Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Quantile regression 3D examples
In this notebook we develop in detail Quantile Regression (QR) examples over 3D data.
Load the Quantile regression paclet
In[1]:=
Needs["AntonAntonov`QuantileRegression`"]
Set random seed
SeedRandom[9903]
Noisy arrow wave
Generate random, "noisy wave" data
In[99]:=
{b,c}={-6,6};data=RandomReal[{b,c},{1200,2}];data=Map[Append[#,Sqrt[#〚1〛-b]+Sin[#〚1〛+Abs[#〚2〛]]+RandomVariate[NormalDistribution[0,0.3]]]&,data];Dimensions[data]
Out[102]=
{1200,3}
3D list plot of the data
In[103]:=
ListPointPlot3D[data,PlotRangeAll,PlotLabel"Noisy wave data",ImageSizeMedium]
Out[103]=
Data summary
In[104]:=
ResourceFunction["RecordsSummary"][data]
Out[104]=
,
,
1 column 1 | ||||||||||||
|
2 column 2 | ||||||||||||
|
3 column 3 | ||||||||||||
|
NURBS basis
In[105]:=
basis=
[data〚All,1;;2〛,{7,4}];Length[basis]
 | NURBSBasis |
Out[106]=
28
Quantile regression of probability 0.5
In[107]:=
AbsoluteTimingfuncs=
[data,Through[Values[basis][x,y]],{x,y},0.5];
 | QuantileRegressionFit |
Out[107]=
{0.3872,Null}
Plot the obtained function and data
In[108]:=
Show[ListPointPlot3D[data,PlotStyleRed,PlotRangeAll],Plot3D[funcs,{x,b,c},{y,b,c},PlotRangeAll,PlotStyle{Opacity[0.6]},PlotLegends0.5,MeshNone,PerformanceGoal"Quality"],BoxRatios{1,1,1/1.5},ImageSizeMedium]
Out[108]=
 | 0.5 |
Quantile regression of probabilities 0.1 and 0.9
In[109]:=
qs={0.1,0.9};AbsoluteTimingfuncs=AssociationThreadqs,
[data,Through[Values[basis][x,y]],{x,y},qs];
 | QuantileRegressionFit |
Out[110]=
{0.62364,Null}
3D list plot of the data
In[111]:=
Show[ListPointPlot3D[data,PlotStyleRed,PlotRangeAll],Plot3D[Evaluate@Values@funcs,{x,b,c},{y,b,c},PlotRangeAll,PlotStyle{Opacity[0.6]},MeshNone,PerformanceGoal"Quality",PlotLegendsKeys[funcs]],BoxRatios{1,1,1/1.5},ImageSizeMedium]
Out[111]=
 |
|
Count the number points under each surface
In[112]:=
sepPoints=Map[Function[{f},Length[Select[data,#〚-1〛<(f/.{x#〚1〛,y#〚2〛})〚1〛&]]],funcs]
Out[112]=
0.1127,0.91086
Here are the corresponding fractions (should correspond to the probabilities)
In[113]:=
sepFractions=N[sepPoints/Length[data]]
Out[113]=
0.10.105833,0.90.905
Pyramid basis
Define pyramid basis function
In[114]:=
Clear[PyramidBasisFunc];PyramidBasisFunc[{x0_,y0_},{x_,y_}]:=
;
|
Here is a plot of a basis function
Make basis for the sombrero data
Find regression quantiles for probability 0.2
Plot data and regression quantiles together
Square sombrero
Generate random, "square sombrero" data
3D list plot of the data
Data summary
NURBS basis
Quantile regression of probability 0.9
Plot functions and data
Partial sombrero
Generate random, "partial sombrero" data
3D list plot of the data
NURBS basis
Regression quantiles
Plot data and regression quantiles together
The plot above with corresponding exclusion region
Count the number points under each surface
Here are the corresponding fractions (should correspond to the probabilities)