Wolfram Language Paclet Repository

Community-contributed installable additions to the Wolfram Language

AntonAntonov/ MonadicQuantileRegression

Software monad for Quantile Regression workflows

Contributed by: Anton Antonov

A software monad implementation for Quantile Regression workflows. B-spline, Chebyshev, and custom function bases are supported.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["AntonAntonov/MonadicQuantileRegression"]


To load the code after installation, evaluate this code:
Needs["AntonAntonov`MonadicQuantileRegression`"]

Details

The curves and (hyper-)surfaces found by Quantile Regression (QR) are called "regression quantiles".
For two-dimensional data QR is done with a B-spline basis, a Chebyshev functions basis, or a custom function basis.
For higher dimensional data QR is doen with a Non-Uniform Rational B-Spline (NURBS) basis or a custom function basis.
QR is used to find "contextual outliers".
Using the found regression quantiles a conditional distribution estimate can be found at each regressor point.
The found regression quantiles can be used to generate random data that closely resembles the original data.
The software monad has functions for computing linear regession, neural nets regression, and QR.

Paclet Guide

Examples

Basic Examples (2) 

Here is temperature data:

In[1]:=
tsTemp = WeatherData[{"Atlanta", "Georgia"}, "Temperature", {{2018, 1, 1}, {2023, 1, 1}, "Day"}]
Out[1]=

Here is a monadic pipeline for finding regression quantiles at probabilities 0.25, 0.5, and 0.75:

In[2]:=
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List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["AntonAntonov/MonadicQuantileRegression", "AntonAntonov`MonadicQuantileRegression`QRMonDateListPlot"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][AspectRatio -> 1/3, ImageSize -> Large];

Scope (3) 

Here we find "contextual" outliers in the data -- points that are "outside" the regression quantiles at probabilities 0.02 and 0.98:

In[3]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/70138672-4687-4ea4-9479-0c1475b29dfe"]

Here the temperature time series is simulated:

In[4]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/21137c88-a266-498f-abb2-133e4e5abd00"]

Multidimensional data is also supported:

In[5]:=
SeedRandom[1122]; Block[{c = 2, h = 0.1}, data = Flatten[Table[{x, y, Exp[-(x^2 + y^2)/4]*(1 + RandomReal[1.2])}, {x, -c, c, h}, {y, x, c, h}], 1]; ]; reg = ConvexHullRegion[Most /@ data]; qrObj = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 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Publisher

Anton Antonov

Disclosures

Version History

  • 1.1.2 – 25 August 2026
  • 1.1.1 – 20 August 2026
  • 1.1.0 – 16 August 2026
  • 1.0.4 – 29 July 2024
  • 1.0.3 – 01 June 2023
  • 1.0.2 – 28 April 2023
  • 1.0.1 – 27 April 2023
  • 1.0.0 – 27 April 2023

License Information

Artistic License 2.0

Paclet Source

Source Metadata

See Also