KL Divergence

Interactive plot that shows why the KL Divergence is not symmetric.

forked from phil-pedruco's block: Plotting a bell (Gaussian) curve in d3

<!DOCTYPE html>
<html>

<head>
  <meta charset="utf-8">
  <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
  <title>KL Divergence</title>
  <meta name="description" content="">
	<script src="https://d3js.org/d3.v4.min.js"></script>
  <style type="text/css">
	body {
    font: 10px sans-serif;
  }
  .axis path,
  .axis line {
    fill: none;
    stroke: #000;
    shape-rendering: crispEdges;
  }
  .line {
    fill: none;
    stroke: steelblue;
    stroke-width: 1.5px;
  }
  .ticks {
  font: 10px sans-serif;
}

.track,
.track-inset,
.track-overlay {
  stroke-linecap: round;
}

.track {
  stroke: #000;
  stroke-opacity: 0.3;
  stroke-width: 10px;
}

.track-inset {
  stroke: #ddd;
  stroke-width: 8px;
}

.track-overlay {
  pointer-events: stroke;
  stroke-width: 50px;
  stroke: transparent;
  cursor: crosshair;
}

.handle {
  fill: #fff;
  stroke: #000;
  stroke-opacity: 0.5;
  stroke-width: 1.25px;
}  
  </style>
</head>

<body>

</body>

var x = d3.scaleLinear()
  .range([0, width])
	.clamp(true);

var y = d3.scaleLinear()
  .range([height, 0]);
  
x.domain(d3.extent(data, function(d) {
	return d.x;
}));  
y.domain(d3.extent(data, function(d) {
  return d.p;
}));
  
var xAxis = d3.axisBottom()
  .scale(x);

var yAxis = d3.axisLeft()
  .scale(y);

var svg = d3.select("body").append("svg")
  .attr("width", width + margin.left + margin.right)
  .attr("height", height + margin.top + margin.bottom)
  .append("g")
  .attr("transform", "translate(" + margin.left + "," + margin.top + ")");
  
var slider = svg.append("g")
    .attr("class", "slider")
    .attr("transform", "translate(" + (margin.left-20) + "," + margin.top + ")");

slider.append("line")
    .attr("class", "track")
    .attr("x1", 0)
    .attr("x2", 159)
  .select(function() { return this.parentNode.appendChild(this.cloneNode(true)); })
    .attr("class", "track-inset")
  .select(function() { return this.parentNode.appendChild(this.cloneNode(true)); })
    .attr("class", "track-overlay")
    .call(d3.drag()
        .on("start.interrupt", function() { slider.interrupt(); })
        .on("start drag", function() { 
  				q_mean = x.invert(d3.event.x);
  				handle.attr("cx", x(q_mean));
  				getData(q_mean); 
				}));

var handle = slider.insert("circle", ".track-overlay")
    .attr("class", "handle")
    .attr("r", 9);

svg.append("g")
  .attr("class", "x axis")
  .attr("transform", "translate(0," + height + ")")
  .call(xAxis);

svg.append("g")
  .attr("class", "y axis")
  .call(yAxis);

svg.append("path")
  .datum(data)
  .attr("class", "line")
  .attr("d", line1);
  
svg.append("path")
  .datum(data)
  .attr("class", "line")
	.style("stroke", "red")
  .attr("d", line2);
  
//calculate KL divergences  
var KL_pq = data.reduce(function(kl, item){
  return kl + item.p * Math.log(item.p/item.q);
}, 0);

var KL_qp = data.reduce(function(kl, item){
  return kl + item.q * Math.log(item.q/item.p);
}, 0);

var myText =  svg.append("text")
   .attr("x", 0.8*width)
	 .attr("y", 2)
   .attr('text-anchor', 'left')
   .attr("class", "myLabel")//easy to style with CSS
	 .attr("font-size", "20px")
   .text("KL(p,q) = " + KL_pq);  
  
var myText =  svg.append("text")
   .attr("x", 0.8*width)
	 .attr("y", 25)
   .attr('text-anchor', 'left')
   .attr("class", "myLabel")//easy to style with CSS
	 .attr("font-size", "20px")
   .text("KL(q,p) = " + KL_qp); 
  
//taken from Jason Davies science library
// https://github.com/jasondavies/science.js/
function gaussian(x, mean, std) {
	var gaussianConstant = 1 / Math.sqrt(2 * Math.PI);

x = (x - mean) / std;
  return gaussianConstant * Math.exp(-.5 * x * x) / std;
};
  
</script>

</html>

https://d3js.org/d3.v4.min.js