Iris - Boosting PDP

README.md

A partial dependence plot of a BigML boosted ensemble built on the iris dataset.

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grid.js

function cartesianProduct() {
    var args = [].slice.call(arguments);
    var end = args.length - 1;
    var result = [];

    function addTo(curr, start) {
        var first = args[start];
        var last = (start === end);

        for (var i = 0; i < first.length; ++i) {
            var copy = curr.slice();
            copy.push(first[i]);

            if (last) {
                result.push(copy);
            } else {
                addTo(copy, start + 1);
            }
        }
    }

    if (args.length) {
        addTo([], 0);
    } else {
        result.push([]);
    }
    return result;
}

function range (v) {
    return Array.apply(null, Array(v)).map(function (_, i) {return i;})
}

function initAxis (field, canvasSize, grid) {
    var axis = {id: field.id,
                optype: field.optype};
    if (axis.optype == "numeric") {
        axis.binCount = grid.maxNumBins;
        axis.initRange = [field.minimum, field.maximum];
    } else {
        axis.binCount = Math.min(field.order.length, grid.maxCatBins);
        axis.initRange = field.order.slice(0, axis.binCount);
    }
    axis.currentRange = axis.initRange.slice(0);
    axis.binCanvasSize = canvasSize / axis.binCount;
    return axis;
}

function dataAxisFn (axis) {
    if (axis.optype == "categorical") {
        return function (index) {return axis.currentRange[index]};
    } else {
        var start = axis.currentRange[0];
        var width = (axis.currentRange[1] - axis.currentRange[0]) / axis.binCount;
        return function (index) {return start + index * width};
    }
}

function dataFn (grid) {
    var xFn = dataAxisFn(grid.x);
    var yFn = dataAxisFn(grid.y);
    return function (binId) {return [xFn(binId[0]), yFn(binId[1])]};
}

function initGrid(targetFields, canvasWidth, canvasHeight, maxNumBins, maxCatBins) {
    var grid = {canvasWidth: canvasWidth,
                canvasHeight: canvasHeight,
                maxNumBins: maxNumBins,
                maxCatBins: maxCatBins};
    grid.x = initAxis(targetFields[0], canvasWidth, grid);
    grid.y = initAxis(targetFields[1], canvasHeight, grid);
    grid.dataFn = dataFn(grid);
    return grid;
}

function gridFieldChange (grid, targetFields) {
    if (grid.x.id != targetFields[0].id) {
        grid.x = initAxis(targetFields[0], grid.canvasWidth, grid);
    }
    if (grid.y.id != targetFields[1].id) {
        grid.y = initAxis(targetFields[1], grid.canvasHeight, grid);
    }
    grid.dataFn = dataFn(grid);
    return grid;
}

function resetGridRanges(grid) {
    grid.x.currentRange = grid.x.initRange;
    if (grid.x.optype == "categorical") {
        var bins = grid.x.initRange.length;
        grid.x.binCount = bins;
        grid.x.binCanvasSize = grid.canvasWidth / bins;
    }
    grid.y.currentRange = grid.y.initRange;
    if (grid.y.optype == "categorical") {
        var bins = grid.y.initRange.length;
        grid.y.binCount = bins;
        grid.y.binCanvasSize = grid.canvasHeight / bins;
    }
    grid.dataFn = dataFn(grid);
    return grid;
}

function updateGridRanges(grid, xRange, yRange) {
    grid.x.currentRange = xRange;
    if (grid.x.optype == "categorical") {
        grid.x.binCount = xRange.length;
        grid.x.binCanvasSize = grid.canvasWidth / xRange.length;
    }
    grid.y.currentRange = yRange;
    if (grid.y.optype == "categorical") {
        grid.y.binCount = yRange.length;
        grid.y.binCanvasSize = grid.canvasHeight / yRange.length;
    }
    grid.dataFn = dataFn(grid);
    return grid;
}

function canvasXFn (grid) {
    var size = grid.x.binCanvasSize;
    return function(binId) {return binId[0] * size};
}

function canvasYFn (grid) {
    var size = grid.y.binCanvasSize;
    var canvasHeight = grid.canvasHeight;
    return function(binId) {return canvasHeight - size - (binId[1] * size)};
}

function binList (grid) {
    return cartesianProduct(range(grid.x.binCount), range(grid.y.binCount));
}

function coordsToGridIndex (grid, coords) {
    var x = Math.floor(coords[0] / grid.x.binCanvasSize);
    var y = Math.floor((grid.canvasHeight - coords[1]) / grid.y.binCanvasSize);
    return [x, y];
}

index.html

</script>
<!DOCTYPE html>
<meta charset="utf-8">
<style>


 .domain {
     stroke: none;
     fill: none;
 }

 .field {
     cursor: pointer;
     -moz-user-select: none;
     -khtml-user-select: none;
     -webkit-user-select: none;
     -ms-user-select: none;
     user-select: none;
 }

 .brush .extent {
     stroke: #fff;
     fill-opacity: .125;
     shape-rendering: crispEdges;
 }

 svg {
     -webkit-user-select: none; /* webkit (safari, chrome) browsers */
     -moz-user-select: none; /* mozilla browsers */
     -khtml-user-select: none; /* webkit (konqueror) browsers */
     -ms-user-select: none; /* IE10+ */
 }

 .selector {
     margin-bottom: 15px;
 }

 div#pdp {
     float: left;
     margin-right: 5px;
 }

 div#sidebar {
     padding-top: 20px;
 }


 div.field-info {
     margin-bottom: 10px;
 }

 div.field-name {
     color: #999;
     margin-right: 10px;
 }

 div.field-value {
 }


</style>
<body oncontextmenu="return false;">
    <div id="pdp"></div>
    <div id="sidebar">
        <form id="controls-form">
            <div class="selector">
                <div>X-Axis</div>
                <select id="x-select"></select>
            </div>
            <div class="selector">
                <div>Y-Axis</div>
                <select id="y-select"></select>
            </div>
            <div class="selector">
                <div>Show Class</div>
                <select id="focus-select"></select>
            </div>
            <div class="selector">
                <div>Dynamic Colors</div>
                <select id="dynamic-colors-select">
                    <option value="true">True</option>
                    <option value="false">False</option>
                </select>
            </div>
        </form>
        <div id="x-field" class="field-info">
            <div id="x-name" class="field-name"></div>
            <div id="x-value" class="field-value"></div>
        </div>
        <div id="y-field" class="field-info">
            <div id="y-name" class="field-name"></div>
            <div id="y-value" class="field-value"></div>
        </div>
        <div id="objective" class="field-info">
            <div id="objective-name" class="field-name"></div>
            <div id="objective-value" class="field-value"></div>
        </div>
    </div>


    <script src="http://d3js.org/d3.v3.min.js"></script>
    <script src="mulch.js"></script>
    <script src="grid.js"></script>
    <script>

     function toggle_option (selectId, index, disabled) {
         document.getElementById(selectId)
                 .getElementsByTagName("option")[index].disabled = disabled;
     }

     var margin = {bottom: 40, left: 50, right: 20, top: 20};
     var width = 640 - margin.left;
     var height = 480 - margin.bottom;


     var svg = d3.select("#pdp").append("svg")
                 .attr("width", width + margin.left + margin.right)
                 .attr("height", height + margin.bottom + margin.top);
     var gridSVG = svg.append("g")
                      .attr("transform",
                            "translate(" + margin.left + "," + margin.top + ")");

     var axisSVG = svg.append("g")
                      .attr("transform",
                            "translate(" + margin.left + "," + margin.top + ")");

     var heatmapRange = ["#61f", "#1f6"];

     d3.json("iris-cache.json", function(error, rawCache) {
         var maxNumBins = 32;
         var maxCatBins = 16;

         rawCache = mulch.core.import_cache(rawCache);
         var impOrder = mulch.core.importance(rawCache)
                             .map(function(pair) {return pair[0];});
         var fields = mulch.core.fields(rawCache);

         var opts = {combiner: "weighted"};
         var dynamicColors = true;
         var x = 0;
         var y = 1;

         var fieldsMap = {};
         for (i in fields) {
             var field = fields[i];
             fieldsMap[field.id] = field;
         }

         var mulchedCache = mulch.core.cache_to_mulch(rawCache,
                                                      [impOrder[x], impOrder[y]]);
         var objective = mulch.core.objective(mulchedCache);
         var targetFields = mulch.core.fields(mulchedCache);
         var regression = (objective["optype"] == "numeric");
         var allClasses = !regression;

         var classColors;
         if (!regression) {
             if (objective.categories.length > 10) {
                 classColors = d3.scale.category20();
             } else {
                 classColors = d3.scale.category10();
             }
             classColors.domain(objective.categories);
         }

         d3.select("#x-name").text(targetFields[0].name);
         d3.select("#x-value").text("-");
         d3.select("#y-name").text(targetFields[1].name);
         d3.select("#y-value").text("-");
         if (allClasses) {
             d3.select("#objective-name").text(objective.name + " (purity)");
         } else {
             d3.select("#objective-name").text(objective.name);
         }
         d3.select("#objective-value").text("-");
         var grid = initGrid(targetFields, width, height, maxNumBins, maxCatBins);

         var xSelector = d3.select("#x-select");
         xSelector.selectAll(".x-option")
                  .data(impOrder).enter()
                  .append("option")
                  .attr("class", "x-option")
                  .attr("value", function(d) {return d;})
                  .text(function(d) {return fieldsMap[d].name;});
         document.getElementById("x-select").selectedIndex = x;
         toggle_option("x-select", y, true);
         xSelector.on("change",
                      function change() {
                          var oldX = x;
                          var newX = this.selectedIndex;
                          toggle_option("y-select", oldX, false);
                          toggle_option("y-select", newX, true);
                          document.getElementById("y-select")
                                  .getElementsByTagName("option")[newX].disabled = true;
                          x = newX;
                          updateMulch();
                          d3.select("#x-name").text(targetFields[0].name);
                      });

         var ySelector = d3.select("#y-select");
         ySelector.selectAll(".y-option")
                  .data(impOrder).enter()
                  .append("option")
                  .attr("class", "y-option")
                  .attr("value", function(d) {return d;})
                  .text(function(d) {return fieldsMap[d].name;});
         document.getElementById("y-select").selectedIndex = y;
         toggle_option("y-select", x, true);
         ySelector.on("change",
                      function change() {
                          var oldY = y;
                          var newY = this.selectedIndex;
                          toggle_option("x-select", oldY, false);
                          toggle_option("x-select", newY, true);
                          document.getElementById("x-select")
                                  .getElementsByTagName("option")[newY].disabled = true;
                          y = newY;
                          updateMulch();
                          d3.select("#y-name").text(targetFields[1].name);
                      });

         d3.select("#dynamic-colors-select")
           .on("change",
               function change() {
                   dynamicColors = ("true" == this.options[this.selectedIndex].value);
                   updatePredictor(false, false);
               });
         document.getElementById("dynamic-colors-select").selectedIndex = 0;
         document.getElementById("dynamic-colors-select").disabled = false;

         var focusSelector = d3.select("#focus-select");
         focusSelector.append("option").attr("value", "#noValue").text("Most common");
         if (regression) {
             document.getElementById("focus-select").disabled = true;
         } else {
             focusSelector.selectAll(".focus-option")
                          .data(objective.categories).enter()
                          .append("option")
                          .attr("class", "focus-option")
                          .attr("value", function(d) {return d;})
                          .text(function(d) {return d;});
             focusSelector.on("change",
                              function change() {
                                  var focus = this.options[this.selectedIndex].value;
                                  if (focus == "#noValue") {
                                      delete opts["focus"];
                                      d3.select("#objective-name")
                                        .text(objective.name + " (purity)");
                                      allClasses = true;
                                  } else {
                                      opts["focus"] = focus;
                                      d3.select("#objective-name")
                                        .text(objective.name + ": " + focus);
                                      allClasses = false;
                                  }
                                  updatePredictor(false, false);
                              });
         }
         document.getElementById("focus-select").selectedIndex = 0;

         var brushX = d3.scale.identity().domain([0, width]);
         var brushY = d3.scale.identity().domain([0, height]);

         function brushed() {
             brushExtent = brush.extent();
         }

         function sortNumber(a,b) {
             return a - b;
         }

         function findRange(axis, canvasRange, scale, isX) {
             var newRange = [];
             if (axis.optype == "numeric") {
                 newRange.push(scale.invert(canvasRange[0]));
                 newRange.push(scale.invert(canvasRange[1]));
                 newRange.sort(sortNumber);
             } else {
                 var size = axis.binCanvasSize;
                 var tempRange = [];
                 if (isX) {
                     tempRange.push(Math.floor(canvasRange[0] / size));
                     tempRange.push(Math.floor(canvasRange[1] / size));
                 } else {
                     tempRange.push(Math.floor((height - canvasRange[0]) / size));
                     tempRange.push(Math.floor((height - canvasRange[1]) / size));
                 }
                 tempRange.sort(sortNumber);
                 newRange = axis.currentRange.slice(tempRange[0], tempRange[1] + 1);
             }
             return newRange;
         }

         function brushended() {
             if (!d3.event.sourceEvent) return; // only transition after input

             var canvasX = [brushExtent[0][0], brushExtent[1][0]];
             var canvasY = [brushExtent[0][1], brushExtent[1][1]];

             if (canvasX[0] == canvasX[1] || canvasY[0] == canvasY[1]) {
                 grid = resetGridRanges(grid);
             } else {
                 var xRange = findRange(grid.x, canvasX, xScale, true);
                 var yRange = findRange(grid.y, canvasY, yScale, false);
                 grid = updateGridRanges(grid, xRange, yRange);
             }

             d3.select(this).call(brush.extent([[0, 0], [0, 0]]));
             var cat = grid.x.optype == "categorical" || grid.y.optype == "categorical";
             redraw(true, cat);
         }

         var gx, gy;
         var xAxis, yAxis;
         var xScale;
         var yScale;

         var predictor;
         var colorScale;
         var pMin, pMax;

         makeAxis();
         updatePredictor(true, true);

         var brushExtent;
         var brush = d3.svg.brush()
                       .x(brushX)
                       .y(brushY)
                       .on("brush", brushed)
                       .on("brushend", brushended);

         axisSVG.append("g")
                .attr("class", "brush")
                .on("mousemove",
                    function(d) {
                        var coords = d3.mouse(this);
                        var inputs = grid.dataFn(coordsToGridIndex(grid, coords));
                        var output = predictor(inputs);
                        d3.select("#x-value").text(prettyVal(inputs[0]));
                        d3.select("#y-value").text(prettyVal(inputs[1]));

                        var outText;
                        if (allClasses) {
                            outText = output[0] + " ("
                                    + prettyVal(100 * prettyVal(output[1])) + "%)";
                        } else if (regression) {
                            outText = prettyVal(output);
                        } else {
                            outText = prettyVal(100 * prettyVal(output)) + "%";
                        }
                        d3.select("#objective-value").text(outText);
                    })
                .on("mouseout", function(d) {
                    d3.select("#x-value").text("-");
                    d3.select("#y-value").text("-");
                    d3.select("#objective-value").text("-");
                })
                .call(brush)
                .call(brush.event);

         function updateColorScale() {
             if (dynamicColors) {
                 var binIds = binList(grid);
                 pMin = 1E20;
                 pMax = -1E20;

                 /* Kind of stupid, as we're doubling the # or
                    predictions to scale the colors */
                 for (var i = 0; i < binIds.length; i++) {
                     var p = predictor(grid.dataFn(binIds[i]));
                     if (allClasses) {
                         p = p[1];
                     }
                     pMin = Math.min(pMin, p);
                     pMax = Math.max(pMax, p);
                 }
             }

             if (regression || !allClasses) {
                 if (dynamicColors) {
                     colorScale = d3.scale.linear().domain([pMin, pMax]);
                 } else {
                     if (opts["focus"] != null) {
                         colorScale = d3.scale.linear().domain([0, 1]);
                     } else {
                         var min = objective.minimum_output;
                         var max = objective.maximum_output;
                         colorScale = d3.scale.linear().domain([min, max]);
                     }
                 }
                 if (regression) {
                     colorScale.range(heatmapRange);
                 } else {
                     var classColor = d3.rgb(classColors(opts["focus"]));
                     var base = d3.rgb("#000");
                     if (dynamicColors) {
                         var minLevel = Math.min(pMin, 0.2);
                         base.r = Math.round(classColor.r * minLevel);
                         base.g = Math.round(classColor.g * minLevel);
                         base.b = Math.round(classColor.b * minLevel);
                     }
                     colorScale.range([base, classColor]);
                 }
             }
         }

         function redraw(redrawAxis, rebuildCells) {
             updateColorScale();
             if (redrawAxis) {
                 updateScales();
                 updateAxis();
             }
             if (rebuildCells) {
                 makeCells();
             }
             updateCells();
         }

         function updatePredictor(redrawAxis, redrawCells) {
             predictor = mulch.core.mulch_to_predictor(mulchedCache, opts);
             redraw(redrawAxis, redrawCells);
         }

         function updateMulch() {
             mulchedCache = mulch.core.cache_to_mulch(rawCache,
                                                      [impOrder[x], impOrder[y]]);
             objective = mulch.core.objective(mulchedCache);
             targetFields = mulch.core.fields(mulchedCache);
             gridFieldChange(grid, targetFields);
             updatePredictor(true, true);
         }

         function makeAxis() {
             gy = axisSVG.append("g").attr("class", "y-axis");
             gx = axisSVG.append("g")
                     .attr("class", "x-axis")
                     .attr("transform", "translate(" + 0 + "," + height + ")");
         }

         function updateAxis() {
             var currentY = gy.transition().duration(700).call(yAxis);
             if (targetFields[1].optype == "categorical") {
                 currentY.selectAll("text")
                         .attr("y", (grid.y.binCanvasSize / 2) - 10)
                         .attr("x", 4)
                         .style("fill", "#fff")
                         .style("font-size", "13")
                         .style("text-anchor", "start");
             }

             var currentX = gx.transition().duration(700).call(xAxis);
             if (targetFields[0].optype == "categorical") {
                 currentX.selectAll("text")
                         .attr("y", (grid.x.binCanvasSize / 2) - 15)
                         .attr("x", 4)
                         .attr("transform", "rotate(-90)")
                         .style("fill", "#fff")
                         .style("font-size", "13")
                         .style("text-anchor", "start");
             }
         }

         function customAxisFormat(d) {
             return d3.format("s")(Math.round(d * 1E4) / 1E4);
         }

         function updateScales () {
             if (targetFields[0].optype == "numeric") {
                 xScale = d3.scale.linear()
                            .range([0, width])
                            .domain([grid.x.currentRange[0],
                                     grid.x.currentRange[1]]);
             } else {
                 xScale = d3.scale.ordinal()
                            .domain(grid.x.currentRange)
                            .rangePoints([0, width], 1);
             }

             if (targetFields[1].optype == "numeric") {
                 yScale = d3.scale.linear()
                            .range([height, 0])
                            .domain([grid.y.currentRange[0],
                                     grid.y.currentRange[1]]);
             } else {
                 yScale = d3.scale.ordinal()
                            .domain(grid.y.currentRange)
                            .rangePoints([height, 0], 1);
             }

             xAxis = d3.svg.axis()
                       .scale(xScale)
                       .orient("bottom");

             yAxis = d3.svg.axis()
                       .scale(yScale)
                       .orient("left");

             if (targetFields[0].optype == "numeric") {
                 xAxis.tickFormat(customAxisFormat);
             }

             if (targetFields[1].optype == "numeric") {
                 yAxis.tickFormat(customAxisFormat);
             }
         }

         function prettyVal(d) {
             if (typeof d === 'string' || d instanceof String) {
                 return d;
             } else {
                 return d = Math.round(d * 1000) / 1000;
             }
         }

         var fastUpdate;

         function makeCells() {
             fastUpdate = true;
             var cxFn = canvasXFn(grid);
             var cyFn = canvasYFn(grid);

             gridSVG.selectAll(".cell").remove();
             gridSVG.selectAll(".cell")
                    .data(binList(grid))
                    .enter()
                    .append("rect")
                    .attr("class", "cell")
                    .style("opacity", "0.01")
                    .attr("x", function(d) { return cxFn(d); })
                    .attr("y", function(d) { return cyFn(d); })
                    .attr("width", grid.x.binCanvasSize + 1)
                    .attr("height", grid.y.binCanvasSize + 1);

             gridSVG.selectAll(".cell-xline").remove();
             gridSVG.selectAll(".cell-xline")
                    .data(range(grid.x.binCount))
                    .enter()
                    .append("line")
                    .attr("class", "cell-xline")
                    .style("opacity", "0.2")
                    .style("stroke", "#000")
                    .attr("x1", function(d) { return grid.x.binCanvasSize * d; })
                    .attr("x2", function(d) { return grid.x.binCanvasSize * d; })
                    .attr("y1", 0)
                    .attr("y2", height);

             gridSVG.selectAll(".cell-yline").remove();
             gridSVG.selectAll(".cell-yline")
                    .data(range(grid.y.binCount))
                    .enter()
                    .append("line")
                    .attr("class", "cell-yline")
                    .style("opacity", "0.2")
                    .style("stroke", "#000")
                    .attr("x1", 0)
                    .attr("x2", width)
                    .attr("y1", function(d) { return grid.y.binCanvasSize * d + 1; })
                    .attr("y2", function(d) { return grid.y.binCanvasSize * d + 1; });

         }

         function updateCells() {
             var updateTime;
             if (fastUpdate) {
                 updateTime = 0;
             } else {
                 updateTime = 700;
             }

             var scalePurity;
             if (allClasses && dynamicColors) {
                 var pDiff = pMax - pMin;
                 if (pDiff == 0) {
                     scalePurity = function(d) {return d;}
                 } else {
                     scalePurity = function(d) {
                         return (0.75 * (d - pMin) / pDiff) + 0.25;
                     };
                 }
             }
             gridSVG.selectAll(".cell")
                    .transition()
                    .duration(updateTime)
                    .style("fill", function(d) {
                        var p = predictor(grid.dataFn(d));
                        var color;
                        if (allClasses) {
                            color = d3.rgb(classColors(p[0]));
                            var purity = p[1];
                            if (dynamicColors) {
                                purity = scalePurity(purity);
                            }
                            color.r = Math.round(color.r * purity);
                            color.g = Math.round(color.g * purity);
                            color.b = Math.round(color.b * purity);
                        } else {
                            color = d3.rgb(colorScale(p));
                        }
                        return color;
                    })
                    .style("stroke", "none")
                    .style("opacity", "1");
             fastUpdate = false;
         }

     });

    </script>
</body>

iris-cache.json

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mulch.js

if(typeof Math.imul == "undefined" || (Math.imul(0xffffffff,5) == 0)) {
    Math.imul = function (a, b) {
        var ah  = (a >>> 16) & 0xffff;
        var al = a & 0xffff;
        var bh  = (b >>> 16) & 0xffff;
        var bl = b & 0xffff;
        // the shift by 0 fixes the sign on the high part
        // the final |0 converts the unsigned value into a signed value
        return ((al * bl) + (((ah * bl + al * bh) << 16) >>> 0)|0);
    }
}


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