{ "cells": [ { "cell_type": "markdown", "id": "1e432a3d", "metadata": {}, "source": [ "# rf615_simulation_based_inference\n", "Use Simulation Based Inference (SBI) in RooFit.\n", "\n", "This tutorial shows how to use SBI in ROOT. As reference distribution we\n", "choose a simple uniform distribution. The target distribution is chosen to\n", "be gaussian with different mean values.\n", "The classifier is trained to discriminate between the reference and target\n", "distribution.\n", "We see how the neural networks generalize to unknown mean values.\n", "\n", "We compare the approach of using the likelihood ratio trick to morphing.\n", "\n", "An introduction of SBI can be found in https://arxiv.org/pdf/2010.06439.\n", "\n", "A short recap:\n", "The idea of SBI is to fit a surrogate model to the data, in order to really\n", "learn the likelihood function instead of calculating it. Therefore, a classifier is trained to discriminate between\n", "samples from a target distribution (here the Gaussian) $$x\\sim p(x|\\theta)$$ and a reference distribution (here the Uniform)\n", "$$x\\sim p_{ref}(x|\\theta)$$.\n", "\n", "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\n", "via $$\\hat{r}(\\theta)=\\frac{1-\\hat{s}(\\theta)}{\\hat{s}(\\theta)}.$$\n", "This is called the likelihood ratio trick.\n", "\n", "In the end we compare the negative logarithmic likelihoods of the learned, morphed and analytical likelihood with minuit and as a plot.\n", "\n", "\n", "\n", "\n", "**Author:** Robin Syring \n", "This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:33 PM." ] }, { "cell_type": "code", "execution_count": 1, "id": "6e448a01", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:54.242976Z", "iopub.status.busy": "2026-05-19T20:33:54.242856Z", "iopub.status.idle": "2026-05-19T20:33:56.132374Z", "shell.execute_reply": "2026-05-19T20:33:56.131805Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import ROOT\n", "from sklearn.neural_network import MLPClassifier" ] }, { "cell_type": "markdown", "id": "b868dac8", "metadata": {}, "source": [ "The samples used for training the classifier in this tutorial / rescale for more accuracy" ] }, { "cell_type": "code", "execution_count": 2, "id": "3db31b0a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:56.134419Z", "iopub.status.busy": "2026-05-19T20:33:56.134207Z", "iopub.status.idle": "2026-05-19T20:33:56.250855Z", "shell.execute_reply": "2026-05-19T20:33:56.250457Z" } }, "outputs": [], "source": [ "n_samples = 10000" ] }, { "cell_type": "markdown", "id": "059441ef", "metadata": {}, "source": [ "Kills warning messages" ] }, { "cell_type": "code", "execution_count": 3, "id": "df463700", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:56.253132Z", "iopub.status.busy": "2026-05-19T20:33:56.253006Z", "iopub.status.idle": "2026-05-19T20:33:56.403139Z", "shell.execute_reply": "2026-05-19T20:33:56.402372Z" } }, "outputs": [], "source": [ "ROOT.RooMsgService.instance().setGlobalKillBelow(ROOT.RooFit.WARNING)" ] }, { "cell_type": "markdown", "id": "73a30364", "metadata": {}, "source": [ "Morphing as a baseline" ] }, { "cell_type": "code", "execution_count": 4, "id": "8f8709c8", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:56.424629Z", "iopub.status.busy": "2026-05-19T20:33:56.424459Z", "iopub.status.idle": "2026-05-19T20:33:56.529514Z", "shell.execute_reply": "2026-05-19T20:33:56.528932Z" } }, "outputs": [], "source": [ "def morphing(setting, workspace):\n", " # Define binning for morphing\n", " grid = ROOT.RooMomentMorphFuncND.Grid(ROOT.RooBinning(4, 0.0, 4.0))\n", " x_var.setBins(50)\n", "\n", " # Number of 'sampled' gaussians, if you change it, adjust the binning properly\n", " n_grid = 5\n", "\n", " for i in range(n_grid):\n", " # Define the sampled gausians\n", " mu_help = ROOT.RooRealVar(f\"mu{i}\", f\"mu{i}\", i)\n", " help = ROOT.RooGaussian(f\"g{i}\", f\"g{i}\", x_var, mu_help, sigma)\n", " workspace.Import(help, Silence=True)\n", "\n", " # Fill the histograms\n", " hist = workspace[f\"g{i}\"].generateBinned([x_var], n_samples)\n", "\n", " # Make sure that every bin is filled and we don't get zero probability\n", " for i_bin in range(hist.numEntries()):\n", " hist.add(hist.get(i_bin), 1.0)\n", "\n", " # Add the pdf to the workspace\n", " workspace.Import(ROOT.RooHistPdf(f\"histpdf{i}\", f\"histpdf{i}\", [x_var], hist, 1), Silence=True)\n", "\n", " # Add the pdf to the grid\n", " grid.addPdf(workspace[f\"histpdf{i}\"], i)\n", "\n", " # Create the morphing and add it to the workspace\n", " morph_func = ROOT.RooMomentMorphFuncND(\"morph_func\", \"morph_func\", [mu_var], [x_var], grid, setting)\n", " morph = ROOT.RooWrapperPdf(\"morph\", \"morph\", morph_func, True)\n", " workspace.Import(morph, Silence=True)\n", "\n", " # Uncomment to see input plots for the first dimension (you might need to increase the morphed samples)\n", " # f1 = x_var.frame(Title=\"linear morphing;x;pdf\", Range=(-4, 8))\n", " # for i in range(n_grid):\n", " # workspace[f\"histpdf{i}\"].plotOn(f1)\n", " # workspace[\"morph\"].plotOn(f1, LineColor=\"r\")\n", " # c0 = ROOT.TCanvas()\n", " # f1.Draw()\n", " # input() # Wait for user input to proceed" ] }, { "cell_type": "markdown", "id": "5570c523", "metadata": {}, "source": [ "Class used in this case to demonstrate the use of SBI in Root" ] }, { "cell_type": "code", "execution_count": 5, "id": "5e5c565e", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:56.531632Z", "iopub.status.busy": "2026-05-19T20:33:56.531494Z", "iopub.status.idle": "2026-05-19T20:33:56.637006Z", "shell.execute_reply": "2026-05-19T20:33:56.636429Z" } }, "outputs": [], "source": [ "class SBI:\n", " # Initializing the class SBI\n", " def __init__(self, workspace):\n", " # Choose the hyperparameters for training the neural network\n", " self.classifier = MLPClassifier(hidden_layer_sizes=(20, 20), max_iter=1000, random_state=42)\n", " self.data_model = None\n", " self.data_ref = None\n", " self.X_train = None\n", " self.y_train = None\n", " self.workspace = workspace\n", "\n", " # Defining the target / training data for different values of mean value mu\n", " def model_data(self, model, x, mu, n_samples):\n", " ws = self.workspace\n", " data_test_model = []\n", " samples_gaussian = ws[model].generate([ws[x], ws[mu]], n_samples).to_numpy()\n", " self._training_mus = samples_gaussian[mu]\n", " data_test_model.extend(samples_gaussian[x])\n", "\n", " self.data_model = np.array(data_test_model).reshape(-1, 1)\n", "\n", " # Generating samples for the reference distribution\n", " def reference_data(self, model, x, n_samples):\n", " ws = self.workspace\n", " # Ensuring the normalization with generating as many reference data as target data\n", " samples_uniform = ws[model].generate(ws[x], n_samples)\n", " data_reference_model = np.array(\n", " [samples_uniform.get(i).getRealValue(\"x\") for i in range(samples_uniform.numEntries())]\n", " )\n", " self.data_ref = data_reference_model.reshape(-1, 1)\n", "\n", " # Bringing the data in the right format for training\n", " def preprocessing(self):\n", " thetas_model = self._training_mus.reshape(-1, 1)\n", " thetas_reference = self._training_mus.reshape(-1, 1)\n", " thetas = np.concatenate((thetas_model, thetas_reference), axis=0)\n", " X = np.concatenate([self.data_model, self.data_ref])\n", " self.y_train = np.concatenate([np.ones(len(self.data_model)), np.zeros(len(self.data_ref))])\n", " self.X_train = np.concatenate([X, thetas], axis=1)\n", "\n", " # Train the classifier\n", " def train_classifier(self):\n", " self.classifier.fit(self.X_train, self.y_train)" ] }, { "cell_type": "markdown", "id": "6c645dfe", "metadata": {}, "source": [ "Setting the training and toy data samples; the factor 5 to enable a fair comparison to morphing" ] }, { "cell_type": "code", "execution_count": 6, "id": "4a6436e0", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:56.639082Z", "iopub.status.busy": "2026-05-19T20:33:56.638954Z", "iopub.status.idle": "2026-05-19T20:33:56.742274Z", "shell.execute_reply": "2026-05-19T20:33:56.741623Z" } }, "outputs": [], "source": [ "n_samples_train = n_samples * 5" ] }, { "cell_type": "markdown", "id": "591777ee", "metadata": {}, "source": [ "Define the \"observed\" data in a workspace" ] }, { "cell_type": "code", "execution_count": 7, "id": "a70a8b86", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:56.744266Z", "iopub.status.busy": "2026-05-19T20:33:56.744142Z", "iopub.status.idle": "2026-05-19T20:33:56.847797Z", "shell.execute_reply": "2026-05-19T20:33:56.847368Z" } }, "outputs": [], "source": [ "def build_ws(mu_observed, sigma):\n", " # using a workspace for easier processing inside the class\n", " ws = ROOT.RooWorkspace()\n", " ws.factory(f\"Gaussian::gauss(x[-5,15], mu[0,4], {sigma})\")\n", " ws.factory(\"Uniform::uniform(x)\")\n", " ws[\"mu\"].setVal(mu_observed)\n", " ws.Print(\"v\")\n", " obs_data = ws[\"gauss\"].generate(ws[\"x\"], 1000)\n", " obs_data.SetName(\"obs_data\")\n", " ws.Import(obs_data, Silence=True)\n", "\n", " return ws" ] }, { "cell_type": "markdown", "id": "7128cc32", "metadata": {}, "source": [ "The \"observed\" data" ] }, { "cell_type": "code", "execution_count": 8, "id": "e5a27222", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:56.850057Z", "iopub.status.busy": "2026-05-19T20:33:56.849931Z", "iopub.status.idle": "2026-05-19T20:33:57.117978Z", "shell.execute_reply": "2026-05-19T20:33:57.117258Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "RooWorkspace() contents\n", "\n", "variables\n", "---------\n", "(mu,x)\n", "\n", "p.d.f.s\n", "-------\n", "RooGaussian::gauss[ x=x mean=mu sigma=1.5 ] = 0.249352\n", "RooUniform::uniform[ x=(x) ] = 1\n", "\n" ] } ], "source": [ "mu_observed = 2.5\n", "sigma = 1.5\n", "workspace = build_ws(mu_observed, sigma)\n", "x_var = workspace[\"x\"]\n", "mu_var = workspace[\"mu\"]\n", "gauss = workspace[\"gauss\"]\n", "uniform = workspace[\"uniform\"]\n", "obs_data = workspace[\"obs_data\"]" ] }, { "cell_type": "markdown", "id": "352f2660", "metadata": {}, "source": [ "Training the model" ] }, { "cell_type": "code", "execution_count": 9, "id": "f680a0a9", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:57.119653Z", "iopub.status.busy": "2026-05-19T20:33:57.119515Z", "iopub.status.idle": "2026-05-19T20:33:59.648847Z", "shell.execute_reply": "2026-05-19T20:33:59.648254Z" } }, "outputs": [], "source": [ "model = SBI(workspace)\n", "model.model_data(\"gauss\", \"x\", \"mu\", n_samples_train)\n", "model.reference_data(\"uniform\", \"x\", n_samples_train)\n", "model.preprocessing()\n", "model.train_classifier()\n", "sbi_model = model" ] }, { "cell_type": "markdown", "id": "27e16e11", "metadata": {}, "source": [ "Compute the likelihood ratio of the classifier for analysis purposes" ] }, { "cell_type": "code", "execution_count": 10, "id": "92f80fcc", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:59.650876Z", "iopub.status.busy": "2026-05-19T20:33:59.650747Z", "iopub.status.idle": "2026-05-19T20:33:59.754984Z", "shell.execute_reply": "2026-05-19T20:33:59.753936Z" } }, "outputs": [], "source": [ "def learned_likelihood_ratio(x, mu):\n", " n = max(len(x), len(mu))\n", " X = np.zeros((n, 2))\n", " X[:, 0] = x\n", " X[:, 1] = mu\n", " prob = sbi_model.classifier.predict_proba(X)[:, 1]\n", " return prob / (1 - prob)" ] }, { "cell_type": "markdown", "id": "778ae9a8", "metadata": {}, "source": [ "Compute the learned likelihood ratio" ] }, { "cell_type": "code", "execution_count": 11, "id": "40114a8a", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:33:59.756613Z", "iopub.status.busy": "2026-05-19T20:33:59.756474Z", "iopub.status.idle": "2026-05-19T20:34:00.195212Z", "shell.execute_reply": "2026-05-19T20:34:00.194127Z" } }, "outputs": [], "source": [ "llhr_learned = ROOT.RooFit.bindFunction(\"MyBinFunc\", learned_likelihood_ratio, x_var, mu_var)" ] }, { "cell_type": "markdown", "id": "8e8de44b", "metadata": {}, "source": [ "Compute the real likelihood ratio" ] }, { "cell_type": "code", "execution_count": 12, "id": "49ba30e9", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:00.196879Z", "iopub.status.busy": "2026-05-19T20:34:00.196751Z", "iopub.status.idle": "2026-05-19T20:34:00.315172Z", "shell.execute_reply": "2026-05-19T20:34:00.314131Z" } }, "outputs": [], "source": [ "llhr_calc = ROOT.RooFormulaVar(\"llhr_calc\", \"x[0] / x[1]\", [gauss, uniform])" ] }, { "cell_type": "markdown", "id": "9f364ae1", "metadata": {}, "source": [ "Create the exact negative log likelihood functions for Gaussian model" ] }, { "cell_type": "code", "execution_count": 13, "id": "f20f4653", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:00.316838Z", "iopub.status.busy": "2026-05-19T20:34:00.316708Z", "iopub.status.idle": "2026-05-19T20:34:00.459912Z", "shell.execute_reply": "2026-05-19T20:34:00.458812Z" } }, "outputs": [], "source": [ "nll_gauss = gauss.createNLL(obs_data)\n", "ROOT.SetOwnership(nll_gauss, True)" ] }, { "cell_type": "markdown", "id": "ae5f2d9b", "metadata": {}, "source": [ "Create the learned pdf and NLL sum based on the learned likelihood ratio" ] }, { "cell_type": "code", "execution_count": 14, "id": "be2cd2bd", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:00.461529Z", "iopub.status.busy": "2026-05-19T20:34:00.461403Z", "iopub.status.idle": "2026-05-19T20:34:00.590474Z", "shell.execute_reply": "2026-05-19T20:34:00.589374Z" } }, "outputs": [], "source": [ "pdf_learned = ROOT.RooWrapperPdf(\"learned_pdf\", \"learned_pdf\", llhr_learned, True)\n", "\n", "nllr_learned = pdf_learned.createNLL(obs_data)\n", "ROOT.SetOwnership(nllr_learned, True)" ] }, { "cell_type": "markdown", "id": "2aa2b2cc", "metadata": {}, "source": [ "Compute the morphed nll" ] }, { "cell_type": "code", "execution_count": 15, "id": "c9b97339", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:00.592110Z", "iopub.status.busy": "2026-05-19T20:34:00.591983Z", "iopub.status.idle": "2026-05-19T20:34:00.865669Z", "shell.execute_reply": "2026-05-19T20:34:00.864639Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[#0] ERROR:Eval -- RooAbsReal::logEvalError(morph_func_offset_0_0) evaluation error, \n", " origin : RooFormulaVar::morph_func_offset_0_0[ actualVars=(histpdf0_MOMENT_1_x,morph_func_pos_0,morph_func_slope_0_0) formula=\"x[0]-(x[1]*x[2])\" ]\n", " message : function value is NAN\n", " server values: actualVars=(histpdf0_MOMENT_1_x = 0.0504296,morph_func_pos_0 = 0,morph_func_slope_0_0 = inf)\n", "[#0] ERROR:Eval -- RooAbsReal::logEvalError(morph_func_offset_1_0) evaluation error, \n", " origin : RooFormulaVar::morph_func_offset_1_0[ actualVars=(histpdf1_MOMENT_1_x,morph_func_pos_0,morph_func_slope_1_0) formula=\"x[0]-(x[1]*x[2])\" ]\n", " message : function value is NAN\n", " server values: actualVars=(histpdf1_MOMENT_1_x = 0.997298,morph_func_pos_0 = 0,morph_func_slope_1_0 = inf)\n", "[#0] ERROR:Eval -- RooAbsReal::logEvalError(morph_func_offset_2_0) evaluation error, \n", " origin : RooFormulaVar::morph_func_offset_2_0[ actualVars=(histpdf2_MOMENT_1_x,morph_func_pos_0,morph_func_slope_2_0) formula=\"x[0]-(x[1]*x[2])\" ]\n", " message : function value is NAN\n", " server values: actualVars=(histpdf2_MOMENT_1_x = 2.01481,morph_func_pos_0 = 0,morph_func_slope_2_0 = inf)\n", "[#0] ERROR:Eval -- RooAbsReal::logEvalError(morph_func_offset_3_0) evaluation error, \n", " origin : RooFormulaVar::morph_func_offset_3_0[ actualVars=(histpdf3_MOMENT_1_x,morph_func_pos_0,morph_func_slope_3_0) formula=\"x[0]-(x[1]*x[2])\" ]\n", " message : function value is NAN\n", " server values: actualVars=(histpdf3_MOMENT_1_x = 3.04583,morph_func_pos_0 = 0,morph_func_slope_3_0 = inf)\n", "[#0] ERROR:Eval -- RooAbsReal::logEvalError(morph_func_offset_4_0) evaluation error, \n", " origin : RooFormulaVar::morph_func_offset_4_0[ actualVars=(histpdf4_MOMENT_1_x,morph_func_pos_0,morph_func_slope_4_0) formula=\"x[0]-(x[1]*x[2])\" ]\n", " message : function value is NAN\n", " server values: actualVars=(histpdf4_MOMENT_1_x = 4.00616,morph_func_pos_0 = 0,morph_func_slope_4_0 = inf)\n" ] } ], "source": [ "morphing(ROOT.RooMomentMorphFuncND.Linear, workspace)\n", "nll_morph = workspace[\"morph\"].createNLL(obs_data)\n", "ROOT.SetOwnership(nll_morph, True)" ] }, { "cell_type": "markdown", "id": "7ab80398", "metadata": {}, "source": [ "Plot the negative logarithmic summed likelihood" ] }, { "cell_type": "code", "execution_count": 16, "id": "32423534", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:00.867331Z", "iopub.status.busy": "2026-05-19T20:34:00.867201Z", "iopub.status.idle": "2026-05-19T20:34:01.152890Z", "shell.execute_reply": "2026-05-19T20:34:01.151822Z" } }, "outputs": [], "source": [ "frame1 = mu_var.frame(Title=\"NLL of SBI vs. Morphing;mu;NLL\", Range=(2.2, 2.8))\n", "nllr_learned.plotOn(frame1, LineColor=\"kP6Blue\", ShiftToZero=True, Name=\"learned\")\n", "nll_gauss.plotOn(frame1, LineColor=\"kP6Yellow\", ShiftToZero=True, Name=\"gauss\")\n", "ROOT.RooAbsReal.setEvalErrorLoggingMode(\"Ignore\") # Silence some warnings\n", "nll_morph.plotOn(frame1, LineColor=\"kP6Red\", ShiftToZero=True, Name=\"morphed\")\n", "ROOT.RooAbsReal.setEvalErrorLoggingMode(\"PrintErrors\")" ] }, { "cell_type": "markdown", "id": "7ef8f5f0", "metadata": {}, "source": [ "Plot the likelihood functions" ] }, { "cell_type": "code", "execution_count": 17, "id": "d61299b0", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:01.154566Z", "iopub.status.busy": "2026-05-19T20:34:01.154439Z", "iopub.status.idle": "2026-05-19T20:34:01.280705Z", "shell.execute_reply": "2026-05-19T20:34:01.279643Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "frame2 = x_var.frame(Title=\"Likelihood ratio r(x|#mu=2.5);x;p_{gauss}/p_{uniform}\")\n", "llhr_learned.plotOn(frame2, LineColor=\"kP6Blue\", Name=\"learned_ratio\")\n", "llhr_calc.plotOn(frame2, LineColor=\"kP6Yellow\", Name=\"exact\")" ] }, { "cell_type": "markdown", "id": "b097a021", "metadata": {}, "source": [ "Write the plots into one canvas to show, or into separate canvases for saving." ] }, { "cell_type": "code", "execution_count": 18, "id": "acf50206", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:01.282367Z", "iopub.status.busy": "2026-05-19T20:34:01.282239Z", "iopub.status.idle": "2026-05-19T20:34:01.457001Z", "shell.execute_reply": "2026-05-19T20:34:01.455930Z" } }, "outputs": [], "source": [ "single_canvas = True\n", "\n", "c = ROOT.TCanvas(\"\", \"\", 1200 if single_canvas else 600, 600)\n", "if single_canvas:\n", " c.Divide(2)\n", " c.cd(1)\n", " ROOT.gPad.SetLeftMargin(0.15)\n", " frame1.GetYaxis().SetTitleOffset(1.8)\n", "frame1.Draw()\n", "\n", "legend1 = ROOT.TLegend(0.43, 0.63, 0.8, 0.87)\n", "legend1.SetFillColor(\"kWhite\")\n", "legend1.SetLineColor(\"kWhite\")\n", "legend1.SetTextSize(0.04)\n", "legend1.AddEntry(\"learned\", \"learned (SBI)\", \"L\")\n", "legend1.AddEntry(\"gauss\", \"true NLL\", \"L\")\n", "legend1.AddEntry(\"morphed\", \"moment morphing\", \"L\")\n", "legend1.Draw()\n", "\n", "if single_canvas:\n", " c.cd(2)\n", " ROOT.gPad.SetLeftMargin(0.15)\n", " frame2.GetYaxis().SetTitleOffset(1.8)\n", "else:\n", " c.SaveAs(\"rf615_plot_1.png\")\n", " c = ROOT.TCanvas(\"\", \"\", 600, 600)\n", "\n", "frame2.Draw()\n", "\n", "legend2 = ROOT.TLegend(0.53, 0.73, 0.87, 0.87)\n", "legend2.SetFillColor(\"kWhite\")\n", "legend2.SetLineColor(\"kWhite\")\n", "legend2.SetTextSize(0.04)\n", "legend2.AddEntry(\"learned_ratio\", \"learned (SBI)\", \"L\")\n", "legend2.AddEntry(\"exact\", \"true ratio\", \"L\")\n", "legend2.Draw()\n", "\n", "if not single_canvas:\n", " c.SaveAs(\"rf615_plot_2.png\")" ] }, { "cell_type": "markdown", "id": "849a771f", "metadata": {}, "source": [ "Compute the minimum via minuit and display the results" ] }, { "cell_type": "code", "execution_count": 19, "id": "4f7814b2", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:01.458622Z", "iopub.status.busy": "2026-05-19T20:34:01.458482Z", "iopub.status.idle": "2026-05-19T20:34:01.632808Z", "shell.execute_reply": "2026-05-19T20:34:01.632148Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " RooFitResult: minimized FCN value: 1862.97, estimated distance to minimum: 2.32702e-05\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " mu 2.5399e+00 +/- 4.74e-02\n", "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " RooFitResult: minimized FCN value: -1126.14, estimated distance to minimum: 4.23342e-05\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " mu 2.5511e+00 +/- 7.15e-02\n", "\n", "\n", " RooFitResult: minimized FCN value: -7350.75, estimated distance to minimum: 0.000125595\n", " covariance matrix quality: Full, accurate covariance matrix\n", " Status : MINIMIZE=0 \n", "\n", " Floating Parameter FinalValue +/- Error \n", " -------------------- --------------------------\n", " mu 2.5103e+00 +/- 4.08e-02\n", "\n" ] } ], "source": [ "for nll in [nll_gauss, nllr_learned, nll_morph]:\n", " minimizer = ROOT.RooMinimizer(nll)\n", " minimizer.setErrorLevel(0.5) # Adjust the error level in the minimization to work with likelihoods\n", " minimizer.setPrintLevel(-1)\n", " minimizer.minimize(\"Minuit2\")\n", " result = minimizer.save()\n", " ROOT.SetOwnership(result, True)\n", " result.Print()\n", "\n", "del nll_morph\n", "del nllr_learned\n", "del nll_gauss\n", "del workspace" ] }, { "cell_type": "markdown", "id": "6427f652", "metadata": {}, "source": [ "Draw all canvases " ] }, { "cell_type": "code", "execution_count": 20, "id": "515858d1", "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2026-05-19T20:34:01.634502Z", "iopub.status.busy": "2026-05-19T20:34:01.634377Z", "iopub.status.idle": "2026-05-19T20:34:01.828990Z", "shell.execute_reply": "2026-05-19T20:34:01.828080Z" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "
\n", "
\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ROOT import gROOT \n", "gROOT.GetListOfCanvases().Draw()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.12" } }, "nbformat": 4, "nbformat_minor": 5 }