rf615_simulation_based_inference.py

Go to the documentation of this file.

## \file
## \ingroup tutorial_roofit_main
## \notebook
## Use Simulation Based Inference (SBI) in RooFit.
##
## This tutorial shows how to use SBI in ROOT. As reference distribution we
## choose a simple uniform distribution. The target distribution is chosen to
## be gaussian with different mean values.
## The classifier is trained to discriminate between the reference and target
## distribution.
## We see how the neural networks generalize to unknown mean values.
##
## We compare the approach of using the likelihood ratio trick to morphing.
##
## An introduction of SBI can be found in https://arxiv.org/pdf/2010.06439.
##
## A short recap:
## The idea of SBI is to fit a surrogate model to the data, in order to really
## learn the likelihood function instead of calculating it. Therefore, a classifier is trained to discriminate between
## samples from a target distribution (here the Gaussian) $$x\sim p(x|\theta)$$ and a reference distribution (here the Uniform)
## $$x\sim p_{ref}(x|\theta)$$.
##
## The output of the classifier $$\hat{s}(\theta)$$ is a monotonic function of the likelihood ration and can be turned into an estimate of the likelihood ratio
## via $$\hat{r}(\theta)=\frac{1-\hat{s}(\theta)}{\hat{s}(\theta)}.$$
## This is called the likelihood ratio trick.
##
## In the end we compare the negative logarithmic likelihoods of the learned, morphed and analytical likelihood with minuit and as a plot.
##
## \macro_image
## \macro_code
## \macro_output
##
## \date July 2024
## \author Robin Syring
 
import ROOT
import numpy as np
from sklearn.neural_network import MLPClassifier
 
# The samples used for training the classifier in this tutorial / rescale for more accuracy
n_samples = 10000
 
# Kills warning messages
ROOT.RooMsgService.instance().setGlobalKillBelow(ROOT.RooFit.WARNING)
 
 
# Morphing as a baseline
def morphing(setting):
 
    # Define binning for morphing
    grid = ROOT.RooMomentMorphFuncND.Grid(ROOT.RooBinning(4, 0.0, 4.0))
    x_var.setBins(50)
 
    # Number of 'sampled' gaussians, if you change it, adjust the binning properly
    n_grid = 5
 
    for i in range(n_grid):
        # Define the sampled gausians
        mu_help = ROOT.RooRealVar(f"mu{i}", f"mu{i}", i)
        help = ROOT.RooGaussian(f"g{i}", f"g{i}", x_var, mu_help, sigma)
        workspace.Import(help, Silence=True)
 
        # Fill the histograms
        hist = workspace[f"g{i}"].generateBinned([x_var], n_samples)
 
        # Make sure that every bin is filled and we don't get zero probability
        for i_bin in range(hist.numEntries()):
            hist.add(hist.get(i_bin), 1.0)
 
        # Add the pdf to the workspace
        workspace.Import(ROOT.RooHistPdf(f"histpdf{i}", f"histpdf{i}", [x_var], hist, 1), Silence=True)
 
        # Add the pdf to the grid
        grid.addPdf(workspace[f"histpdf{i}"], i)
 
    # Create the morphing and add it to the workspace
    morph_func = ROOT.RooMomentMorphFuncND("morph_func", "morph_func", [mu_var], [x_var], grid, setting)
    morph = ROOT.RooWrapperPdf("morph", "morph", morph_func, True)
    workspace.Import(morph, Silence=True)
 
    # Uncomment to see input plots for the first dimension (you might need to increase the morphed samples)
    # f1 = x_var.frame(Title="linear morphing;x;pdf", Range=(-4, 8))
    # for i in range(n_grid):
    # workspace[f"histpdf{i}"].plotOn(f1)
    # workspace["morph"].plotOn(f1, LineColor="r")
    # c0 = ROOT.TCanvas()
    # f1.Draw()
    # input() # Wait for user input to proceed
 
 
# Class used in this case to demonstrate the use of SBI in Root
class SBI:
    # Initializing the class SBI
    def __init__(self, workspace):
        # Choose the hyperparameters for training the neural network
        self.classifier = MLPClassifier(hidden_layer_sizes=(20, 20), max_iter=1000, random_state=42)
        self.data_model = None
        self.data_ref = None
        self.X_train = None
        self.y_train = None
        self.workspace = workspace
 
    # Defining the target / training data for different values of mean value mu
    def model_data(self, model, x, mu, n_samples):
        ws = self.workspace
        data_test_model = []
        samples_gaussian = ws[model].generate([ws[x], ws[mu]], n_samples).to_numpy()
        self._training_mus = samples_gaussian[mu]
        data_test_model.extend(samples_gaussian[x])
 
        self.data_model = np.array(data_test_model).reshape(-1, 1)
 
    # Generating samples for the reference distribution
    def reference_data(self, model, x, n_samples):
        ws = self.workspace
        # Ensuring the normalization with generating as many reference data as target data
        samples_uniform = ws[model].generate(ws[x], n_samples)
        data_reference_model = np.array(
            [samples_uniform.get(i).getRealValue("x") for i in range(samples_uniform.numEntries())]
        )
        self.data_ref = data_reference_model.reshape(-1, 1)
 
    # Bringing the data in the right format for training
    def preprocessing(self):
        thetas_model = self._training_mus.reshape(-1, 1)
        thetas_reference = self._training_mus.reshape(-1, 1)
        thetas = np.concatenate((thetas_model, thetas_reference), axis=0)
        X = np.concatenate([self.data_model, self.data_ref])
        self.y_train = np.concatenate([np.ones(len(self.data_model)), np.zeros(len(self.data_ref))])
        self.X_train = np.concatenate([X, thetas], axis=1)
 
    # Train the classifier
    def train_classifier(self):
        self.classifier.fit(self.X_train, self.y_train)
 
 
# Setting the training and toy data samples; the factor 5 to enable a fair comparison to morphing
n_samples_train = n_samples * 5
 
 
# Define the "observed" data in a workspace
def build_ws(mu_observed, sigma):
    # using a workspace for easier processing inside the class
    ws = ROOT.RooWorkspace()
    ws.factory(f"Gaussian::gauss(x[-5,15], mu[0,4], {sigma})")
    ws.factory("Uniform::uniform(x)")
    ws["mu"].setVal(mu_observed)
    ws.Print("v")
    obs_data = ws["gauss"].generate(ws["x"], 1000)
    obs_data.SetName("obs_data")
    ws.Import(obs_data, Silence=True)
 
    return ws
 
 
# The "observed" data
mu_observed = 2.5
sigma = 1.5
workspace = build_ws(mu_observed, sigma)
x_var = workspace["x"]
mu_var = workspace["mu"]
gauss = workspace["gauss"]
uniform = workspace["uniform"]
obs_data = workspace["obs_data"]
 
# Training the model
model = SBI(workspace)
model.model_data("gauss", "x", "mu", n_samples_train)
model.reference_data("uniform", "x", n_samples_train)
model.preprocessing()
model.train_classifier()
sbi_model = model
 
 
# Compute the likelihood ratio of the classifier for analysis purposes
def learned_likelihood_ratio(x, mu):
    n = max(len(x), len(mu))
    X = np.zeros((n, 2))
    X[:, 0] = x
    X[:, 1] = mu
    prob = sbi_model.classifier.predict_proba(X)[:, 1]
    return prob / (1 - prob)
 
 
# Compute the learned likelihood ratio
llhr_learned = ROOT.RooFit.bindFunction("MyBinFunc", learned_likelihood_ratio, x_var, mu_var)
 
# Compute the real likelihood ratio
llhr_calc = ROOT.RooFormulaVar("llhr_calc", "x[0] / x[1]", [gauss, uniform])
 
# Create the exact negative log likelihood functions for Gaussian model
nll_gauss = gauss.createNLL(obs_data)
ROOT.SetOwnership(nll_gauss, True)
 
# Create the learned pdf and NLL sum based on the learned likelihood ratio
pdf_learned = ROOT.RooWrapperPdf("learned_pdf", "learned_pdf", llhr_learned, True)
 
nllr_learned = pdf_learned.createNLL(obs_data)
ROOT.SetOwnership(nllr_learned, True)
 
# Compute the morphed nll
morphing(ROOT.RooMomentMorphFuncND.Linear)
nll_morph = workspace["morph"].createNLL(obs_data)
ROOT.SetOwnership(nll_morph, True)
 
# Plot the negative logarithmic summed likelihood
frame1 = mu_var.frame(Title="NLL of SBI vs. Morphing;mu;NLL", Range=(2.2, 2.8))
nllr_learned.plotOn(frame1, LineColor="kP6Blue", ShiftToZero=True, Name="learned")
nll_gauss.plotOn(frame1, LineColor="kP6Yellow", ShiftToZero=True, Name="gauss")
ROOT.RooAbsReal.setEvalErrorLoggingMode("Ignore")  # Silence some warnings
nll_morph.plotOn(frame1, LineColor="kP6Red", ShiftToZero=True, Name="morphed")
ROOT.RooAbsReal.setEvalErrorLoggingMode("PrintErrors")
 
# Plot the likelihood functions
frame2 = x_var.frame(Title="Likelihood ratio r(x|#mu=2.5);x;p_{gauss}/p_{uniform}")
llhr_learned.plotOn(frame2, LineColor="kP6Blue", Name="learned_ratio")
llhr_calc.plotOn(frame2, LineColor="kP6Yellow", Name="exact")
 
# Write the plots into one canvas to show, or into separate canvases for saving.
single_canvas = True
 
c = ROOT.TCanvas("", "", 1200 if single_canvas else 600, 600)
if single_canvas:
    c.Divide(2)
    c.cd(1)
    ROOT.gPad.SetLeftMargin(0.15)
    frame1.GetYaxis().SetTitleOffset(1.8)
frame1.Draw()
 
legend1 = ROOT.TLegend(0.43, 0.63, 0.8, 0.87)
legend1.SetFillColor("kWhite")
legend1.SetLineColor("kWhite")
legend1.SetTextSize(0.04)
legend1.AddEntry("learned", "learned (SBI)", "L")
legend1.AddEntry("gauss", "true NLL", "L")
legend1.AddEntry("morphed", "moment morphing", "L")
legend1.Draw()
 
if single_canvas:
    c.cd(2)
    ROOT.gPad.SetLeftMargin(0.15)
    frame2.GetYaxis().SetTitleOffset(1.8)
else:
    c.SaveAs("rf615_plot_1.png")
    c = ROOT.TCanvas("", "", 600, 600)
 
frame2.Draw()
 
legend2 = ROOT.TLegend(0.53, 0.73, 0.87, 0.87)
legend2.SetFillColor("kWhite")
legend2.SetLineColor("kWhite")
legend2.SetTextSize(0.04)
legend2.AddEntry("learned_ratio", "learned (SBI)", "L")
legend2.AddEntry("exact", "true ratio", "L")
legend2.Draw()
 
if not single_canvas:
    c.SaveAs("rf615_plot_2.png")
 
# Compute the minimum via minuit and display the results
for nll in [nll_gauss, nllr_learned, nll_morph]:
    minimizer = ROOT.RooMinimizer(nll)
    minimizer.setErrorLevel(0.5)  # Adjust the error level in the minimization to work with likelihoods
    minimizer.setPrintLevel(-1)
    minimizer.minimize("Minuit2")
    result = minimizer.save()
    ROOT.SetOwnership(result, True)
    result.Print()
 
del nll_morph
del nllr_learned
del nll_gauss
del workspace