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rf612_recoverFromInvalidParameters.C File Reference

Detailed Description

View in nbviewer Open in SWAN 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.

␛[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby␛[0m
Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
All rights reserved, please read http://roofit.sourceforge.net/license.txt
[#0] WARNING:Plotting -- Cannot apply a bin width correction and use Poisson errors. Not correcting for bin width.
[#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 = 2.60781 +/- 11.9002,a2 = -1 +/- 11.5683,a3 = 0.01)
-------------- Starting second fit ---------------
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
**********
** 15 **SET NOGRAD
**********
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 a1 1.00000e+01 1.19002e+01 -1.00000e+01 2.00000e+01
2 a2 -1.00000e+00 1.15683e+01 -1.00000e+01 2.00000e+01
**********
** 16 **SET ERR 0.5
**********
**********
** 17 **SET PRINT 0
**********
**********
** 18 **SET STR 1
**********
**********
** 19 **MIGRAD 1000 1
**********
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
FCN=-858.564 FROM MIGRAD STATUS=CONVERGED 243 CALLS 244 TOTAL
EDM=7.33131e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 a1 -4.98209e-01 2.27025e-02 2.77075e-05 -2.18163e+00
2 a2 1.98271e-01 5.64128e-03 1.48249e-05 -2.54212e+01
ERR DEF= 0.5
**********
** 20 **SET ERR 0.5
**********
**********
** 21 **SET PRINT 0
**********
**********
** 22 **HESSE 1000
**********
FCN=-858.564 FROM HESSE STATUS=OK 10 CALLS 254 TOTAL
EDM=7.3377e-05 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 a1 -4.98209e-01 2.27254e-02 8.14968e-06 -3.41822e+01
2 a2 1.98271e-01 5.64697e-03 7.41245e-06 3.10901e+01
ERR DEF= 0.5
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
RooFitResult: minimized FCN value: 0, estimated distance to minimum: 0
covariance matrix quality: Approximation only, not accurate
Status : MINIMIZE=0 HESSE=0
Floating Parameter FinalValue +/- Error
-------------------- --------------------------
a1 2.6078e+00 +/- 1.19e+01
a2 -1.0000e+00 +/- 1.16e+01
Without recovery, the fitter encountered 66 invalid function values. The parameters are unchanged.
RooFitResult: minimized FCN value: 29650.9, estimated distance to minimum: 7.3377e-05
covariance matrix quality: Full, accurate covariance matrix
Status : MINIMIZE=0 HESSE=0
Floating Parameter FinalValue +/- Error
-------------------- --------------------------
a1 -4.9821e-01 +/- 2.27e-02
a2 1.9827e-01 +/- 5.65e-03
With recovery, the fitter encountered 72 invalid function values, but the parameters are fitted.
#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:
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:
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(frame->findObject("data"), "Data", "P");
legend->AddEntry(frame->findObject("noRecovery"), "Without recovery (cannot be plotted)", "L");
legend->AddEntry(frame->findObject("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
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:35
RooFitResult is a container class to hold the input and output of a PDF fit to a dataset.
Definition: RooFitResult.h:40
virtual void Print(Option_t *options=0) const
Print TNamed name and title.
Definition: RooFitResult.h:66
Int_t numInvalidNLL() const
Return number of NLL evaluations with problems.
Definition: RooFitResult.h:91
RooPlot * plotOn(RooPlot *frame, const RooAbsArg &par1, const RooAbsArg &par2, const char *options="ME") const
Add objects to a 2D plot.
Definition: RooFitResult.h:144
static RooMsgService & instance()
Return reference to singleton instance.
StreamConfig & getStream(Int_t id)
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
TObject * findObject(const char *name, const TClass *clas=0) const
Find the named object in our list of items and return a pointer to it.
Definition: RooPlot.cxx:982
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:691
RooPolynomial implements a polynomial p.d.f of the form.
Definition: RooPolynomial.h:28
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:39
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:330
virtual void Draw(Option_t *option="")
Draw this legend with its current attributes.
Definition: TLegend.cxx:423
virtual void SetBorderSize(Int_t bordersize=4)
Definition: TPave.h:73
RooCmdArg PrintEvalErrors(Int_t numErrors)
RooCmdArg Save(Bool_t flag=kTRUE)
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)
Date
10/2020
Author
Stephan Hageboeck

Definition in file rf612_recoverFromInvalidParameters.C.