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[259]:=
Needs["AntonAntonov`QuantileRegression`"]
Set random seed
In[260]:=
SeedRandom[9903]
Out[260]=
RandomGeneratorState
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Define plot function
In[261]:=
QRPlot[data_List,funcs_Association,opts___]:=Show[ListPointPlot3D[data,PlotStyleRed,PlotRangeAll],Plot3D[Evaluate@Values@funcs,{x,Min[data〚All,1〛],Max[data〚All,1〛]},{y,Min[data〚All,2〛],Max[data〚All,2〛]},opts,PlotRangeAll,PlotStyle{Opacity[0.7]},MeshTrue,PlotTheme"LightMesh",PerformanceGoal"Quality",PlotLegendsKeys[funcs]],BoxRatios{1,1,1/2},ImageSizeMedium];
Noisy arrow wave
Generate random, "noisy wave" data
In[262]:=
{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[265]=
{1200,3}
3D list plot of the data
In[266]:=
ListPointPlot3D[data,PlotRangeAll,PlotLabel"Noisy wave data",BoxRatios{1,1,1/2},ImageSizeMedium]
Out[266]=
Data summary
In[267]:=
ResourceFunction["RecordsSummary"][data]
Out[267]=
,
,
1 column 1 | ||||||||||||
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2 column 2 | ||||||||||||
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3 column 3 | ||||||||||||
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NURBS basis
In[268]:=
basis=
[data〚All,1;;2〛,{7,4}];Length[basis]
 | NURBSBasis |
Out[269]=
28
Quantile regression of probability 0.5
In[270]:=
AbsoluteTimingfuncs=
[data,Through[Values[basis][x,y]],{x,y},0.5];
 | QuantileRegressionFit |
Out[270]=
{0.351396,Null}
Plot the obtained function and data
In[271]:=
QRPlot[data,0.5First[funcs]]
Out[271]=
 |
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Quantile regression of probabilities 0.1 and 0.9
In[272]:=
probs={0.1,0.9};AbsoluteTimingfuncs=AssociationThreadprobs,
[data,Through[Values[basis][x,y]],{x,y},probs];
 | QuantileRegressionFit |
Out[273]=
{0.612908,Null}
3D list plot of the data
In[274]:=
QRPlot[data,funcs]
Out[274]=
Count the number points under each surface
In[275]:=
sepPoints=Map[Function[{f},Length[Select[data,#〚-1〛<(f/.{x#〚1〛,y#〚2〛})〚1〛&]]],funcs]
Out[275]=
0.1119,0.91080
Show the corresponding fractions (should correspond to the probabilities)
In[276]:=
sepFractions=N[sepPoints/Length[data]]
Out[276]=
0.10.0991667,0.90.9
Square sombrero
Generate random, "square sombrero" data
In[277]:=
{b,c}={-6,6};data=RandomReal[{b,c},{1200,2}];data=Map[Append[#,Exp[-#.#/(c-b)/2](Sin[Abs[#〚1〛]+Abs[#〚2〛]]+RandomVariate[NormalDistribution[0,0.2]])]&,data];Dimensions[data]
3D list plot of the data
Data summary
NURBS basis
Quantile regression of probability 0.9
Plot functions and data
Pyramid basis
Define a pyramid basis function
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
Partial sombrero
Generate random, "partial sombrero" data
3D list plot of the data
NURBS basis
Regression quantiles
Plot data and regression quantiles together
Create a region object for the convex hull of the data points
The plot data and regression quantiles over the region above
Count the number points under each surface
Show the corresponding fractions (should correspond to the probabilities)