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rf612_recoverFromInvalidParameters.C File Reference

Detailed Description

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Likelihood and minimization: Recover from regions where the function is not defined.

We demonstrate improved recovery from disallowed parameters. For this, we use a polynomial PDF of the form

\[ \mathrm{Pol2} = \mathcal{N} \left( c + a_1 \cdot x + a_2 \cdot x^2 + 0.01 \cdot x^3 \right), \]

where \( \mathcal{N} \) is a normalisation factor. Unless the parameters are chosen carefully, this function can be negative, and hence, it cannot be used as a PDF. In this case, RooFit passes an error to the minimiser, which might try to recover.

Before ROOT 6.24, RooFit always passed the highest function value that was encountered during the minimisation to the minimiser. If a parameter is far in a disallowed region, the minimiser has to blindly test various values of the parameters. It might find the correct values by chance, but often be unable to recover from bad starting values. Here, we use a model with such bad values.

Starting with ROOT 6.24, the minimiser receives more information. For example, when a PDF is negative, the magnitude of the "undershoot" is passed to the minimiser. The minimiser can use this to compute a gradient, which will eventually lead it out of the disallowed region. The steepness of this gradient can be chosen using RooFit::RecoverFromUndefinedRegions(double). A value of zero is equivalent to RooFit before ROOT 6.24. Positive values activate the recovery. Values between 1. and 10. were found to be a good default. If no argument is passed, RooFit uses 10.

#include <RooRealVar.h>
#include <RooPolynomial.h>
#include <RooPlot.h>
#include <RooDataSet.h>
#include <RooGlobalFunc.h>
#include <RooFitResult.h>
#include <RooMsgService.h>
#include <TCanvas.h>
#include <TLegend.h>
// Create a fit model:
// The polynomial is notoriously unstable, because it can quickly go negative.
// Since PDFs need to be positive, one often ends up with an unstable fit model.
RooRealVar x("x", "x", -15, 15);
RooRealVar a1("a1", "a1", -0.5, -10., 20.);
RooRealVar a2("a2", "a2", 0.2, -10., 20.);
RooRealVar a3("a3", "a3", 0.01);
RooPolynomial pdf("pol3", "c + a1 * x + a2 * x*x + 0.01 * x*x*x", x, RooArgSet(a1, a2, a3));
// Create toy data with all-positive coefficients:
std::unique_ptr<RooDataSet> data(pdf.generate(x, 10000));
// For plotting.
// We create pointers to the plotted objects. We want these objects to leak out of the function,
// so we can still see them after it returns.
TCanvas* c = new TCanvas();
RooPlot* frame = x.frame();
data->plotOn(frame, RooFit::Name("data"));
// Plotting a PDF with disallowed parameters doesn't work. We would get a lot of error messages.
// Therefore, we disable plotting messages in RooFit's message streams:
// RooFit before ROOT 6.24
// --------------------------------
// Before 6.24, RooFit wasn't able to recover from invalid parameters. The minimiser just errs around
// the starting values of the parameters without finding any improvement.
// Set up the parameters such that the PDF would come out negative. The PDF is now undefined.
a1.setVal(10.);
a2.setVal(-1.);
// Perform a fit:
std::unique_ptr<RooFitResult> fitWithoutRecovery{pdf.fitTo(*data, RooFit::Save(),
RooFit::RecoverFromUndefinedRegions(0.), // This is how RooFit behaved prior to ROOT 6.24
RooFit::PrintEvalErrors(-1), // We are expecting a lot of evaluation errors. -1 switches off printing.
pdf.plotOn(frame, RooFit::LineColor(kRed), RooFit::Name("noRecovery"));
// RooFit since ROOT 6.24
// --------------------------------
// The minimiser gets information about the "badness" of the violation of the function definition. It uses this
// to find its way out of the disallowed parameter regions.
std::cout << "\n\n\n-------------- Starting second fit ---------------\n\n" << std::endl;
// Reset the parameters such that the PDF is again undefined.
a1.setVal(10.);
a2.setVal(-1.);
// Fit again, but pass recovery information to the minimiser:
std::unique_ptr<RooFitResult> fitWithRecovery{pdf.fitTo(*data, RooFit::Save(),
RooFit::RecoverFromUndefinedRegions(1.), // The magnitude of the recovery information can be chosen here.
// Higher values mean more aggressive recovery.
RooFit::PrintEvalErrors(-1), // We are still expecting a few evaluation errors.
pdf.plotOn(frame, RooFit::LineColor(kBlue), RooFit::Name("recovery"));
// Collect results and plot.
// --------------------------------
// We print the two fit results, and plot the fitted curves.
// The curve of the fit without recovery cannot be plotted, because the PDF is undefined if a2 < 0.
fitWithoutRecovery->Print();
std::cout << "Without recovery, the fitter encountered " << fitWithoutRecovery->numInvalidNLL()
<< " invalid function values. The parameters are unchanged." << std::endl;
fitWithRecovery->Print();
std::cout << "With recovery, the fitter encountered " << fitWithRecovery->numInvalidNLL()
<< " invalid function values, but the parameters are fitted." << std::endl;
TLegend* legend = new TLegend(0.5, 0.7, 0.9, 0.9);
legend->SetBorderSize(0);
legend->SetFillStyle(0);
legend->AddEntry("data", "Data", "P");
legend->AddEntry("noRecovery", "Without recovery (cannot be plotted)", "L");
legend->AddEntry("recovery", "With recovery", "L");
frame->Draw();
legend->Draw();
c->Draw();
}
#define c(i)
Definition RSha256.hxx:101
@ kRed
Definition Rtypes.h:66
@ kBlue
Definition Rtypes.h:66
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void data
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition RooArgSet.h:55
static RooMsgService & instance()
Return reference to singleton instance.
StreamConfig & getStream(Int_t id)
Plot frame and a container for graphics objects within that frame.
Definition RooPlot.h:43
static RooPlot * frame(const RooAbsRealLValue &var, double xmin, double xmax, Int_t nBins)
Create a new frame for a given variable in x.
Definition RooPlot.cxx:237
void Draw(Option_t *options=nullptr) override
Draw this plot and all of the elements it contains.
Definition RooPlot.cxx:649
RooPolynomial implements a polynomial p.d.f of the form.
Variable that can be changed from the outside.
Definition RooRealVar.h:37
virtual void SetFillStyle(Style_t fstyle)
Set the fill area style.
Definition TAttFill.h:39
The Canvas class.
Definition TCanvas.h:23
This class displays a legend box (TPaveText) containing several legend entries.
Definition TLegend.h:23
TLegendEntry * AddEntry(const TObject *obj, const char *label="", Option_t *option="lpf")
Add a new entry to this legend.
Definition TLegend.cxx:320
void Draw(Option_t *option="") override
Draw this legend with its current attributes.
Definition TLegend.cxx:425
virtual void SetBorderSize(Int_t bordersize=4)
Sets the border size of the TPave box and shadow.
Definition TPave.h:77
RooCmdArg Save(bool flag=true)
RooCmdArg PrintEvalErrors(Int_t numErrors)
RooCmdArg PrintLevel(Int_t code)
RooCmdArg RecoverFromUndefinedRegions(double strength)
When parameters are chosen such that a PDF is undefined, try to indicate to the minimiser how to leav...
RooCmdArg LineColor(Color_t color)
RooCmdArg Name(const char *name)
Double_t x[n]
Definition legend1.C:17
void removeTopic(RooFit::MsgTopic oldTopic)
[#1] INFO:Fitting -- RooAbsPdf::fitTo(pol3_over_pol3_Int[x]) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- using CPU computation library compiled with -mavx2
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_pol3_over_pol3_Int[x]_pol3Data) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#0] ERROR:Eval -- RooAbsReal::logEvalError(pol3) evaluation error,
origin : RooPolynomial::pol3[ x=x coefList=(a1,a2,a3) ]
message : p.d.f normalization integral is zero or negative: -2220.000000
server values: x=x=0, coefList=(a1 = 10 +/- 0,a2 = -1 +/- 0,a3 = 0.01)
-------------- Starting second fit ---------------
[#1] INFO:Fitting -- RooAbsPdf::fitTo(pol3_over_pol3_Int[x]) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_pol3_over_pol3_Int[x]_pol3Data) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
Minuit2Minimizer: Minimize with max-calls 1000 convergence for edm < 1 strategy 1
Minuit2Minimizer : Valid minimum - status = 0
FVAL = -1002.2262595660759
Edm = 2.95538313214564806e-09
Nfcn = 251
a1 = -0.498159 +/- 0.0227242 (limited)
a2 = 0.198316 +/- 0.00564906 (limited)
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
RooFitResult: minimized FCN value: 0, estimated distance to minimum: 0
covariance matrix quality: Not calculated at all
Status : MINIMIZE=-1 HESSE=302
Floating Parameter FinalValue +/- Error
-------------------- --------------------------
a1 1.0000e+01 +/- 0.00e+00
a2 -1.0000e+00 +/- 0.00e+00
Without recovery, the fitter encountered 23 invalid function values. The parameters are unchanged.
RooFitResult: minimized FCN value: 29650.9, estimated distance to minimum: 2.95925e-09
covariance matrix quality: Full, accurate covariance matrix
Status : MINIMIZE=0 HESSE=0
Floating Parameter FinalValue +/- Error
-------------------- --------------------------
a1 -4.9816e-01 +/- 2.27e-02
a2 1.9832e-01 +/- 5.65e-03
With recovery, the fitter encountered 76 invalid function values, but the parameters are fitted.
Date
10/2020
Author
Stephan Hageboeck

Definition in file rf612_recoverFromInvalidParameters.C.