fitLinearRobust¶

This tutorial shows how the least trimmed squares regression, included in the TLinearFitter class, can be used for fitting in cases when the data contains outliers. Here the fitting is done via the TGraph::Fit function with option "rob": If you want to use the linear fitter directly for computing the robust fitting coefficients, just use the TLinearFitter::EvalRobust function instead of TLinearFitter::Eval

Author: Anna Kreshuk
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, March 27, 2023 at 09:47 AM.

First generate a dataset, where 20% of points are spoiled by large errors

In [1]:

int npoints = 250;
int fraction = int(0.8*npoints);
double *x = new double[npoints];
double *y = new double[npoints];
double *e = new double[npoints];
TRandom r;
int i;
for (i=0; i<fraction; i++){
   //the good part of the sample
   x[i]=r.Uniform(-2, 2);
   e[i]=1;
   y[i]=1 + 2*x[i] + 3*x[i]*x[i] + 4*x[i]*x[i]*x[i] + e[i]*r.Gaus();
}
for (i=fraction; i<npoints; i++){
   //the bad part of the sample
   x[i]=r.Uniform(-1, 1);
   e[i]=1;
   y[i] = 1 + 2*x[i] + 3*x[i]*x[i] + 4*x[i]*x[i]*x[i] + r.Landau(10, 5);
}

TGraphErrors *grr = new TGraphErrors(npoints, x, y, 0, e);
grr->SetMinimum(-30);
grr->SetMaximum(80);
TF1 *ffit1 = new TF1("ffit1", "pol3", -5, 5);
TF1 *ffit2 = new TF1("ffit2", "pol3", -5, 5);
ffit1->SetLineColor(kBlue);
ffit2->SetLineColor(kRed);
TCanvas *myc = new TCanvas("myc", "Linear and robust linear fitting");
myc->SetGrid();
grr->Draw("ap");

first, let's try to see the result sof ordinary least-squares fit:

In [2]:

printf("Ordinary least squares:\n");
grr->Fit(ffit1);

Ordinary least squares:
****************************************
Minimizer is Linear / Migrad
Chi2                      =       606758
NDf                       =          246
p0                        =       15.724   +/-   0.0887641   
p1                        =    -0.835912   +/-   0.14096     
p2                        =     -3.40616   +/-   0.0607296   
p3                        =      4.82569   +/-   0.0602628

the fitted function doesn't really follow the pattern of the data and the coefficients are far from the real ones

In [3]:

printf("Resistant Least trimmed squares fit:\n");

Resistant Least trimmed squares fit:

Now let's try the resistant regression The option "rob=0.75" means that we want to use robust fitting and we know that at least 75% of data is good points (at least 50% of points should be good to use this algorithm). If you don't specify any number and just use "rob" for the option, default value of (npoints+nparameters+1)/2 will be taken

In [4]:

grr->Fit(ffit2, "+rob=0.75");

****************************************
Minimizer is Linear / Robust (h=0.75)
Chi2                      =       634792
NDf                       =          246
p0                        =      1.00953
p1                        =      1.71148
p2                        =      2.97937
p3                        =      4.07752

In [5]:

TLegend *leg = new TLegend(0.6, 0.8, 0.89, 0.89);
leg->AddEntry(ffit1, "Ordinary least squares", "l");
leg->AddEntry(ffit2, "LTS regression", "l");
leg->Draw();

delete [] x;
delete [] y;
delete [] e;

Draw all canvases

In [6]:

%jsroot on
gROOT->GetListOfCanvases()->Draw()