLE&&\"function\"==typeof t.slice&&n(t.slice(0,0))}(t)||!!t._isBuffer)}},{}],466:[function(t,e,r){\"use strict\";e.exports=\"undefined\"!=typeof navigator&&(/MSIE/.test(navigator.userAgent)||/Trident\\//.test(navigator.appVersion))},{}],467:[function(t,e,r){\"use strict\";e.exports=a,e.exports.isMobile=a,e.exports.default=a;var n=/(android|bb\\d+|meego).+mobile|avantgo|bada\\/|blackberry|blazer|compal|elaine|fennec|hiptop|iemobile|ip(hone|od)|iris|kindle|lge |maemo|midp|mmp|mobile.+firefox|netfront|opera m(ob|in)i|palm( os)?|phone|p(ixi|re)\\/|plucker|pocket|psp|series[46]0|symbian|treo|up\\.(browser|link)|vodafone|wap|windows (ce|phone)|xda|xiino/i,i=/(android|bb\\d+|meego).+mobile|avantgo|bada\\/|blackberry|blazer|compal|elaine|fennec|hiptop|iemobile|ip(hone|od)|iris|kindle|lge |maemo|midp|mmp|mobile.+firefox|netfront|opera m(ob|in)i|palm( os)?|phone|p(ixi|re)\\/|plucker|pocket|psp|series[46]0|symbian|treo|up\\.(browser|link)|vodafone|wap|windows (ce|phone)|xda|xiino|android|ipad|playbook|silk/i;function a(t){t||(t={});var e=t.ua;if(e||\"undefined\"==typeof navigator||(e=navigator.userAgent),e&&e.headers&&\"string\"==typeof e.headers[\"user-agent\"]&&(e=e.headers[\"user-agent\"]),\"string\"!=typeof e)return!1;var r=t.tablet?i.test(e):n.test(e);return!r&&t.tablet&&t.featureDetect&&navigator&&navigator.maxTouchPoints>1&&-1!==e.indexOf(\"Macintosh\")&&-1!==e.indexOf(\"Safari\")&&(r=!0),r}},{}],468:[function(t,e,r){\"use strict\";e.exports=function(t){var e=typeof t;return null!==t&&(\"object\"===e||\"function\"===e)}},{}],469:[function(t,e,r){\"use strict\";var n=Object.prototype.toString;e.exports=function(t){var e;return\"[object Object]\"===n.call(t)&&(null===(e=Object.getPrototypeOf(t))||e===Object.getPrototypeOf({}))}},{}],470:[function(t,e,r){\"use strict\";e.exports=function(t){for(var e,r=t.length,n=0;n<r;n++)if(((e=t.charCodeAt(n))<9||e>13)&&32!==e&&133!==e&&160!==e&&5760!==e&&6158!==e&&(e<8192||e>8205)&&8232!==e&&8233!==e&&8239!==e&&8287!==e&&8288!==e&&12288!==e&&65279!==e)return!1;return!0}},{}],471:[function(t,e,r){\"use strict\";e.exports=function(t){return\"string\"==typeof t&&(t=t.trim(),!!(/^[mzlhvcsqta]\\s*[-+.0-9][^mlhvzcsqta]+/i.test(t)&&/[\\dz]$/i.test(t)&&t.length>4))}},{}],472:[function(t,e,r){e.exports=function(t,e,r){return t*(1-r)+e*r}},{}],473:[function(t,e,r){!function(t,n){\"object\"==typeof r&&\"undefined\"!=typeof e?e.exports=n():(t=t||self).mapboxgl=n()}(this,(function(){\"use strict\";var t,e,r;function n(n,i){if(t)if(e){var a=\"var sharedChunk = {}; (\"+t+\")(sharedChunk); (\"+e+\")(sharedChunk);\",o={};t(o),(r=i(o)).workerUrl=window.URL.createObjectURL(new Blob([a],{type:\"text/javascript\"}))}else e=i;else t=i}return n(0,(function(t){function e(t,e){return t(e={exports:{}},e.exports),e.exports}var r=n;function n(t,e,r,n){this.cx=3*t,this.bx=3*(r-t)-this.cx,this.ax=1-this.cx-this.bx,this.cy=3*e,this.by=3*(n-e)-this.cy,this.ay=1-this.cy-this.by,this.p1x=t,this.p1y=n,this.p2x=r,this.p2y=n}n.prototype.sampleCurveX=function(t){return((this.ax*t+this.bx)*t+this.cx)*t},n.prototype.sampleCurveY=function(t){return((this.ay*t+this.by)*t+this.cy)*t},n.prototype.sampleCurveDerivativeX=function(t){return(3*this.ax*t+2*this.bx)*t+this.cx},n.prototype.solveCurveX=function(t,e){var r,n,i,a,o;for(void 0===e&&(e=1e-6),i=t,o=0;o<8;o++){if(a=this.sampleCurveX(i)-t,Math.abs(a)<e)return i;var s=this.sampleCurveDerivativeX(i);if(Math.abs(s)<1e-6)break;i-=a/s}if((i=t)<(r=0))return r;if(i>(n=1))return n;for(;r<n;){if(a=this.sampleCurveX(i),Math.abs(a-t)<e)return i;t>a?r=i:n=i,i=.5*(n-r)+r}return i},n.prototype.solve=function(t,e){return this.sampleCurveY(this.solveCurveX(t,e))};var i=a;function a(t,e){this.x=t,this.y=e}function o(t,e,n,i){var a=new r(t,e,n,i);return function(t){return a.solve(t)}}a.prototype={clone:function(){return new a(this.x,this.y)},add:function(t){return this.clone()._add(t)},sub:function(t){return this.clone()._sub(t)},multByPoint:function(t){return this.clone()._multByPoint(t)},divByPoi
       "/*\n",
       "object-assign\n",
       "(c) Sindre Sorhus\n",
       "@license MIT\n",
       "*/\n",
       "\"use strict\";var n=Object.getOwnPropertySymbols,i=Object.prototype.hasOwnProperty,a=Object.prototype.propertyIsEnumerable;function o(t){if(null==t)throw new TypeError(\"Object.assign cannot be called with null or undefined\");return Object(t)}e.exports=function(){try{if(!Object.assign)return!1;var t=new String(\"abc\");if(t[5]=\"de\",\"5\"===Object.getOwnPropertyNames(t)[0])return!1;for(var e={},r=0;r<10;r++)e[\"_\"+String.fromCharCode(r)]=r;if(\"0123456789\"!==Object.getOwnPropertyNames(e).map((function(t){return e[t]})).join(\"\"))return!1;var n={};return\"abcdefghijklmnopqrst\".split(\"\").forEach((function(t){n[t]=t})),\"abcdefghijklmnopqrst\"===Object.keys(Object.assign({},n)).join(\"\")}catch(t){return!1}}()?Object.assign:function(t,e){for(var r,s,l=o(t),c=1;c<arguments.length;c++){for(var u in r=Object(arguments[c]))i.call(r,u)&&(l[u]=r[u]);if(n){s=n(r);for(var f=0;f<s.length;f++)a.call(r,s[f])&&(l[s[f]]=r[s[f]])}}return l}},{}],500:[function(t,e,r){\"use strict\";e.exports=function(t,e,r,n,i,a,o,s,l,c){var u=e+a+c;if(f>0){var f=Math.sqrt(u+1);t[0]=.5*(o-l)/f,t[1]=.5*(s-n)/f,t[2]=.5*(r-a)/f,t[3]=.5*f}else{var h=Math.max(e,a,c);f=Math.sqrt(2*h-u+1);e>=h?(t[0]=.5*f,t[1]=.5*(i+r)/f,t[2]=.5*(s+n)/f,t[3]=.5*(o-l)/f):a>=h?(t[0]=.5*(r+i)/f,t[1]=.5*f,t[2]=.5*(l+o)/f,t[3]=.5*(s-n)/f):(t[0]=.5*(n+s)/f,t[1]=.5*(o+l)/f,t[2]=.5*f,t[3]=.5*(r-i)/f)}return t}},{}],501:[function(t,e,r){\"use strict\";e.exports=function(t){var e=(t=t||{}).center||[0,0,0],r=t.rotation||[0,0,0,1],n=t.radius||1;e=[].slice.call(e,0,3),u(r=[].slice.call(r,0,4),r);var i=new f(r,e,Math.log(n));i.setDistanceLimits(t.zoomMin,t.zoomMax),(\"eye\"in t||\"up\"in t)&&i.lookAt(0,t.eye,t.center,t.up);return i};var n=t(\"filtered-vector\"),i=t(\"gl-mat4/lookAt\"),a=t(\"gl-mat4/fromQuat\"),o=t(\"gl-mat4/invert\"),s=t(\"./lib/quatFromFrame\");function l(t,e,r){return Math.sqrt(Math.pow(t,2)+Math.pow(e,2)+Math.pow(r,2))}function c(t,e,r,n){return Math.sqrt(Math.pow(t,2)+Math.pow(e,2)+Math.pow(r,2)+Math.pow(n,2))}function u(t,e){var r=e[0],n=e[1],i=e[2],a=e[3],o=c(r,n,i,a);o>1e-6?(t[0]=r/o,t[1]=n/o,t[2]=i/o,t[3]=a/o):(t[0]=t[1]=t[2]=0,t[3]=1)}function f(t,e,r){this.radius=n([r]),this.center=n(e),this.rotation=n(t),this.computedRadius=this.radius.curve(0),this.computedCenter=this.center.curve(0),this.computedRotation=this.rotation.curve(0),this.computedUp=[.1,0,0],this.computedEye=[.1,0,0],this.computedMatrix=[.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],this.recalcMatrix(0)}var h=f.prototype;h.lastT=function(){return Math.max(this.radius.lastT(),this.center.lastT(),this.rotation.lastT())},h.recalcMatrix=function(t){this.radius.curve(t),this.center.curve(t),this.rotation.curve(t);var e=this.computedRotation;u(e,e);var r=this.computedMatrix;a(r,e);var n=this.computedCenter,i=this.computedEye,o=this.computedUp,s=Math.exp(this.computedRadius[0]);i[0]=n[0]+s*r[2],i[1]=n[1]+s*r[6],i[2]=n[2]+s*r[10],o[0]=r[1],o[1]=r[5],o[2]=r[9];for(var l=0;l<3;++l){for(var c=0,f=0;f<3;++f)c+=r[l+4*f]*i[f];r[12+l]=-c}},h.getMatrix=function(t,e){this.recalcMatrix(t);var r=this.computedMatrix;if(e){for(var n=0;n<16;++n)e[n]=r[n];return e}return r},h.idle=function(t){this.center.idle(t),this.radius.idle(t),this.rotation.idle(t)},h.flush=function(t){this.center.flush(t),this.radius.flush(t),this.rotation.flush(t)},h.pan=function(t,e,r,n){e=e||0,r=r||0,n=n||0,this.recalcMatrix(t);var i=this.computedMatrix,a=i[1],o=i[5],s=i[9],c=l(a,o,s);a/=c,o/=c,s/=c;var u=i[0],f=i[4],h=i[8],p=u*a+f*o+h*s,d=l(u-=a*p,f-=o*p,h-=s*p);u/=d,f/=d,h/=d;var g=i[2],m=i[6],v=i[10],y=g*a+m*o+v*s,x=g*u+m*f+v*h,b=l(g-=y*a+x*u,m-=y*o+x*f,v-=y*s+x*h);g/=b,m/=b,v/=b;var _=u*e+a*r,w=f*e+o*r,T=h*e+s*r;this.center.move(t,_,w,T);var k=Math.exp(this.computedRadius[0]);k=Math.max(1e-4,k+n),this.radius.set(t,Math.log(k))},h.rotate=function(t,e,r,n){this.recalcMatrix(t),e=e||0,r=r||0;var i=this.computedMatrix,a=i[0],o=i[4],s=i[8],u=i[1],f=i[5],h=i[9],p=i[2],d=i[6],g=i[10],m=e*a+r*u,v=e*o+r*f,y=e*s+r*h,x=-(d*y-g*v),b=-(g*m-p*y),_=-(p*v-d*m),w=Math.sqrt(Math.max(0,1-Math.pow(x,2)-Math.pow(b,2)-Math.pow(_,2))),T=c(x,b,_,w);T>1e-6?(x/=T,b/=
       "/*!\n",
       " * pad-left <https://github.com/jonschlinkert/pad-left>\n",
       " *\n",
       " * Copyright (c) 2014-2015, Jon Schlinkert.\n",
       " * Licensed under the MIT license.\n",
       " */\n",
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   "source": [
    "import KernelRegression\n",
    "import plotly.express as px\n",
    "import numpy as np\n",
    "kernel_x = np.arange(-4,4,0.1)\n",
    "col = KernelRegression.kernel_function(1, kernel_x, 0)\n",
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   "source": [
    "* jądro Epanechnikova\n",
    "\\begin{equation}\n",
    "K(x) = (\\frac34)(1-(\\frac{x - x_i}h)^2) \\text{ dla } {|x|\\leq1}\n",
    "\\end{equation}"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kernel_x = np.arange(-2,2,0.1)\n",
    "col = KernelRegression.epanechnikov_list(1, kernel_x, 0)\n",
    "px.line(x=kernel_x, y=col, title='Funkcja jądrowa Epanechnikova')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d60bbc1",
   "metadata": {},
   "source": [
    "Istotne znaczenie ma nie tylko dobór jądra, ale również parametru wygładzania, czyli szerokości okna. W zależności od niego, punkty są grupowane i dla każdej grupy wyliczana jest wartość funkcji. Jeśli okno będzie zbyt szerokie, funkcja będzie bardziej przypominała prostą (under-fitting). Natomiast jeśli będzie zbyt wąskie, funkcja będzie za bardzo \"skakać\" (over-fitting).\n",
    "\n",
    "Wyliczenie wartości funkcji polega na wzięciu średniej ważonej z $y_{i}$\n",
    " dla takich $x_{i}$, które znajdują się blisko x, dla którego wyznaczamy wartość. Wagi przy $y_{i}$ dla x sumują się do 1 i są wyższe, kiedy $x_{i}$ jest bliżej x oraz niższe w przeciwnym przypadku.\n",
    "<br/><br/>\n",
    "<div style=\"font-size: 26px\">\\begin{equation}w_i= \\frac{K_i}{\\sum\\limits_{i=1}^n K_i} \\end{equation}\n",
    "<br/><br/>\n",
    "\\begin{equation} Y=w_1*x_1+w_2*x_2+ \\text{...} +w_n*x_n \\end{equation}</div>\n",
    "<img src=\"files/est_weights.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4ae1bce9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import ipywidgets as widgets\n",
    "import plotly.graph_objs as go\n",
    "import pandas as pd \n",
    "\n",
    "fires_thefts = pd.read_csv('fires_thefts.csv', names=['x','y'])\n",
    "fires_thefts=fires_thefts.sort_values('x')\n",
    "X = np.array(fires_thefts.x)\n",
    "Y = np.array(fires_thefts.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "loved-clinton",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "dropdown_bw = widgets.Dropdown(options=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], value=1, description='Szerokość okna')\n",
    "\n",
    "def interactive_kernel(bw_manual):    \n",
    "    Y_pred_gauss = KernelRegression.ker_reg(X, Y, bw_manual, 'gauss')\n",
    "    Y_pred_epanechnikov = KernelRegression.ker_reg(X, Y, bw_manual, 'epanechnikov')\n",
    "\n",
    "    fig = px.scatter(x=X,y=Y)\n",
    "    fig.add_trace(go.Scatter(x=X, y=np.array(Y_pred_gauss), name='Gauss',  mode='lines'))\n",
    "    fig.add_trace(go.Scatter(x=X, y=np.array(Y_pred_epanechnikov), name='Epanechnikov',  mode='lines'))\n",
    "    fig.show()\n",
    "    \n",
    "    # kernel regression\n",
    "    kernel_x = np.arange(min(X)-5,max(X)+5, 0.1)\n",
    "\n",
    "    ## Plotting gaussian for all input x points \n",
    "    kernel_fns = {'kernel_x': kernel_x}\n",
    "    for input_x in X: \n",
    "        input_string= 'x_value_{}'.format(np.round(input_x,2)) \n",
    "        kernel_fns[input_string] = KernelRegression.kernel_function(bw_manual, kernel_x, input_x)\n",
    "\n",
    "    kernels_df = pd.DataFrame(data=kernel_fns)\n",
    "    y_all = kernels_df.drop(columns='kernel_x')\n",
    "    fig = px.line(kernels_df, x='kernel_x', y=y_all.columns, title='Gaussian for all input points', range_x=[min(X)-5,max(X)+5])    \n",
    "    fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "injured-english",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "722bc244f3d24c5ba1875e43ed5be82c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='Szerokość okna', options=(1, 2, 3, 4, 5, 6, 7, 8, 9, 10), value=1)…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.interactive_kernel(bw_manual)>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "widgets.interact(interactive_kernel, bw_manual=dropdown_bw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "demographic-clearing",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Input_x</th>\n",
       "      <th>kernel_x</th>\n",
       "      <th>weigth</th>\n",
       "      <th>Y</th>\n",
       "      <th>Y=w0*x0+w1*x1+...+w41*x41</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(2.0)</td>\n",
       "      <td>0.0000001506</td>\n",
       "      <td>11</td>\n",
       "      <td></td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(2.2)</td>\n",
       "      <td>0.0000001862</td>\n",
       "      <td>9</td>\n",
       "      <td></td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(2.2)</td>\n",
       "      <td>0.0000001862</td>\n",
       "      <td>14</td>\n",
       "      <td></td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(2.5)</td>\n",
       "      <td>0.0000002551</td>\n",
       "      <td>22</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(3.4)</td>\n",
       "      <td>0.0000006423</td>\n",
       "      <td>17</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(3.6)</td>\n",
       "      <td>0.0000007851</td>\n",
       "      <td>15</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(4.0)</td>\n",
       "      <td>0.0000011675</td>\n",
       "      <td>16</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(4.8)</td>\n",
       "      <td>0.0000025327</td>\n",
       "      <td>19</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(5.0)</td>\n",
       "      <td>0.0000030615</td>\n",
       "      <td>32</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(5.4)</td>\n",
       "      <td>0.0000044518</td>\n",
       "      <td>27</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(5.6)</td>\n",
       "      <td>0.0000053554</td>\n",
       "      <td>23</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(5.7)</td>\n",
       "      <td>0.0000058703</td>\n",
       "      <td>11</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(6.2)</td>\n",
       "      <td>0.0000092341</td>\n",
       "      <td>29</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(6.9)</td>\n",
       "      <td>0.0000171209</td>\n",
       "      <td>18</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(7.2)</td>\n",
       "      <td>0.0000221736</td>\n",
       "      <td>29</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(7.3)</td>\n",
       "      <td>0.0000241504</td>\n",
       "      <td>31</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(7.7)</td>\n",
       "      <td>0.0000338487</td>\n",
       "      <td>37</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(8.6)</td>\n",
       "      <td>0.0000706756</td>\n",
       "      <td>53</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(9.0)</td>\n",
       "      <td>0.0000970184</td>\n",
       "      <td>39</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(9.5)</td>\n",
       "      <td>0.0001428651</td>\n",
       "      <td>44</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(10.5)</td>\n",
       "      <td>0.0003006361</td>\n",
       "      <td>42</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(10.5)</td>\n",
       "      <td>0.0003006361</td>\n",
       "      <td>36</td>\n",
       "      <td>32.501314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(10.7)</td>\n",
       "      <td>0.0003471999</td>\n",
       "      <td>43</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(10.8)</td>\n",
       "      <td>0.0003728964</td>\n",
       "      <td>34</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(11.0)</td>\n",
       "      <td>0.0004296198</td>\n",
       "      <td>75</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(11.3)</td>\n",
       "      <td>0.0005296946</td>\n",
       "      <td>34</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(11.9)</td>\n",
       "      <td>0.0007965586</td>\n",
       "      <td>46</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(12.2)</td>\n",
       "      <td>0.0009715577</td>\n",
       "      <td>46</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(15.1)</td>\n",
       "      <td>0.0055032862</td>\n",
       "      <td>25</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(15.1)</td>\n",
       "      <td>0.0055032862</td>\n",
       "      <td>30</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(16.5)</td>\n",
       "      <td>0.0112700122</td>\n",
       "      <td>40</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(17.4)</td>\n",
       "      <td>0.0171422369</td>\n",
       "      <td>32</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(18.4)</td>\n",
       "      <td>0.0262993813</td>\n",
       "      <td>32</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(18.5)</td>\n",
       "      <td>0.0273891079</td>\n",
       "      <td>22</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(21.6)</td>\n",
       "      <td>0.0790709391</td>\n",
       "      <td>31</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(21.8)</td>\n",
       "      <td>0.0835583686</td>\n",
       "      <td>4</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(23.3)</td>\n",
       "      <td>0.1201265071</td>\n",
       "      <td>29</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(28.6)</td>\n",
       "      <td>0.2106810573</td>\n",
       "      <td>27</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(29.1)</td>\n",
       "      <td>0.2096302812</td>\n",
       "      <td>34</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(34.1)</td>\n",
       "      <td>0.1150475376</td>\n",
       "      <td>68</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(36.2)</td>\n",
       "      <td>0.0663633810</td>\n",
       "      <td>41</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>28.6</td>\n",
       "      <td>K(39.7)</td>\n",
       "      <td>0.0179240863</td>\n",
       "      <td>147</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Input_x kernel_x        weigth    Y Y=w0*x0+w1*x1+...+w41*x41\n",
       "0      28.6   K(2.0)  0.0000001506   11                          \n",
       "1      28.6   K(2.2)  0.0000001862    9                          \n",
       "2      28.6   K(2.2)  0.0000001862   14                          \n",
       "3      28.6   K(2.5)  0.0000002551   22                          \n",
       "4      28.6   K(3.4)  0.0000006423   17                          \n",
       "5      28.6   K(3.6)  0.0000007851   15                          \n",
       "6      28.6   K(4.0)  0.0000011675   16                          \n",
       "7      28.6   K(4.8)  0.0000025327   19                          \n",
       "8      28.6   K(5.0)  0.0000030615   32                          \n",
       "9      28.6   K(5.4)  0.0000044518   27                          \n",
       "10     28.6   K(5.6)  0.0000053554   23                          \n",
       "11     28.6   K(5.7)  0.0000058703   11                          \n",
       "12     28.6   K(6.2)  0.0000092341   29                          \n",
       "13     28.6   K(6.9)  0.0000171209   18                          \n",
       "14     28.6   K(7.2)  0.0000221736   29                          \n",
       "15     28.6   K(7.3)  0.0000241504   31                          \n",
       "16     28.6   K(7.7)  0.0000338487   37                          \n",
       "17     28.6   K(8.6)  0.0000706756   53                          \n",
       "18     28.6   K(9.0)  0.0000970184   39                          \n",
       "19     28.6   K(9.5)  0.0001428651   44                          \n",
       "20     28.6  K(10.5)  0.0003006361   42                          \n",
       "21     28.6  K(10.5)  0.0003006361   36                 32.501314\n",
       "22     28.6  K(10.7)  0.0003471999   43                          \n",
       "23     28.6  K(10.8)  0.0003728964   34                          \n",
       "24     28.6  K(11.0)  0.0004296198   75                          \n",
       "25     28.6  K(11.3)  0.0005296946   34                          \n",
       "26     28.6  K(11.9)  0.0007965586   46                          \n",
       "27     28.6  K(12.2)  0.0009715577   46                          \n",
       "28     28.6  K(15.1)  0.0055032862   25                          \n",
       "29     28.6  K(15.1)  0.0055032862   30                          \n",
       "30     28.6  K(16.5)  0.0112700122   40                          \n",
       "31     28.6  K(17.4)  0.0171422369   32                          \n",
       "32     28.6  K(18.4)  0.0262993813   32                          \n",
       "33     28.6  K(18.5)  0.0273891079   22                          \n",
       "34     28.6  K(21.6)  0.0790709391   31                          \n",
       "35     28.6  K(21.8)  0.0835583686    4                          \n",
       "36     28.6  K(23.3)  0.1201265071   29                          \n",
       "37     28.6  K(28.6)  0.2106810573   27                          \n",
       "38     28.6  K(29.1)  0.2096302812   34                          \n",
       "39     28.6  K(34.1)  0.1150475376   68                          \n",
       "40     28.6  K(36.2)  0.0663633810   41                          \n",
       "41     28.6  K(39.7)  0.0179240863  147                          "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bw_manual = 5\n",
    "input_x = X[37]\n",
    "kernel_x = X\n",
    "weigths = KernelRegression.weights(bw_manual, input_x, X)\n",
    "# Dataframe for a single observation point x_i. In the code x_i comes from new_x\n",
    "data = {'Input_x': [input_x for x in kernel_x],\n",
    "        'kernel_x': kernel_x,\n",
    "        'weigth': weigths,\n",
    "        'Y': Y,\n",
    "        'Y=w0*x0+w1*x1+...+w41*x41': ''\n",
    "        }\n",
    "single_pt_KE = pd.DataFrame(data=data)\n",
    "single_pt_KE.at[len(Y)//2, 'Y=w0*x0+w1*x1+...+w41*x41'] = KernelRegression.single_y_pred_gauss(3, X[37], X, Y)\n",
    "single_pt_KE['weigth'] = single_pt_KE['weigth'].map('{:,.10f}'.format)\n",
    "single_pt_KE['kernel_x'] = single_pt_KE['kernel_x'].map('K({})'.format)\n",
    "single_pt_KE"
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   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "# linear regression\n",
    "reg = LinearRegression().fit(X.reshape(-1, 1), Y.reshape(-1, 1))\n",
    "Y_pred_linear = reg.predict(X.reshape(-1, 1))\n",
    "\n",
    "# kernel regression\n",
    "Y_pred_gauss = KernelRegression.ker_reg(X, Y, bw_manual, 'gauss')\n",
    "Y_pred_epanechnikov = KernelRegression.ker_reg(X, Y, bw_manual, 'epanechnikov')\n",
    "\n",
    "fig = px.scatter(x=X,y=Y)\n",
    "fig.add_trace(go.Scatter(x=X, y=np.array(Y_pred_gauss), name='Gauss',  mode='lines'))\n",
    "fig.add_trace(go.Scatter(x=X, y=np.array(Y_pred_epanechnikov), name='Epanechnikov',  mode='lines'))\n",
    "fig.add_trace(go.Scatter(x=X, y=np.array(Y_pred_linear.flatten().tolist()), name='Linear',  mode='lines'))"
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  }
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