kerreg-MPSKICB/KernelRegression.ipynb

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   "source": [
    "import numpy as np\n",
    "import plotly.express as px\n",
    "from statsmodels.nonparametric.kernel_regression import KernelReg\n",
    "import plotly.graph_objs as go\n",
    "import pandas as pd \n",
    "import KernelRegression"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
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    "np.random.seed(1)# xwidth controls the range of x values.\n",
    "xwidth = 20\n",
    "x = np.arange(0,xwidth,1)# we want to add some noise to the x values so that dont sit at regular intervals\n",
    "x_residuals = np.random.normal(scale=0.2, size=[x.shape[0]])# new_x is the range of x values we will be using all the way through\n",
    "new_x = x + x_residuals# We generate residuals for y values since we want to show some variation in the data\n",
    "num_points = x.shape[0]\n",
    "residuals = np.random.normal(scale=2.0, size=[num_points])# We will be using fun_y to generate y values all the way through\n",
    "fun_y = lambda x: -(x*x) + residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)# xwidth controls the range of x values.\n",
    "xwidth = 20\n",
    "x = np.arange(0,xwidth,1)# we want to add some noise to the x values so that dont sit at regular intervals\n",
    "x_residuals = np.random.normal(scale=0.2, size=[x.shape[0]])# new_x is the range of x values we will be using all the way through\n",
    "new_x = x + x_residuals# We generate residuals for y values since we want to show some variation in the data\n",
    "num_points = x.shape[0]\n",
    "residuals = np.random.normal(scale=2.0, size=[num_points])# We will be using fun_y to generate y values all the way through\n",
    "fun_y = lambda x: -(x*x) + residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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       " * @license  MIT\n",
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       " * The buffer module from node.js, for the browser.\n",
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       " * @author   Feross Aboukhadijeh <https://feross.org>\n",
       " * @license  MIT\n",
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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",
       " */\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": [
    "# Plot the x and y values \n",
    "px.scatter(x=new_x,y=fun_y(new_x), title='Figure 1:  Visualizing the generated data')"
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   "cell_type": "code",
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    "#ker_log = KernelReg(new_x, fun_y(new_x), 'c')\n"
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   "execution_count": 26,
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   "source": [
    "#fig = px.scatter(x=new_x,y=fun_y(new_x),  title='Figure 2: Statsmodels fit to generated data')\n",
    "#fig.add_trace(go.Scatter(x=new_x, y=pred_y, name='Statsmodels fit',  mode='lines'))"
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    "kernel_x = np.arange(-2, 2, 0.01)\n",
    "bw_manual = 3\n",
    "\n",
    "def epanechnikov_one(h, ker_x, xi): \n",
    "    \"\"\"\n",
    "    Returns the epanechnikov function value.\n",
    "    \"\"\"\n",
    "    value = 0.75*(1-np.square((xi-ker_x)/h))\n",
    "    if (value < 0):\n",
    "        value = 0\n",
    "    return value\n",
    "\n",
    "def epanechnikov_list(h, ker_x, xi): \n",
    "    \"\"\"\n",
    "    Returns the epanechnikov function value.\n",
    "    \"\"\"\n",
    "    value = 0.75*(1-np.square((xi-ker_x)/h))\n",
    "    value = [0 if i < 0 else i for i in value]\n",
    "    return value\n",
    "\n",
    "\n",
    "def weights_epanechnikov(bw_manual, input_x, all_input_values ): \n",
    "    w_row = []\n",
    "    for x_i in all_input_values: \n",
    "        ki = epanechnikov_one(bw_manual, x_i, input_x)\n",
    "        ki_sum = np.sum(epanechnikov_list(bw_manual, all_input_values, input_x))\n",
    "        w_row.append(ki/ki_sum)\n",
    "    return w_row\n",
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    "def single_y_pred_epanechnikov(bw_manual, input_x, x_values, y_values): \n",
    "    w = weights_epanechnikov(bw_manual, input_x, x_values)\n",
    "    y_single = np.sum(np.dot(y_values,w))\n",
    "    return y_single\n",
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    "# We are selecting a single point and calculating the Kernel value\n",
    "input_x = 0\n",
    "col1 = KernelRegression.gauss_const(bw_manual)\n",
    "col2= KernelRegression.gauss_exp(kernel_x, input_x, bw_manual)\n",
    "col3 = epanechnikov_list(1, kernel_x, input_x)"
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    "kernel_x = np.arange(-20,20,0.1)\n",
    "## Plotting gaussian for all input x points \n",
    "kernel_fns = {'kernel_x': kernel_x}\n",
    "for input_x in new_x: \n",
    "    input_string= 'x_value_{}'.format(np.round(input_x,2)) \n",
    "    kernel_fns[input_string] = epanechnikov_list(bw_manual, kernel_x, input_x)\n",
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    "kernels_df = pd.DataFrame(data=kernel_fns)\n",
    "y_all = kernels_df.drop(columns='kernel_x')\n",
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   "source": [
    "Y_pred = []\n",
    "for input_x in new_x: \n",
    "    w = []\n",
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