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Machine learning has been recently one of the hottest topics in business and science. In different settings, starting from the intuitive financial ones, through medical usages and ending in high-tech ones as speech recognition, people try to predict outcomes using different statistical models. Previously used algorithms such as linear regression, however simple and interpretable, now often give way to new, more effective models that unfortunately due to their complexity lack interpretability. To maintain both accuracy and interpretability of the model we can use model explanation techniques (so-called eXplainable Artificial Intelligence, XAI) that aim to explain such black-box models through various approaches. One of the most fundamental questions that can be posed regarding model explanation is how model response depends on features from a dataset, which can be answered using Ceteris Paribus Profiles. Such profiles show for given observation how model response would change with the change of its value for given variable, while keeping all other variables fixed (hence the name Ceteris Paribus - Latin phrase for all else unchanged).

ceterisParibusD3 package

ceterisParibusD3 package is an interactive (D3 based) extension of plots from ceterisParibus R package. It allows user to plot standard charts from the parent package for Ceteris Paribus profiles , i.e. each chart can include:

  • ICE curves for single observation / group of observation / whole dataset
  • PDP curves that aggregate chosen ICE curves
  • observation points and rugs corresponding to chosen ICE curves
  • residuals corresponding to chosen ICE curves

Each chart can be also divided into subplots (panels) per variable from dataset and be coloured by variable (to see interactions between variables) or model type (to compare model behaviours).

ceterisParibusD3 package adds to these plots:

  • tooltips (shows info about given element (line, point) after hovering over it, hovering over an element causes also highlighting it on given panel (increasing its stroke, opacity or size) and highlighting elements related to the same data point in other panels)

  • interactive table (user can hover over each row, which causes highlighting elements related to this observation and hiding unrelated elements (apart from rugs and pdps), also filtering and sorting rows is available)

There is available an implementation of this package in R and in Python.


ICE curves for single observation:

ICE curves for single observation - model comparison:

More examples

To see more examples check this file and play with commented examples in code.

How to use / installation

You can load package directly from github along with its dependencies (see section Dependencies) - place this in the head of your HTML code:

// html header
<script src="" charset="utf-8"></script>
<script src="" integrity="sha256-FgpCb/KJQlLNfOu91ta32o/NMZxltwRo8QtmkMRdAu8=" crossorigin="anonymous"></script>
<link rel="stylesheet" type="text/css" href="">
 <script type="text/javascript" charset="utf8" src=""></script>
 <script type="text/javascript" charset="utf8" src=""></script>
<script src="" charset="utf-8" lang="js"></script>

// example of usage in js script

var plot = new ceterisParibusD3.createPlot(div, data, dataObs, options);



ceterisParibusD3.js depends on d3.js, jQuery.js, DataTables.js and its plugin pageResize.js. In section How to use /installation you can find example how to include them on your page.


Package has one main function createPlot that is evoked on global package object ceterisParibusD3:

var plot = new ceterisParibusD3.createPlot(div, data, dataObs, options);


Parameter Type Required Description
div string or div element with id yes id of div container for a plot or div container itself (selected by call of e.g. document.getElementById("myDiv"))
data array of objects yes data with Ceteris Paribus Profiles curves coordinates, see details in section Data paremeters below
dataObs array of objects yes data with observations used to generate Ceteris Paribus Profiles , see details in section Data paremeters below
options object yes options of the chart, see details in section Options below

Data parameters

data contains information about every point of Ceteris Paribus Profiles generated for observations from dataObs. Examples of these objects are included in examples, files such as example1.js include examples of data and files such as example_obs1.js corresponding dataObs arrays. There you can also find R script to generate such files using ceterisParibus R package.

We describe general form of array dataObs on the example_obs1.js shown below. Each object in dataObs corresponds to one observation for which given model predicted target value. In case of example_obs1.js our dataset has only observation no. 1958 and we predict its target value using one model (randomForest), so dataObs has just 1 object in it. Characteristic keys are: _yhat_ (keeps model prediction for given observation), _y_ (real target value for given prediction), _label_ (label of model used for prediction), _ids_ (id of observation). Combination of _label_ and _ids_ make given observation unique in array data. Rest of keys (i.e. m2.price, construction.year, surface, floor, no.rooms, district) are variable from given dataset - each variable has its own key-value entry.

    "m2.price": 4397,
    "construction.year": 2005,
    "surface": 20,
    "floor": 3,
    "no.rooms": 2,
    "district": "Wola",
    "_yhat_": 4094.3828,
    "_y_": 4397,
    "_label_": "randomForest",
    "_ids_": "1958"

General form of array data is described on the example of corresponding example1.js file, which extract is shown below. Each object in it corresponds to one point of Ceteris Paribus Proflie calculated for observation _ids_, model _label_ and variable _vname_. It includes analogical keys corresponding to dataset variables as array dataObs (here: m2.price, construction.year, surface, floor, no.rooms, district), and model prediction for these point in _yhat_. Below we can see two points of the profile calculated for observation 1958 for model randomForest for variable construction.year: one point with construction.year = 1920 and one with construction.year =1921 (while as you can see above in dataObs the real value of construction.year for this observation is 2005).

    "m2.price": 4397,
    "construction.year": 1920,
    "surface": 20,
    "floor": 3,
    "no.rooms": 2,
    "district": "Wola",
    "_yhat_": 4264.6774,
    "_vname_": "construction.year",
    "_ids_": "1958",
    "_label_": "randomForest"
    "m2.price": 4397,
    "construction.year": 1921,
    "surface": 20,
    "floor": 3,
    "no.rooms": 2,
    "district": "Wola",
    "_yhat_": 4291.5103,
    "_vname_": "construction.year",
    "_ids_": "1958",
    "_label_": "randomForest"


Options that can be set by options parameter:

Option Type Default Required Description
variables array of strings all variables from dataset no names of variables to be plotted; should be compatible with variables from data and dataObs
show_profiles boolean true no If true, ICE lines are plotted
show_observations boolean true no If true, observation points are plotted
show_rugs boolean true no If true, rugs are plotted
show_residuals boolean true no If true, residuals are plotted
aggregate_profiles string null no If 'mean', PDPs are plotted (calculated as mean of ICE's), if 'median' PDPs are plotted (calculated as median of ICE's)
width number 600 no width of the plot, in px
height number 400 no height of the plot, in px
auto_resize boolean true no If true, plot will be resized when its container will be resized (it includes resize of subplots, legend and fonts)
color string '#3F547F' no name of variable that should be used for coloring elements of the chart (use _label_ to color by model type) or color name/hex code; if categorical variable is set to be a color variable, it should have max. 10 categories
no_colors number 3 no number of colors to be used for sequential palette when color is set as quantitative variable, from 1 to 9
add_table boolean true no If true, table with observations from dataObs will be plotted below plots (taking half of the whole chart height)
categorical_order array of objects null no definition of order of categories for categorical variables, each object in the array corresponds to one categorical variable and has key variable which value is string with name of variable and keys called rank1, rank2 etc. (number of these keys corresponds to number of categories of this variable) which values are strings with categories, see example in section Usage
size_rugs number 1 no size of rugs, from 0 to 1
size_points number 3 no size of points, in px
size_residuals number 2 no size of residuals lines and points, in px
size_pdps number 3.5 no size of residuals lines and points, in px
size_ices number 2 no size of residuals lines and points, in px
alpha_rugs number 0.9 no transparency of rugs, from 0 to 1
alpha_points number 0.9 no transparency of points, from 0 to 1
alpha_residuals number 0.9 no transparency of residuals points and lines, from 0 to 1
alpha_pdps number 0.4 no transparency of PDP ines, from 0 to 1
alpha_ices number 0.4 no transparency of ICE lines, from 0 to 1
color_rugs string '#3F547F' no rugs color name/hex code, if not given color is taken from color option
color_points string '#3F547F' no points color name/hex code, if not given color is taken from color option
color_residuals string '#3F547F' no residuals points and lines color name/hex code, if not given color is taken from color option
color_pdps string 'grey' no PDP lines color name/hex code
font_size_plot_title number 16 no font size of plot title, in px
font_size_titles number 14 no font size of subplots' title, in px
font_size_legend number 12 no font size of legend elements, in px
font_size_axes number 12 no font size of axes elements, in px
font_size_tootlips number 10 no font size of tooltip text, in px
font_size_table number 12 no font size of table's text, in px
plot_title string 'Ceteris Paribus plots per variable - predictions vs. variable values' no title of plot
yaxis_title string 'y' no title of y axes


Example of code usage on exemplary data example12 and example_obs12:

var plot = new ceterisParibusD3.createPlot(div = "chartDiv", 
                       data = example12,
                       dataObs = example_obs12, 
                       options = {
                                   variables: ["district",  "floor", 'no.rooms'],
                                   color: 'district',
                                   show_profiles: true, 
                                   show_observations: true, 
                                   show_rugs: true, 
                                   show_residuals: true, 
                                   aggregate_profiles: 'mean',
                                   add_table: true,
                                   no_colors: 3,
                                   height: 400,
                                   width: 800,
                                   size_rugs: 0.5,
                                   yaxis_title: '',
                                   color_rugs: 'grey',
                                   categorical_order: [
                                   { 'variable': 'district', 
                                     'rank1': "Bielany", 
                                     'rank2': "Bemowo", 
                                     'rank3': "Mokotow", 
                                     'rank4': "Ochota", 
                                     'rank5': "Praga", 
                                     'rank6': "Srodmiescie", 
                                     'rank7': "Ursus", 
                                     'rank8': "Ursynow", 
                                     'rank9': "Wola", 
                                     'rank10': "Zoliborz"

and its output:

Issues and suggestions

To report a bug or propose a new feature please review these guidelines:

  • make sure you have the latest version of the package
  • check whether it is not already in Issues
  • add an issue following suitable template: for bugs or for suggestions


Work on this package is financially supported by the NCN Opus grant 2017/27/B/ST6/01307.

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