Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
AntonAntonov`QuantileRegression`
QuantileEnvelopeRegion  |
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Examples
(1)
Basic Examples
(1)
Generate data:
In[1]:=
SeedRandom[22];npoints=2000;data={RandomReal[{0,2Pi},npoints],RandomReal[{-Pi,Pi},npoints],RandomVariate[PoissonDistribution[4.8],npoints]};data=MapThread[#3*{Cos[#1]Cos[#2],Sin[#1]Cos[#2],Sin[#2]}&,data];
Plot the data:
In[2]:=
Block[{qs=12},qs=Map[Quantile[#,Range[0,1,1/(qs-1)]]&,Transpose[data]];grData=ListPointPlot3D[data,PlotRangeAll,PlotTheme"Detailed",FaceGrids{{{0,0,-1},Most[qs]},{{0,1,0},qs〚{1,3}〛},{{-1,0,0},Rest[qs]}},ImageSizeLarge]]
Out[2]=
Find the implicit region of Quantile regression envelope for probability :
0.9
In[3]:=
ir=
[data,0.9,20];
 | QuantileEnvelopeRegion |
Approximate the boundary of the region:
In[4]:=
s=BoundaryDiscretizeRegion[ir,PerformanceGoal"Speed",BoxRatios{1,1,1/2}]
Out[4]=
Show the data and the envelope together:
In[5]:=
Show[{grData,s}]
Out[5]=
Find the points inside the envelope:
In[6]:=
inPoints=Select[data,#∈ir&];Length[inPoints]/Length[data]//N
Out[6]=
0.3775
It can be seen that the algorithm produces a region that contains a much smaller number of points than the requested probability (0.9 above.) This property (shortcoming) of the algorithm is discussed in the article "Quantile tomography: using quantiles with multivariate data" by Linglong Kong, Ivan Mizera (2013, arXiv:0805.0056v2).
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