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rf612_recoverFromInvalidParameters.py 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.

import ROOT
# 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.
x = ROOT.RooRealVar("x", "x", -15, 15)
a1 = ROOT.RooRealVar("a1", "a1", -0.5, -10.0, 20.0)
a2 = ROOT.RooRealVar("a2", "a2", 0.2, -10.0, 20.0)
a3 = ROOT.RooRealVar("a3", "a3", 0.01)
pdf = ROOT.RooPolynomial("pol3", "c + a1 * x + a2 * x*x + 0.01 * x*x*x", x, [a1, a2, a3])
# Create toy data with all-positive coefficients:
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.
frame = x.frame()
data.plotOn(frame, 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(10.0)
a2.setVal(-1.0)
# Perform a fit:
fitWithoutRecovery = pdf.fitTo(
data,
Save=True,
RecoverFromUndefinedRegions=0.0, # This is how RooFit behaved prior to ROOT 6.24
PrintEvalErrors=-1, # We are expecting a lot of evaluation errors. -1 switches off printing.
PrintLevel=-1,
)
pdf.plotOn(frame, LineColor="r", 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.
print("\n\n\n-------------- Starting second fit ---------------\n\n")
# Reset the parameters such that the PDF is again undefined.
a1.setVal(10.0)
a2.setVal(-1.0)
# Fit again, but pass recovery information to the minimiser:
fitWithRecovery = pdf.fitTo(
data,
Save=True,
RecoverFromUndefinedRegions=1.0, # The magnitude of the recovery information can be chosen here.
# Higher values mean more aggressive recovery.
PrintEvalErrors=-1, # We are still expecting a few evaluation errors.
PrintLevel=0,
)
pdf.plotOn(frame, LineColor="b", 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.
print(
"Without recovery, the fitter encountered {}".format(fitWithoutRecovery.numInvalidNLL())
+ " invalid function values. The parameters are unchanged.\n"
)
print(
"With recovery, the fitter encountered {}".format(fitWithoutRecovery.numInvalidNLL())
+ " invalid function values, but the parameters are fitted.\n"
)
legend = ROOT.TLegend(0.5, 0.7, 0.9, 0.9)
legend.AddEntry("data", "Data", "P")
legend.AddEntry("noRecovery", "Without recovery (cannot be plotted)", "L")
legend.AddEntry("recovery", "With recovery", "L")
c.SaveAs("rf612_recoverFromInvalidParameters.png")
ROOT::Detail::TRangeCast< T, true > TRangeDynCast
TRangeDynCast is an adapter class that allows the typed iteration through a TCollection.
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t Float_t Float_t Int_t Int_t UInt_t UInt_t Rectangle_t Int_t Int_t Window_t TString Int_t GCValues_t GetPrimarySelectionOwner GetDisplay GetScreen GetColormap GetNativeEvent const char const char dpyName wid window const char font_name cursor keysym reg const char only_if_exist regb h Point_t winding char text const char depth char const char Int_t count const char ColorStruct_t color const char Pixmap_t Pixmap_t PictureAttributes_t attr const char char ret_data h unsigned char height h Atom_t Int_t ULong_t ULong_t unsigned char prop_list Atom_t Atom_t Atom_t Time_t format
[#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 -mavx512
[#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
[#0] ERROR:Minimization -- RooMinimizer: all function calls during minimization gave invalid NLL values!
[#0] ERROR:Minimization -- RooMinimizer::calculateHessErrors() Error when calculating Hessian
[#0] ERROR:Minimization -- RooMinimizer: all function calls during minimization gave invalid NLL values!
[#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 = -1002.22625939860154
Edm = 1.70291335762746681e-07
Nfcn = 245
a1 = -0.49816 +/- 0.0227243 (limited)
a2 = 0.198318 +/- 0.00564929 (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: 1.70451e-07
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 23 invalid function values, but the parameters are fitted.
Date
June 2021
Author
Harshal Shende, Stephan Hageboeck (C++ version)

Definition in file rf612_recoverFromInvalidParameters.py.