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            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          },
          "model_module_version": "1.2.0"
        },
        "7de5fbb0b08b40f68b29d3b8d4f7af55": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [
              {
                "output_type": "display_data",
                "metadata": {
                  "tags": [],
                  "needs_background": "light"
                },
                "image/png": 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\n",
                "text/plain": "<Figure size 720x576 with 1 Axes>"
              }
            ],
            "_view_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_view_count": null,
            "_view_module_version": "1.0.0",
            "layout": "IPY_MODEL_2462f4a464474304bbf26643f7fab70e",
            "_model_module": "@jupyter-widgets/output"
          },
          "model_module_version": "1.0.0"
        },
        "2462f4a464474304bbf26643f7fab70e": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
            "right": null,
            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
            "flex_flow": null,
            "width": null,
            "min_width": null,
            "border": null,
            "align_items": null,
            "bottom": null,
            "_model_module": "@jupyter-widgets/base",
            "top": null,
            "grid_column": null,
            "overflow_y": null,
            "overflow_x": null,
            "grid_auto_flow": null,
            "grid_area": null,
            "grid_template_columns": null,
            "flex": null,
            "_model_name": "LayoutModel",
            "justify_items": null,
            "grid_row": null,
            "max_height": null,
            "align_content": null,
            "visibility": null,
            "align_self": null,
            "height": null,
            "min_height": null,
            "padding": null,
            "grid_auto_rows": null,
            "grid_gap": null,
            "max_width": null,
            "order": null,
            "_view_module_version": "1.2.0",
            "grid_template_areas": null,
            "object_position": null,
            "object_fit": null,
            "grid_auto_columns": null,
            "margin": null,
            "display": null,
            "left": null
          },
          "model_module_version": "1.2.0"
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/fbeilstein/machine_learning/blob/master/workbook_15_kernel_density_estimation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title #Quiz\n",
        "\n",
        "%%html\n",
        "<link   rel=\"stylesheet\" href=\"https://fbeilstein.github.io/machine_learning/js_common/styles.css\"/>\n",
        "<script src=\"https://fbeilstein.github.io/machine_learning/js_common/script.js\"></script>\n",
        "<script>\n",
        "load_quiz_from(\"https://fbeilstein.github.io/machine_learning/lecture_15_kernel_density_estimation/quiz_1.txt\")\n",
        "</script>"
      ],
      "metadata": {
        "cellView": "form",
        "id": "bjgbPz3M8AJh",
        "outputId": "f6d4aa1c-1de3-4d0c-d23a-47a1a6be7661",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 247
        }
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<link   rel=\"stylesheet\" href=\"https://fbeilstein.github.io/machine_learning/js_common/styles.css\"/>\n",
              "<script src=\"https://fbeilstein.github.io/machine_learning/js_common/script.js\"></script>\n",
              "<script>\n",
              "load_quiz_from(\"https://fbeilstein.github.io/machine_learning/lecture_15_kernel_density_estimation/quiz_1.txt\")\n",
              "</script>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-kqkuvkFAFll"
      },
      "source": [
        "#Bandwidth and kernel influence on 1D KDE"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DBOKZhb7oGvY"
      },
      "source": [
        "The following demo uses KDEpy library for Silverman's and ISJ bandwidth estimation methods.\n",
        "Start this code to install it:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8UvovqjzWjFO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        },
        "outputId": "9e986f6a-16a4-4806-cedf-9af95b435987"
      },
      "source": [
        "# install KDEpy library before starting the following demo\n",
        "!pip install KDEpy"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting KDEpy\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/d5/a2/8c07773c71ef2e6de288fd274cc874f876764ef834849e0418fa375e0123/KDEpy-1.0.5-cp36-cp36m-manylinux2010_x86_64.whl (396kB)\n",
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            "\u001b[?25hRequirement already satisfied: numpy>=1.14.2 in /usr/local/lib/python3.6/dist-packages (from KDEpy) (1.18.5)\n",
            "Requirement already satisfied: matplotlib>=2.2.0 in /usr/local/lib/python3.6/dist-packages (from KDEpy) (3.2.2)\n",
            "Requirement already satisfied: scipy>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from KDEpy) (1.4.1)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=2.2.0->KDEpy) (1.2.0)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=2.2.0->KDEpy) (2.4.7)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=2.2.0->KDEpy) (2.8.1)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=2.2.0->KDEpy) (0.10.0)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.6/dist-packages (from python-dateutil>=2.1->matplotlib>=2.2.0->KDEpy) (1.15.0)\n",
            "Installing collected packages: KDEpy\n",
            "Successfully installed KDEpy-1.0.5\n"
          ],
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      "metadata": {
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        "Use the following demo to get the intuition on\n",
        "* How one-dimensional KDE works\n",
        "* How bandwidth influences the result\n",
        "* How good different methods (Silverman, ISJ, Cross validation) estimate the bandwidth"
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N.prototype.P=function(){N.i.P.call(this);this.W&&Fc(this.W);this.isVisible()&&this.isEnabled()&&kd(this,!1)};N.prototype.u=function(){N.i.u.call(this);this.W&&(this.W.N(),delete this.W);delete this.B;this.ga=this.wa=this.ba=null};var hd=function(a,b){a.ba=b};N.prototype.isVisible=function(){return this.Ia};N.prototype.isEnabled=function(){return!(this.o&1)};
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h.ka=function(a){if(this.isEnabled()&&(R(this,2)&&P(this,!0),Ob(a)&&!(y&&z&&a.ctrlKey))){R(this,4)&&qd(this,!0);var b;if(b=this.B){var c;b=this.v&32&&(c=this.f())?sb(c)&&tb(c):!1}b&&this.f().focus()}!Ob(a)||y&&z&&a.ctrlKey||a.g()};h.la=function(a){this.isEnabled()&&(R(this,2)&&P(this,!0),this.o&4&&ud(this,a)&&R(this,4)&&qd(this,!1))};h.Ja=function(a){this.isEnabled()&&ud(this,a)};
var ud=function(a,b){if(R(a,16)){var c=!(a.o&16);O(a,16,c)&&Q(a,16,c)}R(a,8)&&rd(a,!0);R(a,64)&&sd(a,!(a.o&64));c=new E("action",a);b&&(c.altKey=b.altKey,c.ctrlKey=b.ctrlKey,c.metaKey=b.metaKey,c.shiftKey=b.shiftKey,c.A=b.A);return uc(a,c)};N.prototype.Na=function(){R(this,32)&&O(this,32,!0)&&Q(this,32,!0)};N.prototype.Fa=function(){R(this,4)&&qd(this,!1);R(this,32)&&O(this,32,!1)&&Q(this,32,!1)};
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pd.prototype.h=function(){this.a=!1};pd.prototype.j=function(){this.a=!0};var xd=function(a,b){if(!wd)return a.button=0,a.type=b,a;var c=document.createEvent("MouseEvents");c.initMouseEvent(b,a.bubbles,a.cancelable,a.view||null,a.detail,a.screenX,a.screenY,a.clientX,a.clientY,a.ctrlKey,a.altKey,a.shiftKey,a.metaKey,0,a.relatedTarget||null);return c};
pd.prototype.g=function(a){if(this.a)this.a=!1;else{var b=a.b,c=b.button,d=b.type,e=xd(b,"mousedown");this.b.ka(new G(e,a.a));e=xd(b,"mouseup");this.b.la(new G(e,a.a));wd||(b.button=c,b.type=d)}};pd.prototype.u=function(){this.b=null;pd.i.u.call(this)};var S=function(a,b,c){K.call(this,c);this.da=b||Xc.R();this.H=a||"vertical"};n(S,K);h=S.prototype;h.Da=null;h.ca=null;h.da=null;h.H=null;h.T=!0;h.O=!0;h.l=-1;h.s=null;h.V=!1;h.I=null;var yd=function(a){return a.Da||a.f()};h=S.prototype;h.ia=function(){this.a=this.j.b("DIV",this.da.c(this).join(" "))};h.ja=function(){return this.f()};h.xa=function(a){return"DIV"==a.tagName};h.va=function(a){this.a=$c(this.da,this,a);"none"==a.style.display&&(this.T=!1)};
h.D=function(){S.i.D.call(this);Qc(this,function(b){b.m&&zd(this,b)},this);var a=this.f();bd(this.da,this);Ad(this,this.T);H(H(H(H(H(H(H(H(Oc(this),this,"enter",this.Wa),this,"highlight",this.Xa),this,"unhighlight",this.cb),this,"open",this.Ya),this,"close",this.Ua),a,F.L,this.Sa),qb(a),[F.M,F.aa],this.Va),a,[F.L,F.M,F.aa,"mouseover","mouseout","contextmenu"],this.Ta);Bd(this)};var Bd=function(a){var b=Oc(a),c=yd(a);H(H(H(b,c,"focus",a.Ha),c,"blur",a.Qa),a.ca||(a.ca=new J(yd(a))),"key",a.Ra)};h=S.prototype;
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h.Xa=function(a){var b=Tc(this,a.target);if(-1<b&&b!=this.l){var c=L(this,this.l);c&&P(c,!1);this.l=b;c=L(this,this.l);this.V&&qd(c,!0);this.s&&c!=this.s&&(c.v&64?sd(c,!0):sd(this.s,!1))}b=this.f();q(b,"The DOM element for the container cannot be null.");null!=a.target.f()&&xb(b,"activedescendant",a.target.f().id)};h.cb=function(a){a.target==L(this,this.l)&&(this.l=-1);a=this.f();q(a,"The DOM element for the container cannot be null.");a.removeAttribute(wb("activedescendant"))};
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        "#@title Bandwidth and kernel in KDE\n",
        "from google.colab import widgets\n",
        "import ipywidgets\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy\n",
        "from sklearn.neighbors import KernelDensity\n",
        "from sklearn.model_selection import learning_curve, GridSearchCV\n",
        "from sklearn.model_selection import LeaveOneOut #train_test_split\n",
        "from KDEpy import FFTKDE\n",
        "import IPython\n",
        "from google.colab import output\n",
        "\n",
        "\n",
        "main_str = '''\n",
        "<html>\n",
        "\n",
        "<head>\n",
        "  <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script>\n",
        "\n",
        "  <script type=\"application/javascript\">\n",
        "    var xs = [];\n",
        "    var ys = [];\n",
        "    var x_min = -5.0;\n",
        "    var y_min =  0.0;\n",
        "    var x_max = +5.0;\n",
        "    var y_max = +0.8;\n",
        "    for (var x = x_min; x <= x_max; x += 0.01)\n",
        "      xs.push(x);\n",
        "    for (var y = y_min; y <= y_max; y += 0.1)\n",
        "      ys.push(y);\n",
        "    var colors = ['blue', 'green', 'red'];\n",
        "    var coefs = [1.0/3.0, 1.0/3.0, 1.0/3.0];\n",
        "    var rand_pts = [];\n",
        "\n",
        "   function random_point(mu, sigma) {\n",
        "     var z = Math.sqrt(-2.0 * Math.log(Math.random())) * Math.cos(2.0 * Math.PI * Math.random());\n",
        "     return z * sigma + mu;\n",
        "   }\n",
        "\n",
        "    function loss_function_2d() {\n",
        "      var canvas = document.getElementById(\"paint\");\n",
        "      var w = canvas.width;\n",
        "      var h = canvas.height;\n",
        "\n",
        "      //var size = adjust_canvas();\n",
        "      //var w = size[0];\n",
        "      //var h = size[1];\n",
        "\n",
        "      mu = [];\n",
        "      sigma = [];\n",
        "      C = Math.sqrt(2 * Math.PI);\n",
        "      for (var i = 0; i < pts.length; ++i) {\n",
        "          var x = pts[i][0] / w * (x_max - x_min) + x_min;\n",
        "        var y = (1.0 - pts[i][1] / h) * (y_max - y_min) + y_min;\n",
        "          mu.push(x);\n",
        "          sigma.push(1.0 / (y * C));\n",
        "      }\n",
        "\n",
        "      data = [];\n",
        "      for (var trace_idx = 0; trace_idx < pts.length; ++trace_idx) {\n",
        "          var trace = [];\n",
        "          for (var i = 0; i < xs.length; ++i) {\n",
        "              var delta = (xs[i] - mu[trace_idx]) / sigma[trace_idx];\n",
        "              trace.push(Math.exp(-delta*delta / 2.0) / sigma[trace_idx] / C);\n",
        "          }\n",
        "          data.push({\n",
        "            x: xs,\n",
        "            y: trace,\n",
        "            showscale: false,\n",
        "            opacity: coefs[trace_idx],\n",
        "            type: 'scatter',\n",
        "            mode: 'line',\n",
        "            name: 'gaussian ' + trace_idx,\n",
        "            line: {\n",
        "              width: 2,\n",
        "              color: colors[trace_idx]\n",
        "            },\n",
        "          });\n",
        "      }\n",
        "\n",
        "      var sum_trace = [];\n",
        "      for (var i = 0; i < xs.length; ++i) {\n",
        "          var sum = 0.0;\n",
        "          for (var trace_idx = 0; trace_idx < pts.length; ++trace_idx) {\n",
        "              var delta = (xs[i] - mu[trace_idx]) / sigma[trace_idx];\n",
        "              sum += coefs[trace_idx] * Math.exp(-delta*delta / 2.0) / sigma[trace_idx] / C;\n",
        "          }\n",
        "          sum_trace.push(sum);\n",
        "      }\n",
        "      data.push({\n",
        "            x: xs,\n",
        "            y: sum_trace,\n",
        "            showscale: false,\n",
        "            opacity: coefs[trace_idx],\n",
        "            type: 'scatter',\n",
        "            mode: 'line',\n",
        "            name: 'sum',\n",
        "            line: {\n",
        "              width: 2,\n",
        "              color: 'black'\n",
        "            },\n",
        "          });\n",
        "\n",
        "      var N_points = 200;\n",
        "      rand_pts = [];\n",
        "      var ys = [];\n",
        "      for (var i = 0; i < N_points; ++i) {\n",
        "        active_gaussian = 0;\n",
        "        var rnd = Math.random();\n",
        "        if (rnd > coefs[0])\n",
        "            active_gaussian = 1;\n",
        "        if (rnd > coefs[0] + coefs[1])\n",
        "            active_gaussian = 2;\n",
        "        //active_gaussian = Math.floor(Math.random() * Math.floor(3));\n",
        "        rand_pts.push(random_point(mu[active_gaussian], sigma[active_gaussian]));\n",
        "        ys.push(0.0);\n",
        "      }\n",
        "      data.push({\n",
        "            x: rand_pts,\n",
        "            y: ys,\n",
        "            showscale: false,\n",
        "            opacity: 1.0,\n",
        "            type: 'scatter',\n",
        "            mode: 'markers',\n",
        "            name: 'random datapoints',\n",
        "            marker: {\n",
        "              symbol: 'line-ns',\n",
        "              size: 20,\n",
        "              line :{\n",
        "                width: 1,\n",
        "                color: 'black'\n",
        "              }\n",
        "            }\n",
        "          });\n",
        "\n",
        "      var cell_for_plot = document.getElementById(\"for_right_plot\");\n",
        "      var layout = {\n",
        "          //title: 'Error Function',\n",
        "          xaxis: {'range': [x_min, x_max], 'domain': [0.0, 1.0], 'fixedrange': true},\n",
        "          yaxis: {'range': [y_min, y_max], 'domain': [0.0, 1.0], 'fixedrange': true},\n",
        "          width: 800,\n",
        "          height: 500,\n",
        "          autosize: false,\n",
        "          showlegend: true,\n",
        "          margin: {\n",
        "            l: 50,\n",
        "            r: 50,\n",
        "            b: 50,\n",
        "            t: 50\n",
        "          }\n",
        "        };\n",
        "      Plotly.newPlot(cell_for_plot, data, layout);\n",
        "    }\n",
        "\n",
        "    var pts = [[100, 300], [300, 300], [500, 300]];\n",
        "    var active_idx = -1;\n",
        "\n",
        "    function mdown_handle(event) {\n",
        "      //console.log('down');\n",
        "      event.stopPropagation();\n",
        "      x = event.offsetX;\n",
        "      y = event.offsetY;\n",
        "      for (var i = 0; i < pts.length; ++i)\n",
        "        if ((x - pts[i][0])*(x - pts[i][0]) + (y - pts[i][1])*(y - pts[i][1]) < 500)\n",
        "            active_idx = i;\n",
        "      //console.log('ACTIVE', active_idx);\n",
        "    }\n",
        "\n",
        "    function mmove_handle(event) {\n",
        "      event.stopPropagation();\n",
        "      //console.log('move');\n",
        "      if (active_idx < 0)\n",
        "          return;\n",
        "      pts[active_idx] = [event.offsetX, event.offsetY];\n",
        "      loss_function_2d();\n",
        "    }\n",
        "\n",
        "    function mup_handle(event) {\n",
        "      active_idx = -1;\n",
        "    }\n",
        "\n",
        "    async function call_once() {\n",
        "      const result = await google.colab.kernel.invokeFunction('notebook.redraw', [coefs, mu, sigma, rand_pts], {});\n",
        "      //const text = result.data['application/json'];\n",
        "    }\n",
        "    var old_state = false;\n",
        "    function adjust_canvas() {\n",
        "      var plt_div = document.getElementById('for_right_plot');\n",
        "      var el = plt_div.getElementsByClassName('xy')[0];\n",
        "      if (!el)\n",
        "          return [600, 600];\n",
        "      var rect = el.getBoundingClientRect();\n",
        "      var canvas = document.getElementById(\"paint\");\n",
        "      //console.log(rect);\n",
        "      canvas.style.cssText = \"position:absolute; top:\" + parseInt(rect.top)\n",
        "                          + \"px; left: \" + parseInt(rect.left)\n",
        "                          + \"px; width:\" + parseInt(rect.width)\n",
        "                          + \"px; height:\" + parseInt(rect.height)\n",
        "                          + \"px; z-index:1000;\";\n",
        "      canvas.width = rect.width;\n",
        "      canvas.height = rect.height;\n",
        "      var ctx = canvas.getContext('2d');\n",
        "      ctx.clearRect(0, 0, canvas.width, canvas.height);\n",
        "\n",
        "      if ((canvas.offsetParent === null) != old_state)\n",
        "        call_once();\n",
        "      old_state = (canvas.offsetParent === null);\n",
        "\n",
        "      //loss_function_2d();\n",
        "      return [canvas.width, canvas.height];\n",
        "    }\n",
        "\n",
        "    function draw_slider() {\n",
        "        var canvas = document.getElementById(\"slider\");\n",
        "        var ctx = canvas.getContext('2d');\n",
        "        var h = canvas.height;\n",
        "        var w = canvas.width;\n",
        "        var cur_start = 0;\n",
        "        ctx.clearRect(0, 0, canvas.width, canvas.height);\n",
        "        for (var i = 0; i < pts.length; ++i) {\n",
        "            ctx.fillStyle = colors[i];\n",
        "            ctx.fillRect(0, cur_start, w, h*coefs[i]);\n",
        "            cur_start += h*coefs[i];\n",
        "        }\n",
        "\n",
        "    }\n",
        "\n",
        "    var active_coef = -1;\n",
        "    function mdown(event) {\n",
        "    //console.log('ddd');\n",
        "      event.stopPropagation();\n",
        "      x = event.offsetX;\n",
        "      y = event.offsetY;\n",
        "      var canvas = document.getElementById(\"slider\");\n",
        "      var h = canvas.height;\n",
        "      var H = 0;\n",
        "      for (var i = 0; i < coefs.length - 1; ++i) {\n",
        "        H += coefs[i] * h;\n",
        "        if (y > H - 10 && y < H +1)\n",
        "            active_coef = i;\n",
        "      }\n",
        "      //console.log(active_coef, coefs);\n",
        "    }\n",
        "\n",
        "    function mmove(event) { // for double-slider only\n",
        "      event.stopPropagation();\n",
        "      if (active_coef < 0)\n",
        "        return;\n",
        "      x = event.offsetX;\n",
        "      y = event.offsetY;\n",
        "      var canvas = document.getElementById(\"slider\");\n",
        "      var h = canvas.height;\n",
        "      var new_sum = y / h;\n",
        "      if (active_coef == 0) {\n",
        "        if (coefs[0] + coefs[1] < new_sum)\n",
        "            coefs[1] = 0.0;\n",
        "        else\n",
        "            coefs[1] = coefs[0] + coefs[1] - new_sum;\n",
        "        coefs[0] = new_sum;\n",
        "        coefs[2] = 1.0 - coefs[0] - coefs[1];\n",
        "      }\n",
        "      if (active_coef == 1) {\n",
        "        if (coefs[0] > new_sum)\n",
        "            coefs[0] = new_sum;\n",
        "        coefs[1] = new_sum - coefs[0];\n",
        "        coefs[2] = 1.0 - coefs[0] - coefs[1];\n",
        "      }\n",
        "      draw_slider();\n",
        "      loss_function_2d();\n",
        "    }\n",
        "\n",
        "    function mup(event) {\n",
        "      active_coef = -1;\n",
        "    }\n",
        "\n",
        "\n",
        "  </script>\n",
        "</head>\n",
        "\n",
        "<body>\n",
        "\n",
        "<canvas id=\"paint\" width=600 height=600\n",
        "    onmousedown=\"mdown_handle(event)\"\n",
        "    onmousemove=\"mmove_handle(event)\"\n",
        "    onmouseup=\"mup_handle(event)\">\n",
        "</canvas>\n",
        "\n",
        "<canvas id=\"slider\" width=40 height=250\n",
        "    onmousedown=\"mdown(event)\"\n",
        "    onmousemove=\"mmove(event)\"\n",
        "    onmouseup=\"mup(event)\"\n",
        "    style=\"position:absolute;left:700px;top:250px;width:40px;height:250px;z-index:1000;\">\n",
        "</canvas>\n",
        "\n",
        "\n",
        "<div id=\"everything\" style=\"height:600px; width:600px;\">\n",
        "  <div id=\"for_right_plot\">\n",
        "  </div>\n",
        "</div>\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "</body>\n",
        "\n",
        "<script>\n",
        "function init()\n",
        "{\n",
        "  loss_function_2d();\n",
        "  adjust_canvas();\n",
        "  loss_function_2d();\n",
        "  setInterval(adjust_canvas, 1000);\n",
        "  draw_slider();\n",
        "}\n",
        "init();\n",
        "</script>\n",
        "\n",
        "</html>\n",
        "'''\n",
        "\n",
        "params = []\n",
        "X = []\n",
        "b_w = ipywidgets.FloatSlider(description='bandwidth', min=0.01, max=5.0, value=2.0)\n",
        "ker_type = ipywidgets.Dropdown(\n",
        "  options=['gaussian', 'tophat', 'epanechnikov', 'exponential','linear','cosine'],\n",
        "  value='gaussian',\n",
        "  description='Kernel:',\n",
        "  disabled=False)\n",
        "\n",
        "def set_slider(x):\n",
        "  bandwidths = np.linspace(b_w.min, b_w.max, 100)\n",
        "  loo = LeaveOneOut()\n",
        "  grid = GridSearchCV(KernelDensity(kernel=ker_type.value), {'bandwidth': bandwidths}, cv=loo)\n",
        "  grid.fit(np.array(X)[:, None]);\n",
        "  b_w.value = grid.best_params_['bandwidth']\n",
        "\n",
        "def set_slider2(x):\n",
        "  ker = {'gaussian':'gaussian', 'cosine':'cosine',\n",
        "         'tophat':'box', 'epanechnikov':'epa',\n",
        "         'exponential':'exponential', 'linear':'tri'}\n",
        "  kde = FFTKDE(bw='ISJ', kernel=ker[ker_type.value])\n",
        "  kde.fit(X)(None)\n",
        "  b_w.value = kde.bw\n",
        "\n",
        "def set_slider1(x):\n",
        "  #std = np.sqrt(np.var(X, axis=0))\n",
        "  #silverman = ((4/(3* len(np.array(X)[:, None])))*std**5)**(1/5)\n",
        "  #b_w.value = silverman\n",
        "\n",
        "  ker = {'gaussian':'gaussian', 'cosine':'cosine',\n",
        "         'tophat':'box', 'epanechnikov':'epa',\n",
        "         'exponential':'exponential', 'linear':'tri'}\n",
        "  kde = FFTKDE(bw='silverman', kernel=ker[ker_type.value])\n",
        "  kde.fit(X)(None)\n",
        "  b_w.value = kde.bw\n",
        "\n",
        "def plot_pdf(plot_separate, k_d = None):\n",
        "  #return\n",
        "  global params\n",
        "  global X\n",
        "  if not params or not X:\n",
        "    return\n",
        "\n",
        "  pi1, pi2, pi3, mu1, sig1, mu2, sig2, mu3, sig3 = params\n",
        "  x = np.linspace(np.min(X), np.max(X), 1001)\n",
        "  fig = plt.figure(figsize=(10, 8))\n",
        "  P_sum = np.zeros(x.shape)\n",
        "  for mu, sig, c, pi, i in [[mu1, sig1, 'r', pi1, 1], [mu2, sig2, 'g', pi2, 2], [mu3, sig3, 'b', pi3, 3]]:\n",
        "    P = scipy.stats.norm.pdf(x, mu, sig)\n",
        "    P_sum += P * pi\n",
        "    if plot_separate:\n",
        "      plt.plot(x, P, c, linewidth=2.0, label=\"{}\".format(i), alpha=np.clip(pi, 0.0, 1.0))\n",
        "\n",
        "  plt.plot(x, P_sum, 'k', linewidth=3.0, label=\"mixture\")\n",
        "  plt.plot(np.array(X), np.full_like(np.array(X), 0.0), '|k', markeredgewidth=1)\n",
        "  plt.title('True pdf / pdf estimate')\n",
        "  plt.xlabel('x', fontsize=18)\n",
        "  plt.ylabel('pdf', fontsize=18)\n",
        "  plt.legend()\n",
        "  #plt.show()\n",
        "\n",
        "\n",
        "def ker_plot(b_w, k_t):\n",
        "  global params\n",
        "  global X\n",
        "  if not params or not X:\n",
        "    return\n",
        "  kde = KernelDensity(bandwidth=b_w, kernel=k_t)\n",
        "  kde.fit(np.array(X)[:, None])\n",
        "  x_d = np.linspace(np.min(X), np.max(X), 1001)\n",
        "  logprob = kde.score_samples(x_d[:, None])\n",
        "  plot_pdf(False)\n",
        "  plt.fill_between(x_d, np.exp(logprob), alpha=0.5, color='r')\n",
        "\n",
        "def redraw(coefs, mu, sigma, points):\n",
        "  global X\n",
        "  global params\n",
        "  X = points\n",
        "  params = [coefs[0], coefs[1], coefs[2],\n",
        "            mu[0], sigma[0],\n",
        "            mu[1], sigma[1],\n",
        "            mu[2], sigma[2]]\n",
        "  #plot_pdf(False)\n",
        "  b_w.value += 0.0001\n",
        "\n",
        "\n",
        "tb = widgets.TabBar(['mix distribution', 'find KDE'], location='top')\n",
        "with tb.output_to(0):\n",
        "  display(IPython.display.HTML(main_str))\n",
        "  output.register_callback('notebook.redraw', redraw)\n",
        "\n",
        "with tb.output_to(1):\n",
        "  btn = ipywidgets.Button(\n",
        "    description='Cross Validation',\n",
        "    disabled=False,\n",
        "    button_style='')\n",
        "  btn1 = ipywidgets.Button(\n",
        "    description='Silverman',\n",
        "    disabled=False,\n",
        "    button_style='')\n",
        "  btn2 = ipywidgets.Button(\n",
        "    description='ISJ',\n",
        "    disabled=False,\n",
        "    button_style='')\n",
        "  out = ipywidgets.interactive_output(ker_plot, {\"b_w\": b_w, \"k_t\": ker_type})\n",
        "  display(ipywidgets.HBox([ker_type, ipywidgets.VBox([b_w, ipywidgets.HBox([btn1, btn2, btn])])]), out)\n",
        "  btn.on_click(set_slider)\n",
        "  btn1.on_click(set_slider1)\n",
        "  btn2.on_click(set_slider2)\n",
        "  b_w.value += 0.0001\n",
        "\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<link rel=stylesheet type=text/css href='/nbextensions/google.colab/tabbar.css'></link>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": [
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='/nbextensions/google.colab/tabbar_main.min.js'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": [
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div id=\"id3\"></div>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": [
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"0f0060fe-f7ad-11ea-9b9e-0242ac1c0002\"] = colab_lib.createTabBar({\"location\": \"top\", \"elementId\": \"id3\", \"tabNames\": [\"mix distribution\", \"find KDE\"], \"initialSelection\": 0, \"contentBorder\": [\"0px\"], \"contentHeight\": [\"initial\"], \"borderColor\": [\"#a7a7a7\"]});\n",
              "//# sourceURL=js_8ba1890bcf"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": [
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"0f00b07c-f7ad-11ea-9b9e-0242ac1c0002\"] = window[\"id3\"].setSelectedTabIndex(0);\n",
              "//# sourceURL=js_4086314917"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": [
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"0f01ab44-f7ad-11ea-9b9e-0242ac1c0002\"] = google.colab.output.getActiveOutputArea();\n",
              "//# sourceURL=js_82725e5288"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": [
              "id3_content_0",
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"0f01e5f0-f7ad-11ea-9b9e-0242ac1c0002\"] = document.querySelector(\"#id3_content_0\");\n",
              "//# sourceURL=js_4023db1f0c"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": [
              "id3_content_0",
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"0f021eda-f7ad-11ea-9b9e-0242ac1c0002\"] = google.colab.output.setActiveOutputArea(window[\"0f01e5f0-f7ad-11ea-9b9e-0242ac1c0002\"]);\n",
              "//# sourceURL=js_328a992244"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": [
              "id3_content_0",
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"0f025f30-f7ad-11ea-9b9e-0242ac1c0002\"] = window[\"id3\"].setSelectedTabIndex(0);\n",
              "//# sourceURL=js_1b097e43bb"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": [
              "id3_content_0",
              "outputarea_id3"
            ]
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "<html>\n",
              "\n",
              "<head>\n",
              "  <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script> \n",
              "\n",
              "  <script type=\"application/javascript\">\n",
              "    var xs = [];\n",
              "    var ys = [];\n",
              "    var x_min = -5.0;\n",
              "    var y_min =  0.0;\n",
              "    var x_max = +5.0;\n",
              "    var y_max = +0.8;\n",
              "    for (var x = x_min; x <= x_max; x += 0.01)\n",
              "      xs.push(x);\n",
              "    for (var y = y_min; y <= y_max; y += 0.1)\n",
              "      ys.push(y);\n",
              "    var colors = ['blue', 'green', 'red'];\n",
              "    var coefs = [1.0/3.0, 1.0/3.0, 1.0/3.0];\n",
              "    var rand_pts = [];\n",
              "\n",
              "   function random_point(mu, sigma) {\n",
              "     var z = Math.sqrt(-2.0 * Math.log(Math.random())) * Math.cos(2.0 * Math.PI * Math.random());\n",
              "     return z * sigma + mu;\n",
              "   }\n",
              "\n",
              "    function loss_function_2d() {\n",
              "      var canvas = document.getElementById(\"paint\");\n",
              "      var w = canvas.width;\n",
              "      var h = canvas.height;\n",
              "\n",
              "      //var size = adjust_canvas();\n",
              "      //var w = size[0];\n",
              "      //var h = size[1];\n",
              "\n",
              "      mu = [];\n",
              "      sigma = [];\n",
              "      C = Math.sqrt(2 * Math.PI);\n",
              "      for (var i = 0; i < pts.length; ++i) {\n",
              "          var x = pts[i][0] / w * (x_max - x_min) + x_min;\n",
              "        var y = (1.0 - pts[i][1] / h) * (y_max - y_min) + y_min;\n",
              "          mu.push(x);\n",
              "          sigma.push(1.0 / (y * C));\n",
              "      }\n",
              "\n",
              "      data = [];\n",
              "      for (var trace_idx = 0; trace_idx < pts.length; ++trace_idx) {\n",
              "          var trace = [];\n",
              "          for (var i = 0; i < xs.length; ++i) {\n",
              "              var delta = (xs[i] - mu[trace_idx]) / sigma[trace_idx]; \n",
              "              trace.push(Math.exp(-delta*delta / 2.0) / sigma[trace_idx] / C);\n",
              "          }\n",
              "          data.push({\n",
              "            x: xs,\n",
              "            y: trace,\n",
              "            showscale: false, \n",
              "            opacity: coefs[trace_idx], \n",
              "            type: 'scatter',\n",
              "            mode: 'line',\n",
              "            name: 'gaussian ' + trace_idx,\n",
              "            line: {\n",
              "              width: 2,\n",
              "              color: colors[trace_idx]\n",
              "            },\n",
              "          });\n",
              "      }\n",
              "\n",
              "      var sum_trace = [];\n",
              "      for (var i = 0; i < xs.length; ++i) {\n",
              "          var sum = 0.0;\n",
              "          for (var trace_idx = 0; trace_idx < pts.length; ++trace_idx) {\n",
              "              var delta = (xs[i] - mu[trace_idx]) / sigma[trace_idx]; \n",
              "              sum += coefs[trace_idx] * Math.exp(-delta*delta / 2.0) / sigma[trace_idx] / C;\n",
              "          }\n",
              "          sum_trace.push(sum);\n",
              "      }\n",
              "      data.push({\n",
              "            x: xs,\n",
              "            y: sum_trace,\n",
              "            showscale: false, \n",
              "            opacity: coefs[trace_idx], \n",
              "            type: 'scatter',\n",
              "            mode: 'line',\n",
              "            name: 'sum',\n",
              "            line: {\n",
              "              width: 2,\n",
              "              color: 'black'\n",
              "            },\n",
              "          });\n",
              "\n",
              "      var N_points = 200;\n",
              "      rand_pts = [];\n",
              "      var ys = [];\n",
              "      for (var i = 0; i < N_points; ++i) {\n",
              "        active_gaussian = 0;\n",
              "        var rnd = Math.random();\n",
              "        if (rnd > coefs[0])\n",
              "            active_gaussian = 1;\n",
              "        if (rnd > coefs[0] + coefs[1])\n",
              "            active_gaussian = 2;\n",
              "        //active_gaussian = Math.floor(Math.random() * Math.floor(3));\n",
              "        rand_pts.push(random_point(mu[active_gaussian], sigma[active_gaussian]));\n",
              "        ys.push(0.0);\n",
              "      }\n",
              "      data.push({\n",
              "            x: rand_pts,\n",
              "            y: ys,\n",
              "            showscale: false, \n",
              "            opacity: 1.0, \n",
              "            type: 'scatter',\n",
              "            mode: 'markers',\n",
              "            name: 'random datapoints',\n",
              "            marker: {\n",
              "              symbol: 'line-ns',\n",
              "              size: 20,\n",
              "              line :{\n",
              "                width: 1,\n",
              "                color: 'black'\n",
              "              }\n",
              "            }\n",
              "          });\n",
              "\n",
              "      var cell_for_plot = document.getElementById(\"for_right_plot\");\n",
              "      var layout = {\n",
              "          //title: 'Error Function',\n",
              "          xaxis: {'range': [x_min, x_max], 'domain': [0.0, 1.0], 'fixedrange': true},\n",
              "          yaxis: {'range': [y_min, y_max], 'domain': [0.0, 1.0], 'fixedrange': true},\n",
              "          width: 800,\n",
              "          height: 500,\n",
              "          autosize: false,\n",
              "          showlegend: true,\n",
              "          margin: {\n",
              "            l: 50,\n",
              "            r: 50,\n",
              "            b: 50,\n",
              "            t: 50\n",
              "          }\n",
              "        };\n",
              "      Plotly.newPlot(cell_for_plot, data, layout);\n",
              "    }\n",
              "\n",
              "    var pts = [[100, 300], [300, 300], [500, 300]];\n",
              "    var active_idx = -1;\n",
              "\n",
              "    function mdown_handle(event) {\n",
              "      //console.log('down');\n",
              "      event.stopPropagation();\n",
              "      x = event.offsetX;\n",
              "      y = event.offsetY;\n",
              "      for (var i = 0; i < pts.length; ++i)\n",
              "        if ((x - pts[i][0])*(x - pts[i][0]) + (y - pts[i][1])*(y - pts[i][1]) < 500)\n",
              "            active_idx = i;\n",
              "      //console.log('ACTIVE', active_idx);\n",
              "    }\n",
              "\n",
              "    function mmove_handle(event) {\n",
              "      event.stopPropagation();\n",
              "      //console.log('move');\n",
              "      if (active_idx < 0)\n",
              "          return;\n",
              "      pts[active_idx] = [event.offsetX, event.offsetY];\n",
              "      loss_function_2d();\n",
              "    }\n",
              "\n",
              "    function mup_handle(event) {\n",
              "      active_idx = -1;\n",
              "    }\n",
              "\n",
              "    async function call_once() {\n",
              "      const result = await google.colab.kernel.invokeFunction('notebook.redraw', [coefs, mu, sigma, rand_pts], {});\n",
              "      //const text = result.data['application/json'];\n",
              "    }\n",
              "    var old_state = false;\n",
              "    function adjust_canvas() {\n",
              "      var plt_div = document.getElementById('for_right_plot');\n",
              "      var el = plt_div.getElementsByClassName('xy')[0];\n",
              "      if (!el)\n",
              "          return [600, 600];\n",
              "      var rect = el.getBoundingClientRect();\n",
              "      var canvas = document.getElementById(\"paint\");\n",
              "      //console.log(rect);\n",
              "      canvas.style.cssText = \"position:absolute; top:\" + parseInt(rect.top)\n",
              "                          + \"px; left: \" + parseInt(rect.left)\n",
              "                          + \"px; width:\" + parseInt(rect.width)\n",
              "                          + \"px; height:\" + parseInt(rect.height)\n",
              "                          + \"px; z-index:1000;\";\n",
              "      canvas.width = rect.width;\n",
              "      canvas.height = rect.height;\n",
              "      var ctx = canvas.getContext('2d');\n",
              "      ctx.clearRect(0, 0, canvas.width, canvas.height);\n",
              "       \n",
              "      if ((canvas.offsetParent === null) != old_state)\n",
              "        call_once();\n",
              "      old_state = (canvas.offsetParent === null);\n",
              "\n",
              "      //loss_function_2d();\n",
              "      return [canvas.width, canvas.height];\n",
              "    }\n",
              "\n",
              "    function draw_slider() {\n",
              "        var canvas = document.getElementById(\"slider\");\n",
              "        var ctx = canvas.getContext('2d');\n",
              "        var h = canvas.height;\n",
              "        var w = canvas.width;\n",
              "        var cur_start = 0;\n",
              "        ctx.clearRect(0, 0, canvas.width, canvas.height);\n",
              "        for (var i = 0; i < pts.length; ++i) {\n",
              "            ctx.fillStyle = colors[i];\n",
              "            ctx.fillRect(0, cur_start, w, h*coefs[i]);\n",
              "            cur_start += h*coefs[i];\n",
              "        }\n",
              "        \n",
              "    }\n",
              "\n",
              "    var active_coef = -1;\n",
              "    function mdown(event) {\n",
              "    //console.log('ddd');\n",
              "      event.stopPropagation();\n",
              "      x = event.offsetX;\n",
              "      y = event.offsetY;\n",
              "      var canvas = document.getElementById(\"slider\");\n",
              "      var h = canvas.height;\n",
              "      var H = 0;\n",
              "      for (var i = 0; i < coefs.length - 1; ++i) {\n",
              "        H += coefs[i] * h;\n",
              "        if (y > H - 10 && y < H +1)\n",
              "            active_coef = i;\n",
              "      }\n",
              "      //console.log(active_coef, coefs);\n",
              "    }\n",
              "\n",
              "    function mmove(event) { // for double-slider only\n",
              "      event.stopPropagation();\n",
              "      if (active_coef < 0)\n",
              "        return;\n",
              "      x = event.offsetX;\n",
              "      y = event.offsetY;\n",
              "      var canvas = document.getElementById(\"slider\");\n",
              "      var h = canvas.height;\n",
              "      var new_sum = y / h;\n",
              "      if (active_coef == 0) {\n",
              "        if (coefs[0] + coefs[1] < new_sum)\n",
              "            coefs[1] = 0.0;\n",
              "        else\n",
              "            coefs[1] = coefs[0] + coefs[1] - new_sum;\n",
              "        coefs[0] = new_sum;\n",
              "        coefs[2] = 1.0 - coefs[0] - coefs[1];\n",
              "      }\n",
              "      if (active_coef == 1) {\n",
              "        if (coefs[0] > new_sum)\n",
              "            coefs[0] = new_sum;\n",
              "        coefs[1] = new_sum - coefs[0];\n",
              "        coefs[2] = 1.0 - coefs[0] - coefs[1];\n",
              "      }\n",
              "      draw_slider();\n",
              "      loss_function_2d();\n",
              "    }\n",
              "\n",
              "    function mup(event) {\n",
              "      active_coef = -1;\n",
              "    }\n",
              "\n",
              "\n",
              "  </script>\n",
              "</head>\n",
              "\n",
              "<body>\n",
              "\n",
              "<canvas id=\"paint\" width=600 height=600\n",
              "    onmousedown=\"mdown_handle(event)\"\n",
              "    onmousemove=\"mmove_handle(event)\"\n",
              "    onmouseup=\"mup_handle(event)\">\n",
              "</canvas>\n",
              "\n",
              "<canvas id=\"slider\" width=40 height=250\n",
              "    onmousedown=\"mdown(event)\"\n",
              "    onmousemove=\"mmove(event)\"\n",
              "    onmouseup=\"mup(event)\"\n",
              "    style=\"position:absolute;left:700px;top:250px;width:40px;height:250px;z-index:1000;\">\n",
              "</canvas>\n",
              "\n",
              "\n",
              "<div id=\"everything\" style=\"height:600px; width:600px;\">\n",
              "  <div id=\"for_right_plot\">\n",
              "  </div>\n",
              "</div>\n",
              "\n",
              "\n",
              "\n",
              "\n",
              "</body>\n",
              "\n",
              "<script>\n",
              "function init()\n",
              "{\n",
              "  loss_function_2d();\n",
              "  adjust_canvas();\n",
              "  loss_function_2d();\n",
              "  setInterval(adjust_canvas, 1000);\n",
              "  draw_slider();\n",
              "}\n",
              "init();\n",
              "</script>\n",
              "\n",
              "</html>\n"
            ],
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              "<IPython.core.display.HTML object>"
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              "window[\"0f054eca-f7ad-11ea-9b9e-0242ac1c0002\"] = window[\"id3\"].setSelectedTabIndex(1);\n",
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              "<IPython.core.display.Javascript object>"
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              "model_id": "20be466070cd43319544a4db1437d490",
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              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(Dropdown(description='Kernel:', options=('gaussian', 'tophat', 'epanechnikov', 'exponential', '…"
            ]
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              "Output()"
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W3HS22uyAKfr"
      },
      "source": [
        "#KDE in 2D (kernel, bandwidth, sample, metric)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xPOkOFQVo_C-"
      },
      "source": [
        "Use the following demo to get the intuition on\n",
        "* How two-dimensional KDE works\n",
        "* How bandwidth influences the result\n",
        "* How choice of the kernel influences the result\n",
        "* How metric influences the result"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "npHUVDt94MAz"
      },
      "source": [
        "from sklearn.neighbors import KernelDensity\n",
        "# instantiate and fit the KDE model\n",
        "kde = KernelDensity()\n",
        "\n",
        "def fit_distribution(X, bandwidth, ker_name, metric_name):\n",
        "  params = {'bandwidth': bandwidth, 'kernel': ker_name, 'metric': metric_name}\n",
        "  kde.set_params(**params)\n",
        "  kde.fit(X)\n",
        "\n",
        "def evaluate_distribution(X):\n",
        "  logprob = kde.score_samples(X)\n",
        "  return np.exp(logprob)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R_BZreRX4P8t",
        "cellView": "form",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 617
        },
        "outputId": "b0b17250-e6c6-48d2-f8e1-c8703bd905ff"
      },
      "source": [
        "#@title Interactive 2D KDE\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.colors import ListedColormap\n",
        "from matplotlib import cm\n",
        "import seaborn as sns\n",
        "\n",
        "def plot_clusters(x_, y_, z_):\n",
        "  fig = plt.figure(figsize=(10,10))\n",
        "  ax = fig.gca()\n",
        "  #ax = sns.kdeplot(X[:,0], X[:,1], cmap=\"Blues\", shade=True, shade_lowest=False)\n",
        "  sns.set()\n",
        "  ax.contourf(x_, y_, z_, alpha=0.5, cmap=\"Blues\")\n",
        "  ax.tick_params(axis=\"y\",direction=\"in\", pad=-60)\n",
        "  ax.tick_params(axis=\"x\",direction=\"in\", pad=-30)\n",
        "  ax.set_xticks(np.arange(-.75, 1, .25))\n",
        "  ax.set_yticks(np.arange(-.75, 1, .25))\n",
        "  ax.set_xlim([-1, 1])\n",
        "  ax.set_ylim([-1, 1])\n",
        "\n",
        "  plt.close(fig)\n",
        "  return fig\n",
        "\n",
        "import base64\n",
        "import io\n",
        "\n",
        "def figure_to_base64(fig):\n",
        "  buf = io.BytesIO()\n",
        "  fig.savefig(buf, format='png', bbox_inches='tight', pad_inches=0);\n",
        "  image_base64 = base64.b64encode(buf.getvalue()).decode('utf-8').replace('\\n', '')\n",
        "  buf.close()\n",
        "  return image_base64\n",
        "\n",
        "\n",
        "\n",
        "import json\n",
        "from IPython.display import display, clear_output\n",
        "\n",
        "def invoke(pts, n, ker_name, metric_name):\n",
        "  data = np.array(pts).reshape((-1, 2))\n",
        "  X = data / 300.0 - 1.0\n",
        "  X[:, 1] *= -1.0\n",
        "  fit_distribution(X, float(n)/1000.0, ker_name, metric_name)\n",
        "  x_ = np.linspace(-1.0, +1.0, num=300)\n",
        "  y_ = np.linspace(-1.0, +1.0, num=300)\n",
        "  xx, yy = np.meshgrid(x_, y_)\n",
        "  x_vec = np.transpose(np.vstack([xx.ravel(), yy.ravel()]))\n",
        "  G  = evaluate_distribution(x_vec).reshape((x_.shape[0],y_.shape[0]))\n",
        "  figr = plot_clusters(x_, y_, G)\n",
        "  image_base64 = figure_to_base64(figr)\n",
        "\n",
        "  return IPython.display.JSON({'image': image_base64,\n",
        "                               'g_x': x_.tolist(), 'g_y': y_.tolist(), 'g_z': G.tolist(),\n",
        "                               's_x': X[:, 0].tolist(), 's_y': X[:, 1].tolist(), 's_z': [0]*len(X)})\n",
        "\n",
        "\n",
        "import IPython\n",
        "from google.colab import output\n",
        "\n",
        "main_str = '''\n",
        "  <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script>\n",
        "  <script type=\"application/javascript\">\n",
        "\n",
        "    var active_pt = null;\n",
        "    var all_pts = [];\n",
        "    var classAbtn = [650, 100];\n",
        "    var classBbtn = [650, 200];\n",
        "    var ptR = 10.0;\n",
        "    var params = null;\n",
        "    var debug_txt = \"\";\n",
        "    var bg_image = new Image();\n",
        "\n",
        "    function is_close(pt1, pt2) {\n",
        "      return   (pt1[0] - pt2[0])*(pt1[0] - pt2[0])\n",
        "            +  (pt1[1] - pt2[1])*(pt1[1] - pt2[1])\n",
        "            <= ptR*ptR;\n",
        "    }\n",
        "\n",
        "    function circ(ctx, pos) {\n",
        "      ctx.beginPath();\n",
        "      ctx.arc(pos[0], pos[1], ptR, 0.0, 2.0 * Math.PI, 0);\n",
        "      ctx.fillStyle = 'rgba(255, 128, 0, 0.5)';\n",
        "      ctx.fill();\n",
        "    }\n",
        "\n",
        "\n",
        "    function draw() {\n",
        "      var canvas = document.getElementById('canvas');\n",
        "      if (canvas.getContext) {\n",
        "        var ctx = canvas.getContext('2d');\n",
        "\n",
        "        ctx.clearRect(0, 0, canvas.width, canvas.height); // cleanup before start\n",
        "        ctx.drawImage(bg_image, 0, 0, 600, 600);\n",
        "        ctx.strokeRect(0, 0, 600, 600); // field\n",
        "\n",
        "        ctx.font = '20px serif';\n",
        "        ctx.fillStyle = 'black';\n",
        "        ctx.fillText(debug_txt, 200, 200);\n",
        "\n",
        "        if (active_pt) {\n",
        "          circ(ctx, [active_pt[0], active_pt[1]]);\n",
        "        }\n",
        "        all_pts.forEach(function (item, index) {\n",
        "          circ(ctx, [item[0], item[1]]);\n",
        "        });\n",
        "\n",
        "      }\n",
        "    }\n",
        "\n",
        "    var timer\n",
        "\n",
        "    function get_state() {\n",
        "      var rates = document.getElementsByName('rate');\n",
        "      for(var i = 0; i < rates.length; i++)\n",
        "        if(rates[i].checked)\n",
        "          return rates[i].value;\n",
        "      return \"none\";\n",
        "    }\n",
        "\n",
        "\n",
        "    function mdown_handle(evt) {\n",
        "      evt.stopPropagation();\n",
        "      x = evt.offsetX;\n",
        "      y = evt.offsetY;\n",
        "      state = get_state();\n",
        "      if (state == \"add\") {\n",
        "        if (x < 600)\n",
        "            all_pts.push([x, y]);\n",
        "        return;\n",
        "      }\n",
        "\n",
        "      idx = -1;\n",
        "      all_pts.forEach(function (item, index) {\n",
        "        if (is_close([x,y], [item[0], item[1]])) {\n",
        "          idx = index;\n",
        "        }\n",
        "      });\n",
        "      if (idx <= -1)\n",
        "          return;\n",
        "      if (state == \"move\") {\n",
        "        active_pt = all_pts[idx];\n",
        "        all_pts.splice(idx, 1);\n",
        "      }\n",
        "      if (state == \"del\")\n",
        "          all_pts.splice(idx, 1);\n",
        "    }\n",
        "\n",
        "    function mmove_handle(evt) {\n",
        "      evt.stopPropagation();\n",
        "      if (get_state() != \"move\")\n",
        "          return;\n",
        "      x = evt.offsetX;\n",
        "      y = evt.offsetY;\n",
        "      if (active_pt) {\n",
        "        active_pt[0] = x;\n",
        "        active_pt[1] = y;\n",
        "      }\n",
        "    }\n",
        "\n",
        "    function mup_handle(evt) {\n",
        "      evt.stopPropagation();\n",
        "      x = evt.offsetX;\n",
        "      y = evt.offsetY;\n",
        "      if (x >= 600) {\n",
        "        active_pt = null;\n",
        "      }\n",
        "      if (active_pt) {\n",
        "        all_pts.push(active_pt);\n",
        "        active_pt = null;\n",
        "      }\n",
        "    }\n",
        "\n",
        "    function clear_field() {\n",
        "      active_pt = null;\n",
        "      all_pts = [];\n",
        "    }\n",
        "\n",
        "\n",
        "   function plot_3d(g_x, g_y, g_z)\n",
        "   {\n",
        "     cell_for_plot = document.getElementById('for_plotly_plot');\n",
        "     //Plotly.deleteTraces(cell_for_plot, [0, 1]);\n",
        "     var data = [{\n",
        "           x: g_x,\n",
        "           y: g_y,\n",
        "           z: g_z,\n",
        "           type: 'surface',\n",
        "           opacity: 0.9,\n",
        "           showscale: false,\n",
        "           colorscale: \"Viridis\"\n",
        "        }];\n",
        "\n",
        "     var layout = {\n",
        "          title: 'pdf estimate',\n",
        "          autosize: false,\n",
        "          width: 600,\n",
        "          height: 600,\n",
        "          showlegend: false,\n",
        "          scene: {\n",
        "            camera: {\n",
        "              up: {x: 0, y: 1, z: 0},\n",
        "              center: {x: 0, y: 0, z: 0},\n",
        "              eye: {x: 0.0, y: -1.0, z: 1.4}\n",
        "            }\n",
        "          }\n",
        "        };\n",
        "     Plotly.newPlot(cell_for_plot, data, layout);\n",
        "   }\n",
        "\n",
        "   function plot_scatter(s_x, s_y, s_z)\n",
        "   {\n",
        "\n",
        "     cell_for_plot = document.getElementById('for_plotly_plot');\n",
        "     var data = [{\n",
        "           x: s_x,\n",
        "           y: s_y,\n",
        "           z: s_z,\n",
        "           type: 'scatter3d',\n",
        "           mode: 'markers',\n",
        "           marker: {\n",
        "             size: 4,\n",
        "             colorscale: \"Viridis\",\n",
        "             line: {\n",
        "               width: 2,\n",
        "               color: 'rgba(0, 0, 0, 0.5)'\n",
        "             }\n",
        "           }\n",
        "        }];\n",
        "    Plotly.plot(cell_for_plot, data, {});\n",
        "   }\n",
        "\n",
        "\n",
        "    var cur_depth = 100;\n",
        "\n",
        "    async function calculate() {\n",
        "      if (!all_pts)\n",
        "        return;\n",
        "      var merged = [].concat.apply([], all_pts);\n",
        "      var e = document.getElementById(\"select_kernel\");\n",
        "      var ker_name = e.options[e.selectedIndex].value;\n",
        "      var e1 = document.getElementById(\"select_metric\");\n",
        "      var metric_name = e1.options[e1.selectedIndex].value;\n",
        "      const result = await google.colab.kernel.invokeFunction('notebook.InvSVM', [merged, cur_depth, ker_name, metric_name], {});\n",
        "      params = result.data['application/json'];\n",
        "\n",
        "      bg_image.src = 'data:image/  png;base64,' + params.image;\n",
        "      cell_for_plot = document.getElementById('for_plotly_plot');\n",
        "\n",
        "      plot_3d(params.g_x, params.g_y, params.g_z);\n",
        "      plot_scatter(params.s_x, params.s_y, params.s_z);\n",
        "\n",
        "    }\n",
        "\n",
        "   function h_change(x) {\n",
        "    el = document.getElementById(\"slider_val\");\n",
        "    cur_depth = x;\n",
        "    el.innerHTML = x;\n",
        "  }\n",
        "\n",
        " </script>\n",
        "\n",
        "<div id=\"everything\" style=\"height:600px;\">\n",
        "<div id=\"for_plotly_plot\" style=\"position:absolute; top:0px; left:0px; height:600px; width:600px;\">\n",
        "</div>\n",
        "<div id=\"custom_controls\" style=\"position:absolute; top:0px; left:600px;\">\n",
        "  <canvas id=\"canvas\" width=\"800\" height=\"600\"\n",
        "    onmousedown=\"mdown_handle(event)\"\n",
        "    onmousemove=\"mmove_handle(event)\"\n",
        "    onmouseup=\"mup_handle(event)\"></canvas>\n",
        "  <div style=\"position:absolute; top:200px; left:625px;\">\n",
        "   <div style=\"border-style: solid;\">\n",
        "    <input type=\"radio\" id=\"r1\" name=\"rate\" value=\"add\" checked=\"checked\"> Add data point\n",
        "    <br>\n",
        "    <input type=\"radio\" id=\"r2\" name=\"rate\" value=\"move\"> Move data point\n",
        "    <br>\n",
        "    <input type=\"radio\" id=\"r3\" name=\"rate\" value=\"del\"> Delete data point\n",
        "    <br>\n",
        "    <button type=\"button\" onclick=\"clear_field();\">\n",
        "      Clear\n",
        "    </button>\n",
        "   </div>\n",
        "   <br><br>Bandwidth x 1000:<br>\n",
        "    <input type=\"range\" min=\"1\" max=\"200\" value=\"100\" oninput=\"h_change(this.value)\">\n",
        "    <br><div id=\"slider_val\">100</div>\n",
        "   <br>Kernel:<br>\n",
        "   <select id=\"select_kernel\">\n",
        "       <option value=\"gaussian\">gaussian</option>\n",
        "       <option value=\"tophat\">tophat</option>\n",
        "       <option value=\"epanechnikov\">epanechnikov</option>\n",
        "       <option value=\"exponential\">exponential</option>\n",
        "       <option value=\"linear\">linear</option>\n",
        "       <option value=\"cosine\">cosine</option>\n",
        "   </select>\n",
        "   <br>\n",
        "   Metric:\n",
        "   <br>\n",
        "   <select id=\"select_metric\">\n",
        "       <option value=\"euclidean\">euclidean</option>\n",
        "       <option value=\"manhattan\">manhattan</option>\n",
        "       <option value=\"infinity\">infinity</option>\n",
        "   </select>\n",
        "   <br><br>\n",
        "    <button type=\"button\" onclick=\"calculate();\">\n",
        "      KDE\n",
        "    </button>\n",
        "  </div>\n",
        "</div>\n",
        "<div>\n",
        "\n",
        "<script>\n",
        "function init()\n",
        "{\n",
        "  timer = setInterval(draw, 10);\n",
        "}\n",
        "\n",
        "init();\n",
        "</script>\n",
        "'''\n",
        "\n",
        "display(IPython.display.HTML(main_str))\n",
        "output.register_callback('notebook.InvSVM', invoke)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "  <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script> \n",
              "  <script type=\"application/javascript\">\n",
              "  \n",
              "    var active_pt = null;\n",
              "    var all_pts = [];\n",
              "    var classAbtn = [650, 100];\n",
              "    var classBbtn = [650, 200];\n",
              "    var ptR = 10.0;\n",
              "    var params = null;\n",
              "    var debug_txt = \"\";\n",
              "    var bg_image = new Image();\n",
              "\n",
              "    function is_close(pt1, pt2) {\n",
              "      return   (pt1[0] - pt2[0])*(pt1[0] - pt2[0])\n",
              "            +  (pt1[1] - pt2[1])*(pt1[1] - pt2[1])\n",
              "            <= ptR*ptR;\n",
              "    }\n",
              "  \n",
              "    function circ(ctx, pos) {\n",
              "      ctx.beginPath();\n",
              "      ctx.arc(pos[0], pos[1], ptR, 0.0, 2.0 * Math.PI, 0);\n",
              "      ctx.fillStyle = 'rgba(255, 128, 0, 0.5)';\n",
              "      ctx.fill();\n",
              "    }\n",
              "    \n",
              "    \n",
              "    function draw() {\n",
              "      var canvas = document.getElementById('canvas');\n",
              "      if (canvas.getContext) {\n",
              "        var ctx = canvas.getContext('2d');\n",
              "        \n",
              "        ctx.clearRect(0, 0, canvas.width, canvas.height); // cleanup before start\n",
              "        ctx.drawImage(bg_image, 0, 0, 600, 600);\n",
              "        ctx.strokeRect(0, 0, 600, 600); // field\n",
              "        \n",
              "        ctx.font = '20px serif';\n",
              "        ctx.fillStyle = 'black';\n",
              "        ctx.fillText(debug_txt, 200, 200);\n",
              "        \n",
              "        if (active_pt) {\n",
              "          circ(ctx, [active_pt[0], active_pt[1]]);\n",
              "        }\n",
              "        all_pts.forEach(function (item, index) {\n",
              "          circ(ctx, [item[0], item[1]]);\n",
              "        });\n",
              "\n",
              "      }\n",
              "    }\n",
              "    \n",
              "    var timer\n",
              "\n",
              "    function get_state() {\n",
              "      var rates = document.getElementsByName('rate');\n",
              "      for(var i = 0; i < rates.length; i++)\n",
              "        if(rates[i].checked)\n",
              "          return rates[i].value;\n",
              "      return \"none\";\n",
              "    }\n",
              "\n",
              "    \n",
              "    function mdown_handle(evt) {\n",
              "      evt.stopPropagation();\n",
              "      x = evt.offsetX;\n",
              "      y = evt.offsetY;\n",
              "      state = get_state();\n",
              "      if (state == \"add\") {\n",
              "        if (x < 600)\n",
              "            all_pts.push([x, y]);\n",
              "        return;\n",
              "      }\n",
              "\n",
              "      idx = -1;\n",
              "      all_pts.forEach(function (item, index) {\n",
              "        if (is_close([x,y], [item[0], item[1]])) {\n",
              "          idx = index;\n",
              "        }\n",
              "      });\n",
              "      if (idx <= -1)\n",
              "          return;\n",
              "      if (state == \"move\") {\n",
              "        active_pt = all_pts[idx];\n",
              "        all_pts.splice(idx, 1);\n",
              "      }\n",
              "      if (state == \"del\")\n",
              "          all_pts.splice(idx, 1);\n",
              "    }\n",
              "    \n",
              "    function mmove_handle(evt) {\n",
              "      evt.stopPropagation();\n",
              "      if (get_state() != \"move\")\n",
              "          return;\n",
              "      x = evt.offsetX;\n",
              "      y = evt.offsetY;\n",
              "      if (active_pt) {\n",
              "        active_pt[0] = x;\n",
              "        active_pt[1] = y;\n",
              "      }\n",
              "    }\n",
              "    \n",
              "    function mup_handle(evt) {\n",
              "      evt.stopPropagation();\n",
              "      x = evt.offsetX;\n",
              "      y = evt.offsetY;\n",
              "      if (x >= 600) {\n",
              "        active_pt = null;\n",
              "      }\n",
              "      if (active_pt) {\n",
              "        all_pts.push(active_pt);\n",
              "        active_pt = null;\n",
              "      }\n",
              "    }\n",
              "    \n",
              "    function clear_field() {\n",
              "      active_pt = null;\n",
              "      all_pts = [];\n",
              "    }\n",
              "\n",
              "\n",
              "   function plot_3d(g_x, g_y, g_z)\n",
              "   {\n",
              "     cell_for_plot = document.getElementById('for_plotly_plot');\n",
              "     //Plotly.deleteTraces(cell_for_plot, [0, 1]);\n",
              "     var data = [{\n",
              "           x: g_x,\n",
              "           y: g_y,\n",
              "           z: g_z,\n",
              "           type: 'surface',\n",
              "           opacity: 0.9,\n",
              "           showscale: false,\n",
              "           colorscale: \"Viridis\"\n",
              "        }];\n",
              "  \n",
              "     var layout = {\n",
              "          title: 'pdf estimate',\n",
              "          autosize: false,\n",
              "          width: 600,\n",
              "          height: 600,\n",
              "          showlegend: false,\n",
              "          scene: {\n",
              "            camera: {\n",
              "              up: {x: 0, y: 1, z: 0},\n",
              "              center: {x: 0, y: 0, z: 0},\n",
              "              eye: {x: 0.0, y: -1.0, z: 1.4}\n",
              "            }\n",
              "          }\n",
              "        };\n",
              "     Plotly.newPlot(cell_for_plot, data, layout);\n",
              "   }\n",
              "\n",
              "   function plot_scatter(s_x, s_y, s_z)\n",
              "   {\n",
              "          \n",
              "     cell_for_plot = document.getElementById('for_plotly_plot');\n",
              "     var data = [{\n",
              "           x: s_x,\n",
              "           y: s_y,\n",
              "           z: s_z,\n",
              "           type: 'scatter3d',\n",
              "           mode: 'markers',\n",
              "           marker: {\n",
              "             size: 4,\n",
              "             colorscale: \"Viridis\",\n",
              "             line: {\n",
              "               width: 2,\n",
              "               color: 'rgba(0, 0, 0, 0.5)'\n",
              "             }\n",
              "           }\n",
              "        }];\n",
              "    Plotly.plot(cell_for_plot, data, {});\n",
              "   }\n",
              "\n",
              "\n",
              "    var cur_depth = 100;\n",
              "\n",
              "    async function calculate() {\n",
              "      if (!all_pts)\n",
              "        return;\n",
              "      var merged = [].concat.apply([], all_pts);\n",
              "      var e = document.getElementById(\"select_kernel\");\n",
              "      var ker_name = e.options[e.selectedIndex].value;\n",
              "      var e1 = document.getElementById(\"select_metric\");\n",
              "      var metric_name = e1.options[e1.selectedIndex].value;\n",
              "      const result = await google.colab.kernel.invokeFunction('notebook.InvSVM', [merged, cur_depth, ker_name, metric_name], {});\n",
              "      params = result.data['application/json'];\n",
              "            \n",
              "      bg_image.src = 'data:image/  png;base64,' + params.image;\n",
              "      cell_for_plot = document.getElementById('for_plotly_plot');\n",
              "      \n",
              "      plot_3d(params.g_x, params.g_y, params.g_z);\n",
              "      plot_scatter(params.s_x, params.s_y, params.s_z);\n",
              "      \n",
              "    }\n",
              "\n",
              "   function h_change(x) {\n",
              "    el = document.getElementById(\"slider_val\");\n",
              "    cur_depth = x;\n",
              "    el.innerHTML = x;\n",
              "  }\n",
              "\n",
              " </script>\n",
              "\n",
              "<div id=\"everything\" style=\"height:600px;\">\n",
              "<div id=\"for_plotly_plot\" style=\"position:absolute; top:0px; left:0px; height:600px; width:600px;\">\n",
              "</div>\n",
              "<div id=\"custom_controls\" style=\"position:absolute; top:0px; left:600px;\">\n",
              "  <canvas id=\"canvas\" width=\"800\" height=\"600\" \n",
              "    onmousedown=\"mdown_handle(event)\"\n",
              "    onmousemove=\"mmove_handle(event)\"\n",
              "    onmouseup=\"mup_handle(event)\"></canvas>\n",
              "  <div style=\"position:absolute; top:200px; left:625px;\">\n",
              "   <div style=\"border-style: solid;\">\n",
              "    <input type=\"radio\" id=\"r1\" name=\"rate\" value=\"add\" checked=\"checked\"> Add data point\n",
              "    <br>\n",
              "    <input type=\"radio\" id=\"r2\" name=\"rate\" value=\"move\"> Move data point\n",
              "    <br>\n",
              "    <input type=\"radio\" id=\"r3\" name=\"rate\" value=\"del\"> Delete data point\n",
              "    <br>\n",
              "    <button type=\"button\" onclick=\"clear_field();\">\n",
              "      Clear\n",
              "    </button>\n",
              "   </div>\n",
              "   <br><br>Bandwidth x 1000:<br>\n",
              "    <input type=\"range\" min=\"1\" max=\"200\" value=\"100\" oninput=\"h_change(this.value)\">\n",
              "    <br><div id=\"slider_val\">100</div>\n",
              "   <br>Kernel:<br>\n",
              "   <select id=\"select_kernel\">\n",
              "       <option value=\"gaussian\">gaussian</option>\n",
              "       <option value=\"tophat\">tophat</option>\n",
              "       <option value=\"epanechnikov\">epanechnikov</option>\n",
              "       <option value=\"exponential\">exponential</option>\n",
              "       <option value=\"linear\">linear</option>\n",
              "       <option value=\"cosine\">cosine</option>\n",
              "   </select>\n",
              "   <br>\n",
              "   Metric:\n",
              "   <br>\n",
              "   <select id=\"select_metric\">\n",
              "       <option value=\"euclidean\">euclidean</option>\n",
              "       <option value=\"manhattan\">manhattan</option>\n",
              "       <option value=\"infinity\">infinity</option>\n",
              "   </select>\n",
              "   <br><br>\n",
              "    <button type=\"button\" onclick=\"calculate();\">\n",
              "      KDE\n",
              "    </button>\n",
              "  </div>\n",
              "</div>\n",
              "<div>\n",
              "  \n",
              "<script>\n",
              "function init()\n",
              "{\n",
              "  timer = setInterval(draw, 10);\n",
              "}\n",
              "\n",
              "init();\n",
              "</script>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6RG1GigA-C6r"
      },
      "source": [
        "#1849 Broad Street cholera outbreak visualization"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jJ3VwZ_fMwvo"
      },
      "source": [
        "The Broad Street cholera outbreak was a severe outbreak of cholera that occurred in 1854 near Broad Street (now Broadwick Street) in the Soho district of the City of Westminster, London, England, and occurred during the 1846–1860 cholera pandemic happening worldwide. This outbreak, which killed 616 people, is best known for the physician John Snow's study of its causes and his hypothesis that germ-contaminated water was the source of cholera, rather than particles in the air.This discovery came to influence public health and the construction of improved sanitation facilities beginning in the mid-19th century."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4fXVGgGf-F5T"
      },
      "source": [
        "\n",
        "![](https://raw.githubusercontent.com/fbeilstein/machine_learning/master/lecture_15_kernel_density_estimation/snows.png)\n",
        "\n",
        "On 31 August 1854, after several other outbreaks had occurred elsewhere in the city, a major outbreak of cholera occurred in Soho. Snow, the physician who eventually linked the outbreak to contaminated water, later called it \"the most terrible outbreak of cholera which ever occurred in this kingdom.\"\n",
        "\n",
        "Over the next three days, 127 people on or near Broad Street died. During the next week, three quarters of the residents had fled the area. By 10 September, 500 people had died and the mortality rate was 12.8 percent in some parts of the city. By the end of the outbreak, 616 people had died.\n",
        "\n",
        "Many of the victims were taken to the Middlesex Hospital, where their treatment was superintended by Florence Nightingale (we've talked about here in statistics lecture), who briefly joined the hospital in early September in order to help with the outbreak.\n",
        "\n",
        "By talking to local residents Snow identified the source of the outbreak as the public water pump on Broad Street. Although Snow's chemical and microscope examination of a sample of the water from this Broad Street pump water did not conclusively prove its danger, his facts about the patterns of illness and death among residents in Soho persuaded the St James parish authorities to disable the well pump by removing its handle.\n",
        "\n",
        "It's worth mentioning that the germ theory was not established at this point (Louis Pasteur did not propose it until 1861). Snow did not understand the mechanism by which disease was transmitted, but the evidence led him to believe that it was NOT due to breathing foul air. Based on the pattern of illness among residents, Snow hypothesized that cholera was spread by an agent in contaminated water. He first published his theory in 1849, in an essay titled \"On the Mode of Communication of Cholera\".\n",
        "\n",
        "<br>\n",
        "\n",
        "<img src=\"https://raw.githubusercontent.com/fbeilstein/machine_learning/master/lecture_15_kernel_density_estimation/snows_cholera_map.png\" width=\"650px\" />\n",
        "\n",
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fSfWfk_LHhbe"
      },
      "source": [
        "**Preparation**\n",
        "\n",
        "Download the dataset in a `csv` format from github.\n",
        "Following code should do the job."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B1KTWDE7Hde5"
      },
      "source": [
        "# download the dataset\n",
        "!wget https://raw.githubusercontent.com/fbeilstein/machine_learning/master/datasets/pumps.csv\n",
        "!wget https://raw.githubusercontent.com/fbeilstein/machine_learning/master/datasets/deaths.csv\n",
        "!wget https://raw.githubusercontent.com/fbeilstein/machine_learning/master/datasets/cholera_map.jpg"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-OLCG1TUTkFl"
      },
      "source": [
        "The files you have downloaded contain the following information\n",
        "* `pumps.csv` -- coordinates of pumps (sources of water), contains $2$ columns, namely `x` and `y`\n",
        "* `deaths.csv` -- coordinates of households, where anyone had died from cholera. Points can repeat if few deaths in one house were spotted.\n",
        "* `cholera_map.jpg` -- map of London. Coordinates in other files correspond to pixels in this image."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FOSvo-Njcnjc"
      },
      "source": [
        "**Problem 1:**\n",
        "complete the `read_dataframe(filename)` function so that it takes name of the file and returns pandas.dataframe"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J2akMqyzaDwz"
      },
      "source": [
        "import pandas as pd\n",
        "\n",
        "def read_dataframe(filename):\n",
        "  # ENTER YOUR CODE HERE"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5pZNH6Prc0xp"
      },
      "source": [
        "Use the following code to visualize tables."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1LHzjTJGbggm",
        "cellView": "form"
      },
      "source": [
        "#@title Visualize table\n",
        "from google.colab import data_table\n",
        "from google.colab import widgets\n",
        "\n",
        "tb = widgets.TabBar(['pumps.csv', 'deaths.csv'], location='top')\n",
        "with tb.output_to(0):\n",
        "  display(data_table.DataTable(read_dataframe('pumps.csv'), include_index=False, num_rows_per_page=10))\n",
        "with tb.output_to(1):\n",
        "  display(data_table.DataTable(read_dataframe('deaths.csv'), include_index=False, num_rows_per_page=10))\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F_Hkog6_edhH"
      },
      "source": [
        "**Problem 2:**\n",
        "Visualize `cholera_map.jpg` with matplotlib.\n",
        "Complete the following function so that it plots the map.\n",
        "You can use `imread` and `imshow` functions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u0s685vlfDuL"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def plot_map(filename):\n",
        "  # ENTER YOUR CODE HERE\n",
        "\n",
        "plt.figure(figsize=(15, 15));\n",
        "plot_map('cholera_map.jpg')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "exmVtE0LjbuP"
      },
      "source": [
        "**Problem 3:**\n",
        "Visualize points from given dataframe as a scatter plot.\n",
        "Suppose that dataframe contains two columns `x` and `y`.\n",
        "Use parameter `color` to set the color of points."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "meUNoFQ0jqDj"
      },
      "source": [
        "def plot_points(dataframe, color):\n",
        "  # ENTER YOUR CODE HERE\n",
        "\n",
        "plt.figure(figsize=(15, 15));\n",
        "plot_map('cholera_map.jpg')\n",
        "plot_points(read_dataframe('deaths.csv'), 'b')\n",
        "plot_points(read_dataframe('pumps.csv'), 'r')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_nEyVZ72k1Y2"
      },
      "source": [
        "**Problem 4:**\n",
        "Visualize points from the dataframe given as a kernel density.\n",
        "For better visuals tune opacity (e.g. set `alpha=0.8`).\n",
        "You may suppose that dataframe contains columns `x` and `y`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eIVZAg-SlJ8D"
      },
      "source": [
        "import seaborn as sns\n",
        "\n",
        "def plot_kde(dataframe):\n",
        "  # ENTER YOUR CODE HERE\n",
        "\n",
        "plt.figure(figsize=(15, 15));\n",
        "plot_map('cholera_map.jpg')\n",
        "plot_kde(read_dataframe('deaths.csv'))\n",
        "plot_points(read_dataframe('pumps.csv'), 'r')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gmtCPkI9lv75",
        "cellView": "form"
      },
      "source": [
        "#@title Visualize both\n",
        "from google.colab import widgets\n",
        "\n",
        "tb = widgets.TabBar(['Scatter', 'KDE'], location='top')\n",
        "with tb.output_to(0):\n",
        "  plt.figure(figsize=(15, 15));\n",
        "  plot_map('cholera_map.jpg')\n",
        "  plot_points(read_dataframe('deaths.csv'), 'b')\n",
        "  plot_points(read_dataframe('pumps.csv'), 'r')\n",
        "  plt.ylabel('y')\n",
        "  plt.xlabel('x')\n",
        "with tb.output_to(1):\n",
        "  plt.figure(figsize=(15, 15));\n",
        "  plot_map('cholera_map.jpg')\n",
        "  plot_kde(read_dataframe('deaths.csv'))\n",
        "  plot_points(read_dataframe('pumps.csv'), 'r')\n",
        "  plt.ylabel('y')\n",
        "  plt.xlabel('x')"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}