Source code for madminer.sampling

from __future__ import absolute_import, division, print_function, unicode_literals

import time
import logging
import numpy as np
import multiprocessing
from functools import partial

from madminer.analysis import DataAnalyzer
from madminer.utils.interfaces.madminer_hdf5 import madminer_event_loader, load_madminer_settings
from madminer.utils.interfaces.madminer_hdf5 import save_preformatted_events_to_madminer_file
from madminer.utils.interfaces.madminer_hdf5 import save_sample_summary_to_madminer_file
from madminer.utils.various import create_missing_folders, shuffle

logger = logging.getLogger(__name__)


[docs]class SampleAugmenter(DataAnalyzer): """ Sampling / unweighting and data augmentation. After the generated events have been analyzed and the observables and weights have been saved into a MadMiner file, for instance with `madminer.delphes.DelphesReader` or `madminer.lhe.LHEReader`, the next step is typically the generation of training and evaluation data for the machine learning algorithms. This generally involves two (related) tasks: unweighting, i.e. the creation of samples that do not carry individual weights but follow some distribution, and the extraction of the joint likelihood ratio and / or joint score (the "augmented data"). After inializing `SampleAugmenter` with the filename of a MadMiner file, this is done with a single function call. Depending on the downstream infference algorithm, there are different possibilities: * `SampleAugmenter.sample_train_plain()` creates plain training samples without augmented data. * `SampleAugmenter.sample_train_local()` creates training samples for local methods based on the score, such as SALLY and SALLINO. * `SampleAugmenter.sample_train_density()` creates training samples for non-local methods based on density estimation and the score, such as SCANDAL. * `SampleAugmenter.sample_train_ratio()` creates training samples for non-local, ratio-based methods like RASCAL or ALICE. * `SampleAugmenter.sample_train_more_ratios()` does the same, but can extract joint ratios and scores at more parameter points. This additional information can be used efficiently in the setup with a "doubly parameterized" likelihood ratio estimator that models the dependence on both the numerator and denominator hypothesis. * `SampleAugmenter.sample_test()` creates evaluation samples for all methods. Please see the tutorial for a walkthrough. For the curious, let us explain these steps in a little bit more detail (assuming a morphing setup): * The sample augmentation step starts from a set of events `(x_i, z_i)` together with corresponding weights for each morphing basis point `theta_b`, `p(x_i, z_i | theta_b)`. * Morphing: Assume we want to generate data sampled from a parameter point theta, which is not necessarily one of the basis points theta_b. Using the morphing structure, the event weights for p(x_i, z_i | theta) can be calculated. Note that the events (phase-space points) `(x_i, z_i)` are not changed, only their weights. * Unweighting: For the machine learning part, such a weighted event sample is not practical. Instead we aim for an unweighted one, in which events can appear multiple times. If the user request `N` events (which can be larger than the original number of events in the MadGraph runs), SampleAugmenter will draw `N` samples `(x_i, z_i)` from the discrete distribution `p(x_i, z_i | theta)`. In other words, it draws (with replacement) `N` of the original events from MadGraph, with probabilities given by the morphing setup before. This is similar to what `np.random.choice()` does. * Augmentation: For each of the drawn samples, the morphing setup can be used to calculate the joint likelihood ratio and / or the joint score (this depends on which SampleAugmenter function is called). Parameters ---------- filename : str Path to MadMiner file (for instance the output of `madminer.delphes.DelphesProcessor.save()`). disable_morphing : bool, optional If True, the morphing setup is not loaded from the file. Default value: False. include_nuisance_parameters : bool, optional If True, nuisance parameters are taken into account. Default value: True. """ def __init__(self, filename, disable_morphing=False, include_nuisance_parameters=True): super(SampleAugmenter, self).__init__(filename, disable_morphing, include_nuisance_parameters)
[docs] def sample_train_plain( self, theta, n_samples, nu=None, sample_only_from_closest_benchmark=False, folder=None, filename=None, test_split=0.2, switch_train_test_events=False, n_processes=1, n_eff_forced=None, ): """ Extracts plain training samples `x ~ p(x|theta)` without any augmented data. This can be use for standard inference methods such as ABC, histograms of observables, or neural density estimation techniques. It can also be used to create validation or calibration samples. Parameters ---------- theta : tuple Tuple (type, value) that defines the parameter point or prior over parameter points for the sampling. Pass the output of the functions `constant_benchmark_theta()`, `multiple_benchmark_thetas()`, `constant_morphing_theta()`, `multiple_morphing_thetas()`, or `random_morphing_thetas()`. n_samples : int Total number of events to be drawn. nu : None or tuple, optional Tuple (type, value) that defines the nuisance parameter point or prior over parameter points for the sampling. Default value: None folder : str or None Path to the folder where the resulting samples should be saved (ndarrays in .npy format). Default value: None. filename : str or None Filenames for the resulting samples. A prefix such as 'x' or 'theta0' as well as the extension '.npy' will be added automatically. Default value: None. test_split : float or None, optional Fraction of events reserved for the evaluation sample (that will not be used for any training samples). Default value: 0.2. switch_train_test_events : bool, optional If True, this function generates a training sample from the events normally reserved for test samples. Default value: False. n_processes : None or int, optional If None or larger than 1, MadMiner will use multiprocessing to parallelize the sampling. In this case, n_workers sets the number of jobs running in parallel, and None will use the number of CPUs. Default value: 1. n_eff_forced : float, optional If not None, MadMiner will require the relative weights of the events to be smaller than 1/n_eff_forced and ignore other events. This can help to reduce statistical effects caused by a small number of events with very large weights obtained by the morphing procedure. Default value: None Returns ------- x : ndarray Observables with shape `(n_samples, n_observables)`. The same information is saved as a file in the given folder. theta : ndarray Parameter points used for sampling with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. effective_n_samples : int Effective number of samples, defined as 1/max(event_probabilities), where event_probabilities are the fractions of the cross section carried by each event. """ logger.info("Extracting plain training sample. Sampling according to %s", self._format_sampling(theta)) create_missing_folders([folder]) # Parameters parsed_thetas, n_samples_per_theta = self._parse_theta(theta, n_samples) parsed_nus = self._parse_nu(nu, len(parsed_thetas)) sets = self._build_sets([parsed_thetas], [parsed_nus]) # Start x, _, (theta,), effective_n_samples = self._sample( sets=sets, n_samples_per_set=n_samples_per_theta, use_train_events=not switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) # Save data if filename is not None and folder is not None: np.save(folder + "/theta_" + filename + ".npy", theta) np.save(folder + "/x_" + filename + ".npy", x) return x, theta, min(effective_n_samples)
[docs] def sample_train_local( self, theta, n_samples, nu=None, sample_only_from_closest_benchmark=False, folder=None, filename=None, nuisance_score="auto", test_split=0.2, switch_train_test_events=False, n_processes=1, log_message=True, n_eff_forced=None, ): """ Extracts training samples x ~ p(x|theta) as well as the joint score t(x, z|theta). This can be used for inference methods such as SALLY and SALLINO. Parameters ---------- theta : tuple Tuple (type, value) that defines the parameter point for the sampling. This is also where the score is evaluated. Pass the output of the functions `constant_benchmark_theta()` or `constant_morphing_theta()`. n_samples : int Total number of events to be drawn. nu : None or tuple, optional Tuple (type, value) that defines the nuisance parameter point or prior over parameter points for the sampling. Default value: None folder : str or None Path to the folder where the resulting samples should be saved (ndarrays in .npy format). Default value: None. filename : str or None Filenames for the resulting samples. A prefix such as 'x' or 'theta0' as well as the extension '.npy' will be added automatically. Default value: None. nuisance_score : bool or "auto", optional If True, the score with respect to the nuisance parameters (at the default position) will also be calculated. If False, only the score with respect to the physics parameters is calculated. For "auto", the nuisance score will be calculated if a nuisance setup is defined. Default: True. test_split : float or None, optional Fraction of events reserved for the evaluation sample (that will not be used for any training samples). Default value: 0.2. switch_train_test_events : bool, optional If True, this function generates a training sample from the events normally reserved for test samples. Default value: False. n_processes : None or int, optional If None or larger than 1, MadMiner will use multiprocessing to parallelize the sampling. In this case, n_workers sets the number of jobs running in parallel, and None will use the number of CPUs. Default value: 1. log_message : bool, optional If True, logging output. This option is only designed for internal use. n_eff_forced : float, optional If not None, MadMiner will require the relative weights of the events to be smaller than 1/n_eff_forced and ignore other events. This can help to reduce statistical effects caused by a small number of events with very large weights obtained by the morphing procedure. Default value: None Returns ------- x : ndarray Observables with shape `(n_samples, n_observables)`. The same information is saved as a file in the given folder. theta : ndarray Parameter points used for sampling (and evaluation of the joint score) with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. t_xz : ndarray Joint score evaluated at theta with shape `(n_samples, n_parameters + n_nuisance_parameters)` (if nuisance_score is True) or `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. effective_n_samples : int Effective number of samples, defined as 1/max(event_probabilities), where event_probabilities are the fractions of the cross section carried by each event. """ if log_message: logger.info( "Extracting training sample for local score regression. Sampling and score evaluation according to %s", self._format_sampling(theta), ) create_missing_folders([folder]) # Check setup if nuisance_score == "auto": nuisance_score = self.nuisance_morpher is not None if self.morpher is None: raise RuntimeError("No morphing setup loaded. Cannot calculate score.") if self.nuisance_morpher is None and nuisance_score: raise RuntimeError("No nuisance parameters defined. Cannot calculate nuisance score.") # Parameters parsed_thetas, n_samples_per_theta = self._parse_theta(theta, n_samples) parsed_nus = self._parse_nu(nu, len(parsed_thetas)) sets = self._build_sets([parsed_thetas], [parsed_nus]) # Augmented data (gold) augmented_data_definitions = [("score", 0)] # Start x, augmented_data, (theta,), effective_n_samples = self._sample( sets=sets, n_samples_per_set=n_samples_per_theta, augmented_data_definitions=augmented_data_definitions, nuisance_score=nuisance_score, use_train_events=not switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) t_xz = augmented_data[0] # Save data if filename is not None and folder is not None: np.save(folder + "/theta_" + filename + ".npy", theta) np.save(folder + "/x_" + filename + ".npy", x) np.save(folder + "/t_xz_" + filename + ".npy", t_xz) return x, theta, t_xz, min(effective_n_samples)
[docs] def sample_train_density( self, theta, n_samples, nu=None, sample_only_from_closest_benchmark=False, folder=None, filename=None, nuisance_score="auto", test_split=0.2, switch_train_test_events=False, n_processes=1, n_eff_forced=None, ): """ Extracts training samples x ~ p(x|theta) as well as the joint score t(x, z|theta), where theta is sampled from a prior. This can be used for inference methods such as SCANDAL. Parameters ---------- theta : tuple Tuple (type, value) that defines the numerator parameter point or prior over parameter points for the sampling. Pass the output of the functions `constant_benchmark_theta()`, `multiple_benchmark_thetas()`, `constant_morphing_theta()`, `multiple_morphing_thetas()`, or `random_morphing_thetas()`. n_samples : int Total number of events to be drawn. nu : None or tuple, optional Tuple (type, value) that defines the nuisance parameter point or prior over parameter points for the sampling. Default value: None folder : str or None Path to the folder where the resulting samples should be saved (ndarrays in .npy format). Default value: None. filename : str or None Filenames for the resulting samples. A prefix such as 'x' or 'theta0' as well as the extension '.npy' will be added automatically. Default value: None. nuisance_score : bool or "auto", optional If True, the score with respect to the nuisance parameters (at the default position) will also be calculated. If False, only the score with respect to the physics parameters is calculated. For "auto", the nuisance score will be calculated if a nuisance setup is defined. Default: True. test_split : float or None, optional Fraction of events reserved for the evaluation sample (that will not be used for any training samples). Default value: 0.2. switch_train_test_events : bool, optional If True, this function generates a training sample from the events normally reserved for test samples. Default value: False. n_processes : None or int, optional If None or larger than 1, MadMiner will use multiprocessing to parallelize the sampling. In this case, n_workers sets the number of jobs running in parallel, and None will use the number of CPUs. Default value: 1. n_eff_forced : float, optional If not None, MadMiner will require the relative weights of the events to be smaller than 1/n_eff_forced and ignore other events. This can help to reduce statistical effects caused by a small number of events with very large weights obtained by the morphing procedure. Default value: None Returns ------- x : ndarray Observables with shape `(n_samples, n_observables)`. The same information is saved as a file in the given folder. theta : ndarray Parameter points used for sampling (and evaluation of the joint score) with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. t_xz : ndarray Joint score evaluated at theta with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. effective_n_samples : int Effective number of samples, defined as 1/max(event_probabilities), where event_probabilities are the fractions of the cross section carried by each event. """ logger.info( "Extracting training sample for non-local score-based methods. Sampling and score evaluation according " "to %s", theta, ) return self.sample_train_local( theta=theta, n_samples=n_samples, nu=nu, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, folder=folder, filename=filename, nuisance_score=nuisance_score, test_split=test_split, switch_train_test_events=switch_train_test_events, n_processes=n_processes, log_message=False, n_eff_forced=n_eff_forced, )
[docs] def sample_train_ratio( self, theta0, theta1, n_samples, nu0=None, nu1=None, sample_only_from_closest_benchmark=False, folder=None, filename=None, nuisance_score="auto", test_split=0.2, switch_train_test_events=False, n_processes=1, return_individual_n_effective=False, n_eff_forced=None, ): """ Extracts training samples `x ~ p(x|theta0)` and `x ~ p(x|theta1)` together with the class label `y`, the joint likelihood ratio `r(x,z|theta0, theta1)`, and, if morphing is set up, the joint score `t(x,z|theta0)`. This information can be used in inference methods such as CARL, ROLR, CASCAL, and RASCAL. Parameters ---------- theta0 : tuple Tuple (type, value) that defines the numerator parameter point or prior over parameter points for the sampling. Pass the output of the functions `constant_benchmark_theta()`, `multiple_benchmark_thetas()`, `constant_morphing_theta()`, `multiple_morphing_thetas()`, or `random_morphing_thetas()`. theta1 : tuple Tuple (type, value) that defines the denominator parameter point or prior over parameter points for the sampling. Pass the output of the functions `constant_benchmark_theta()`, `multiple_benchmark_thetas()`, `constant_morphing_theta()`, `multiple_morphing_thetas()`, or `random_morphing_thetas()`. n_samples : int Total number of events to be drawn. nu0 : None or tuple, optional Tuple (type, value) that defines the numerator nuisance parameter point or prior over parameter points for the sampling. Default value: None nu1 : None or tuple, optional Tuple (type, value) that defines the denominator nuisance parameter point or prior over parameter points for the sampling. Default value: None folder : str or None Path to the folder where the resulting samples should be saved (ndarrays in .npy format). Default value: None. filename : str or None Filenames for the resulting samples. A prefix such as 'x' or 'theta0' as well as the extension '.npy' will be added automatically. Default value: None. nuisance_score : bool or "auto", optional If True, the score with respect to the nuisance parameters (at the default position) will also be calculated. If False, only the score with respect to the physics parameters is calculated. For "auto", the nuisance score will be calculated if a nuisance setup is defined. Default: True. test_split : float or None, optional Fraction of events reserved for the evaluation sample (that will not be used for any training samples). Default value: 0.2. switch_train_test_events : bool, optional If True, this function generates a training sample from the events normally reserved for test samples. Default value: False. n_processes : None or int, optional If None or larger than 1, MadMiner will use multiprocessing to parallelize the sampling. In this case, n_workers sets the number of jobs running in parallel, and None will use the number of CPUs. Default value: 1. n_eff_forced : float, optional If not None, MadMiner will require the relative weights of the events to be smaller than 1/n_eff_forced and ignore other events. This can help to reduce statistical effects caused by a small number of events with very large weights obtained by the morphing procedure. Default value: None Returns ------- x : ndarray Observables with shape `(n_samples, n_observables)`. The same information is saved as a file in the given folder. theta0 : ndarray Numerator parameter points with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. theta1 : ndarray Denominator parameter points with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. y : ndarray Class label with shape `(n_samples, n_parameters)`. `y=0` (`1`) for events sample from the numerator (denominator) hypothesis. The same information is saved as a file in the given folder. r_xz : ndarray Joint likelihood ratio with shape `(n_samples,)`. The same information is saved as a file in the given folder. t_xz : ndarray or None If morphing is set up, the joint score evaluated at theta0 with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. If morphing is not set up, None is returned (and no file is saved). effective_n_samples : int Effective number of samples, defined as 1/max(event_probabilities), where event_probabilities are the fractions of the cross section carried by each event. """ logger.info( "Extracting training sample for ratio-based methods. Numerator hypothesis: %s, denominator " "hypothesis: %s", self._format_sampling(theta0), self._format_sampling(theta1), ) create_missing_folders([folder]) # Check setup if nuisance_score == "auto": nuisance_score = self.nuisance_morpher is not None if self.morpher is None: logging.warning("No morphing setup loaded. Cannot calculate joint score.") if self.nuisance_morpher is None and nuisance_score: raise RuntimeError("No nuisance parameters defined. Cannot calculate nuisance score.") # Augmented data (gold) augmented_data_definitions = [("ratio", 0, 1)] if self.morpher is not None: augmented_data_definitions.append(("score", 0)) # Thetas for theta0 sampling parsed_theta0s, n_samples_per_theta0 = self._parse_theta(theta0, n_samples // 2) parsed_theta1s, n_samples_per_theta1 = self._parse_theta(theta1, n_samples // 2) parsed_nu0s = self._parse_nu(nu0, len(parsed_theta0s)) parsed_nu1s = self._parse_nu(nu1, len(parsed_theta1s)) sets = self._build_sets([parsed_theta0s, parsed_theta1s], [parsed_nu0s, parsed_nu1s]) n_samples_per_theta = min(n_samples_per_theta0, n_samples_per_theta1) # Start for theta0 if self.morpher is None: x0, (r_xz0,), (theta0_0, theta1_0), n_effective_samples_0 = self._sample( sets=sets, sampling_index=0, n_samples_per_set=n_samples_per_theta, augmented_data_definitions=augmented_data_definitions, nuisance_score=nuisance_score, use_train_events=not switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) t_xz0 = None else: x0, (r_xz0, t_xz0), (theta0_0, theta1_0), n_effective_samples_0 = self._sample( sets=sets, sampling_index=0, n_samples_per_set=n_samples_per_theta, augmented_data_definitions=augmented_data_definitions, nuisance_score=nuisance_score, use_train_events=not switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) if return_individual_n_effective: n_effective_samples_0 = np.repeat(n_effective_samples_0, n_samples_per_theta) # Thetas for theta1 sampling (could be different if num or denom are random) parsed_theta0s, n_samples_per_theta0 = self._parse_theta(theta0, n_samples // 2) parsed_theta1s, n_samples_per_theta1 = self._parse_theta(theta1, n_samples // 2) parsed_nu0s = self._parse_nu(nu0, len(parsed_theta0s)) parsed_nu1s = self._parse_nu(nu1, len(parsed_theta1s)) sets = self._build_sets([parsed_theta0s, parsed_theta1s], [parsed_nu0s, parsed_nu1s]) n_samples_per_theta = min(n_samples_per_theta0, n_samples_per_theta1) # Start for theta1 if self.morpher is None: x1, (r_xz1,), (theta0_1, theta1_1), n_effective_samples_1 = self._sample( sets=sets, sampling_index=1, n_samples_per_set=n_samples_per_theta, augmented_data_definitions=augmented_data_definitions, nuisance_score=nuisance_score, use_train_events=not switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) t_xz1 = None else: x1, (r_xz1, t_xz1), (theta0_1, theta1_1), n_effective_samples_1 = self._sample( sets=sets, sampling_index=1, n_samples_per_set=n_samples_per_theta, augmented_data_definitions=augmented_data_definitions, nuisance_score=nuisance_score, use_train_events=not switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) if return_individual_n_effective: n_effective_samples_1 = np.repeat(n_effective_samples_1, n_samples_per_theta) # Combine x = np.vstack([x0, x1]) r_xz = np.vstack([r_xz0, r_xz1]) if self.morpher is not None: t_xz = np.vstack([t_xz0, t_xz1]) else: t_xz = None theta0 = np.vstack([theta0_0, theta0_1]) theta1 = np.vstack([theta1_0, theta1_1]) y = np.zeros(x.shape[0]) y[x0.shape[0] :] = 1.0 n_effective = np.hstack((n_effective_samples_0, n_effective_samples_1)) # Shuffle x, r_xz, t_xz, theta0, theta1, y, n_effective = shuffle(x, r_xz, t_xz, theta0, theta1, y, n_effective) # y shape y = y.reshape((-1, 1)) # Save data if filename is not None and folder is not None: np.save(folder + "/theta0_" + filename + ".npy", theta0) np.save(folder + "/theta1_" + filename + ".npy", theta1) np.save(folder + "/x_" + filename + ".npy", x) np.save(folder + "/y_" + filename + ".npy", y) np.save(folder + "/r_xz_" + filename + ".npy", r_xz) if self.morpher is not None: np.save(folder + "/t_xz_" + filename + ".npy", t_xz) if not return_individual_n_effective: n_effective = np.min(n_effective) return x, theta0, theta1, y, r_xz, t_xz, n_effective
[docs] def sample_train_more_ratios( self, theta0, theta1, n_samples, nu0=None, nu1=None, sample_only_from_closest_benchmark=False, folder=None, filename=None, additional_thetas=None, nuisance_score="auto", test_split=0.2, switch_train_test_events=False, n_processes=1, n_eff_forced=None, ): """ Extracts training samples `x ~ p(x|theta0)` and `x ~ p(x|theta1)` together with the class label `y`, the joint likelihood ratio `r(x,z|theta0, theta1)`, and the joint score `t(x,z|theta0)`. This information can be used in inference methods such as CARL, ROLR, CASCAL, and RASCAL. With the keyword `additional_thetas`, this function allows to extract joint ratios and scores at more parameter points than just `theta0` and `theta1`. This additional information can be used efficiently in the setup with a "doubly parameterized" likelihood ratio estimator that models the dependence on both the numerator and denominator hypothesis. Parameters ---------- theta0 : Tuple (type, value) that defines the numerator parameter point or prior over parameter points for the sampling. Pass the output of the functions `constant_benchmark_theta()`, `multiple_benchmark_thetas()`, `constant_morphing_theta()`, `multiple_morphing_thetas()`, or `random_morphing_thetas()`. theta1 : Tuple (type, value) that defines the denominator parameter point or prior over parameter points for the sampling. Pass the output of the functions `constant_benchmark_theta()`, `multiple_benchmark_thetas()`, `constant_morphing_theta()`, `multiple_morphing_thetas()`, or `random_morphing_thetas()`. n_samples : int Total number of events to be drawn. nu0 : None or tuple, optional Tuple (type, value) that defines the numerator nuisance parameter point or prior over parameter points for the sampling. Default value: None nu1 : None or tuple, optional Tuple (type, value) that defines the denominator nuisance parameter point or prior over parameter points for the sampling. Default value: None folder : str or None Path to the folder where the resulting samples should be saved (ndarrays in .npy format). Default value: None. filename : str or None Filenames for the resulting samples. A prefix such as 'x' or 'theta0' as well as the extension '.npy' will be added automatically. Default value: None. additional_thetas : list of tuple or None list of tuples `(type, value)` that defines additional theta points at which ratio and score are evaluated, and which are then used to create additional training data points. These can be efficiently used only in the "doubly parameterized" setup where a likelihood ratio estimator models the dependence of the likelihood ratio on both the numerator and denominator hypothesis. Pass the output of the helper functions `constant_benchmark_theta()`, `multiple_benchmark_thetas()`, `constant_morphing_theta()`, `multiple_morphing_thetas()`, or `random_morphing_thetas()`. Default value: None. nuisance_score : bool or "auto", optional If True, the score with respect to the nuisance parameters (at the default position) will also be calculated. If False, only the score with respect to the physics parameters is calculated. For "auto", the nuisance score will be calculated if a nuisance setup is defined. Default: True. test_split : float or None, optional Fraction of events reserved for the evaluation sample (that will not be used for any training samples). Default value: 0.2. switch_train_test_events : bool, optional If True, this function generates a training sample from the events normally reserved for test samples. Default value: False. n_processes : None or int, optional If None or larger than 1, MadMiner will use multiprocessing to parallelize the sampling. In this case, n_workers sets the number of jobs running in parallel, and None will use the number of CPUs. Default value: 1. n_eff_forced : float, optional If not None, MadMiner will require the relative weights of the events to be smaller than 1/n_eff_forced and ignore other events. This can help to reduce statistical effects caused by a small number of events with very large weights obtained by the morphing procedure. Default value: None Returns ------- x : ndarray Observables with shape `(n_samples, n_observables)`. The same information is saved as a file in the given folder. theta0 : ndarray Numerator parameter points with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. theta1 : ndarray Denominator parameter points with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. y : ndarray Class label with shape `(n_samples, n_parameters)`. `y=0` (`1`) for events sample from the numerator (denominator) hypothesis. The same information is saved as a file in the given folder. r_xz : ndarray Joint likelihood ratio with shape `(n_samples,)`. The same information is saved as a file in the given folder. t_xz : ndarray Joint score evaluated at theta0 with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. effective_n_samples : int Effective number of samples, defined as 1/max(event_probabilities), where event_probabilities are the fractions of the cross section carried by each event. """ logger.info( "Extracting training sample for ratio-based methods. Numerator hypothesis: %s, denominator " "hypothesis: %s", self._format_sampling(theta0), self._format_sampling(theta1), ) create_missing_folders([folder]) # Check setup if nuisance_score == "auto": nuisance_score = self.nuisance_morpher is not None if self.morpher is None: raise RuntimeError("No morphing setup loaded. Cannot calculate score.") if self.nuisance_morpher is None and nuisance_score: raise RuntimeError("No nuisance parameters defined. Cannot calculate nuisance score.") if additional_thetas is None: additional_thetas = [] n_additional_thetas = len(additional_thetas) # Augmented data (gold) augmented_data_definitions_0 = [("ratio", 0, 1), ("score", 0), ("score", 1)] augmented_data_definitions_1 = [("ratio", 0, 1), ("score", 0), ("score", 1)] for i in range(n_additional_thetas): augmented_data_definitions_0.append(("ratio", 0, i + 2)) augmented_data_definitions_0.append(("score", i + 2)) augmented_data_definitions_1.append(("ratio", i + 2, 1)) augmented_data_definitions_1.append(("score", i + 2)) # Parse thetas for theta0 sampling parsed_thetas = [] parsed_nus = [] n_samples_per_theta = 1000000 parsed_theta0s, this_n_samples = self._parse_theta(theta0, n_samples // 2) parsed_nu0s = self._parse_nu(nu0, len(parsed_theta0s)) parsed_thetas.append(parsed_theta0s) parsed_nus.append(parsed_nu0s) n_samples_per_theta = min(this_n_samples, n_samples_per_theta) parsed_theta1s, this_n_samples = self._parse_theta(theta1, n_samples // 2) parsed_nu1s = self._parse_nu(nu1, len(parsed_theta1s)) parsed_thetas.append(parsed_theta1s) parsed_nus.append(parsed_nu1s) n_samples_per_theta = min(this_n_samples, n_samples_per_theta) for additional_theta in additional_thetas: additional_parsed_thetas, this_n_samples = self._parse_theta(additional_theta, n_samples // 2) parsed_thetas.append(additional_parsed_thetas) additional_parsed_nu = self._parse_nu(nu1, len(additional_parsed_thetas)) parsed_nus.append(additional_parsed_nu) n_samples_per_theta = min(this_n_samples, n_samples_per_theta) sets = self._build_sets(parsed_thetas, parsed_nus) # Start for theta0 x_0, augmented_data_0, thetas_0, n_effective_samples_0 = self._sample( sets=sets, n_samples_per_set=n_samples_per_theta, augmented_data_definitions=augmented_data_definitions_0, sampling_index=0, nuisance_score=nuisance_score, use_train_events=not switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) n_actual_samples = x_0.shape[0] # Analyse theta values from theta0 run theta0_0 = thetas_0[0] theta1_0 = thetas_0[1] thetas_eval = thetas_0[2:] # Analyse augmented data from theta0 run r_xz_0 = augmented_data_0[0] t_xz0_0 = augmented_data_0[1] t_xz1_0 = augmented_data_0[2] r_xz_eval = [] t_xz_eval = [] for i, theta_eval in enumerate(thetas_eval): r_xz_eval.append(augmented_data_0[3 + i * 2]) t_xz_eval.append(augmented_data_0[4 + i * 2]) x_0 = np.vstack([x_0 for _ in range(1 + n_additional_thetas)]) r_xz_0 = np.vstack([r_xz_0] + r_xz_eval) t_xz0_0 = np.vstack([t_xz0_0 for _ in range(1 + n_additional_thetas)]) t_xz1_0 = np.vstack([t_xz1_0] + t_xz_eval) theta0_0 = np.vstack([theta0_0 for _ in range(1 + n_additional_thetas)]) theta1_0 = np.vstack([theta1_0] + thetas_eval) # Parse thetas for theta1 sampling parsed_thetas = [] parsed_nus = [] n_samples_per_theta = 1000000 parsed_thetas0, this_n_samples = self._parse_theta(theta0, n_samples // 2) parsed_nu0s = self._parse_nu(nu0, len(parsed_theta0s)) parsed_thetas.append(parsed_thetas0) parsed_nus.append(parsed_nu0s) n_samples_per_theta = min(this_n_samples, n_samples_per_theta) parsed_thetas1, this_n_samples = self._parse_theta(theta1, n_samples // 2) parsed_nu1s = self._parse_nu(nu1, len(parsed_theta1s)) parsed_thetas.append(parsed_thetas1) parsed_nus.append(parsed_nu1s) n_samples_per_theta = min(this_n_samples, n_samples_per_theta) for additional_theta in additional_thetas: additional_parsed_thetas, this_n_samples = self._parse_theta(additional_theta, n_samples // 2) additional_parsed_nu = self._parse_nu(nu0, len(additional_parsed_thetas)) parsed_thetas.append(additional_parsed_thetas) parsed_nus.append(additional_parsed_nu) n_samples_per_theta = min(this_n_samples, n_samples_per_theta) sets = self._build_sets(parsed_thetas, parsed_nus) # Start for theta1 x_1, augmented_data_1, thetas_1, n_effective_samples_1 = self._sample( sets=sets, n_samples_per_set=n_samples_per_theta, augmented_data_definitions=augmented_data_definitions_1, sampling_index=1, nuisance_score=nuisance_score, use_train_events=not switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) n_actual_samples += x_1.shape[0] # Analyse theta values from theta1 run theta0_1 = thetas_1[0] theta1_1 = thetas_1[1] thetas_eval = thetas_1[2:] # Analyse augmented data from theta1 run r_xz_1 = augmented_data_1[0] t_xz0_1 = augmented_data_1[1] t_xz1_1 = augmented_data_1[2] r_xz_eval = [] t_xz_eval = [] for i, theta_eval in enumerate(thetas_eval): r_xz_eval.append(augmented_data_1[3 + i * 2]) t_xz_eval.append(augmented_data_1[4 + i * 2]) x_1 = np.vstack([x_1 for _ in range(1 + n_additional_thetas)]) r_xz_1 = np.vstack([r_xz_1] + r_xz_eval) t_xz0_1 = np.vstack([t_xz0_1] + t_xz_eval) t_xz1_1 = np.vstack([t_xz1_1 for _ in range(1 + n_additional_thetas)]) theta0_1 = np.vstack([theta0_1] + thetas_eval) theta1_1 = np.vstack([theta1_1 for _ in range(1 + n_additional_thetas)]) # Combine x = np.vstack([x_0, x_1]) r_xz = np.vstack([r_xz_0, r_xz_1]) t_xz0 = np.vstack([t_xz0_0, t_xz0_1]) t_xz1 = np.vstack([t_xz1_0, t_xz1_1]) theta0 = np.vstack([theta0_0, theta0_1]) theta1 = np.vstack([theta1_0, theta1_1]) y = np.zeros(x.shape[0]) y[x_0.shape[0] :] = 1.0 if n_additional_thetas > 0: logger.info( "Oversampling: created %s training samples from %s original unweighted events", x.shape[0], n_actual_samples, ) # Shuffle x, r_xz, t_xz0, t_xz1, theta0, theta1, y = shuffle(x, r_xz, t_xz0, t_xz1, theta0, theta1, y) # y shape y = y.reshape((-1, 1)) # Save data if filename is not None and folder is not None: np.save(folder + "/theta0_" + filename + ".npy", theta0) np.save(folder + "/theta1_" + filename + ".npy", theta1) np.save(folder + "/x_" + filename + ".npy", x) np.save(folder + "/y_" + filename + ".npy", y) np.save(folder + "/r_xz_" + filename + ".npy", r_xz) np.save(folder + "/t_xz0_" + filename + ".npy", t_xz0) np.save(folder + "/t_xz1_" + filename + ".npy", t_xz1) return x, theta0, theta1, y, r_xz, t_xz0, t_xz1, min(min(n_effective_samples_0), min(n_effective_samples_1))
[docs] def sample_test( self, theta, n_samples, nu=None, sample_only_from_closest_benchmark=False, folder=None, filename=None, test_split=0.2, switch_train_test_events=False, n_processes=1, n_eff_forced=None, ): """ Extracts evaluation samples `x ~ p(x|theta)` without any augmented data. Parameters ---------- theta : tuple Tuple (type, value) that defines the parameter point or prior over parameter points for the sampling. Pass the output of the functions `constant_benchmark_theta()`, `multiple_benchmark_thetas()`, `constant_morphing_theta()`, `multiple_morphing_thetas()`, or `random_morphing_thetas()`. n_samples : int Total number of events to be drawn. nu : None or tuple, optional Tuple (type, value) that defines the nuisance parameter point or prior over parameter points for the sampling. Default value: None folder : str or None Path to the folder where the resulting samples should be saved (ndarrays in .npy format). Default value: None. filename : str or None Filenames for the resulting samples. A prefix such as 'x' or 'theta0' as well as the extension '.npy' will be added automatically. Default value: None. test_split : float or None, optional Fraction of events reserved for the evaluation sample (that will not be used for any training samples). Default value: 0.2. switch_train_test_events : bool, optional If True, this function generates a test sample from the events normally reserved for training samples. Default value: False. n_processes : None or int, optional If None or larger than 1, MadMiner will use multiprocessing to parallelize the sampling. In this case, n_workers sets the number of jobs running in parallel, and None will use the number of CPUs. Default value: 1. Returns ------- x : ndarray Observables with shape `(n_samples, n_observables)`. The same information is saved as a file in the given folder. theta : ndarray Parameter points used for sampling with shape `(n_samples, n_parameters)`. The same information is saved as a file in the given folder. effective_n_samples : int Effective number of samples, defined as 1/max(event_probabilities), where event_probabilities are the fractions of the cross section carried by each event. """ logger.info("Extracting evaluation sample. Sampling according to %s", self._format_sampling(theta)) create_missing_folders([folder]) # Thetas parsed_thetas, n_samples_per_theta = self._parse_theta(theta, n_samples) parsed_nus = self._parse_nu(nu, len(parsed_thetas)) sets = self._build_sets([parsed_thetas], [parsed_nus]) # Extract information x, _, (theta,), n_effective_samples = self._sample( sets=sets, n_samples_per_set=n_samples_per_theta, use_train_events=switch_train_test_events, test_split=test_split, n_processes=n_processes, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, ) # Save data if filename is not None and folder is not None: np.save(folder + "/theta_" + filename + ".npy", theta) np.save(folder + "/x_" + filename + ".npy", x) return x, theta, min(n_effective_samples)
[docs] def cross_sections(self, theta, nu=None): """ Calculates the total cross sections for all specified thetas. Parameters ---------- theta : tuple Tuple (type, value) that defines the parameter point or prior over parameter points at which the cross section is calculated. Pass the output of the functions `benchmark()`, `benchmarks()`, `morphing_point()`, `morphing_points()`, or `random_morphing_points()`. nu : tuple or None, optional Tuple (type, value) that defines the nuisance parameter point or prior over nuisance parameter points at which the cross section is calculated. Pass the output of the functions `benchmark()`, `benchmarks()`, `morphing_point()`, `morphing_points()`, or `random_morphing_points()`. Default valuee: None. Returns ------- thetas : ndarray Parameter points with shape `(n_thetas, n_parameters)` or `(n_thetas, n_parameters + n_nuisance_parameters)`. xsecs : ndarray Total cross sections in pb with shape `(n_thetas, )`. xsec_uncertainties : ndarray Statistical uncertainties on the total cross sections in pb with shape `(n_thetas, )`. """ logger.info("Starting cross-section calculation") parsed_thetas, _ = self._parse_theta(theta, None) theta_values = np.asarray([self._get_theta_value(parsed_theta) for parsed_theta in parsed_thetas]) if nu is not None: parsed_nus = self._parse_nu(nu, len(parsed_thetas)) nu_values = np.asarray([self._get_nu_value(parsed_nu for parsed_nu in parsed_nus)]) param_values = np.hstack((theta_values, nu_values)) else: parsed_nus = None param_values = theta_values xsecs, uncertainties = self.xsecs(thetas=parsed_thetas, nus=parsed_nus) return param_values, xsecs, uncertainties
def _sample( self, sets, n_samples_per_set, sampling_index=0, sample_only_from_closest_benchmark=False, augmented_data_definitions=None, nuisance_score=True, use_train_events=True, test_split=0.2, verbose="some", n_processes=1, update_patience=0.01, force_update_patience=15 * 60.0, n_eff_forced=None, ): """ Low-level function for the extraction of information from the event samples. Do not use this function directly. The sampling is organized in terms of "sets". For each set, a number of parameter points (thetas and nus) is fixed, and `n_samples_per_theta` events are sampled from one of them. Parameters ---------- sets : list of list of tuples The outer list goes over sets, the inner list goes over parameter points, the tuples have the form (theta, nu). Here theta can be a str or int (for benchmarks) or ndarray (with morphing), while nu can be None (for nominal value) or ndarray (for nuisance morphing). n_samples_per_set : int Number of samples to be drawn per entry in theta_sampling_types. sampling_index : int Marking the index of the theta set defined through thetas_types and thetas_values that should be used for sampling. Default value: 0. augmented_data_definitions : list of tuple or None Each tuple can either be ('ratio', num_theta, den_theta) or ('score', theta), where num_theta, den_theta, and theta are indexes marking which of the theta sets defined through thetas_types and thetas_values is used. Default value: None. nuisance_score : bool, optional If True, any joint score in the augmented data definitions is also calculated with respect to the nuisance parameters. Default value: True. use_train_events : bool, optional Decides whether to use the train or test split of the events. Default value: True. test_split : float or None, optional Fraction of events reserved for the evaluation sample (that will not be used for any training samples). Default value: 0.2. n_processes : None or int, optional If None or larger than 1, MadMiner will use multiprocessing to parallelize the sampling. In this case, n_workers sets the number of jobs running in parallel, and None will use the number of CPUs. Default value: 1. update_patience : float, optional Wait time (in s) between log update checks if n_workers > 1 (or None). Default value: 0.01 force_update_patience : float, optional Wait time (in s) between log updates (independent of actual progress) if n_workers > 1 (or None). Default value: 15 * 60. (15 minutes). n_eff_forced : float, optional If not None, MadMiner will require the relative weights of the events to be smaller than 1/n_eff_forced and ignore other events. This can help to reduce statistical effects caused by a small number of events with very large weights obtained by the morphing procedure. Default value: None Returns ------- x : ndarray Observables. augmented_data : list of ndarray Augmented data. theta_values : list of ndarray Parameter values. """ logger.debug("Starting sample extraction") if n_eff_forced is not None: logger.warning( "Trimmed sampling is turned on (n_eff_forced is not None). This option is potentially " "since requiring large values of n_eff_forced can significantly distort distributions." "Check if manually that the sampled distributions are still correct." ) # Check inputs if augmented_data_definitions is None: augmented_data_definitions = [] n_sets, n_params = self._check_sets(sets) # What needs to be calculated? needs_gradients = self._check_gradient_need(augmented_data_definitions) # Prepare outputs all_x = [] all_augmented_data = [[] for _ in augmented_data_definitions] all_thetas = [[] for _ in range(n_params)] all_nus = [[] for _ in range(n_params)] all_effective_n_samples = [] n_stats_warnings = 0 n_neg_weights_warnings = 0 n_too_large_weights_warnings = 0 # Multiprocessing approach if n_processes is None or n_processes > 1: if n_processes is None: n_processes = multiprocessing.cpu_count() job = partial( self._sample_set, n_samples=n_samples_per_set, augmented_data_definitions=augmented_data_definitions, sampling_index=sampling_index, needs_gradients=needs_gradients, use_train_events=use_train_events, test_split=test_split, nuisance_score=nuisance_score, n_stats_warnings=1000, n_neg_weights_warnings=1000, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) logger.info("Starting sampling jobs in parallel, using %s processes", n_processes) pool = multiprocessing.Pool(processes=n_processes) r = pool.map_async(job, sets, chunksize=1) next_verbose = 0 verbose_steps = n_sets // 10 last_update = time.time() while not r.ready(): n_done = max(n_sets - r._number_left * r._chunksize, 0) if n_done >= next_verbose or time.time() - last_update > force_update_patience: logger.info("%s / %s jobs done", max(n_sets - r._number_left * r._chunksize, 0), n_sets) last_update = time.time() while next_verbose <= n_done: next_verbose += verbose_steps time.sleep(update_patience) r.wait() logger.info("All jobs done!") for x, thetas, nus, augmented_data, eff_n_samples, _, _, _ in r.get(): all_x.append(x) for i, values in enumerate(augmented_data): all_augmented_data[i].append(values) for i, values in enumerate(thetas): all_thetas[i].append(values) for i, values in enumerate(nus): all_nus[i].append(values) all_effective_n_samples.append(eff_n_samples) # Serial approach else: logger.info("Starting sampling serially") # Verbosity if verbose == "all": # Print output after every epoch n_sets_verbose = 1 elif verbose == "many": # Print output after 2%, 4%, ..., 100% progress n_sets_verbose = max(int(round(n_sets / 50, 0)), 1) elif verbose == "some": # Print output after 10%, 20%, ..., 100% progress n_sets_verbose = max(int(round(n_sets / 20, 0)), 1) elif verbose == "few": # Print output after 20%, 40%, ..., 100% progress n_sets_verbose = max(int(round(n_sets / 5, 0)), 1) elif verbose == "none": # Never print output n_sets_verbose = n_sets + 2 else: raise ValueError("Unknown value %s for keyword verbose", verbose) logger.debug("Will print training progress every %s sets", n_sets_verbose) # Loop over sets for i_set, set_ in enumerate(sets): if (i_set + 1) % n_sets_verbose == 0: logger.info("Sampling from parameter point %s / %s", i_set + 1, n_sets) else: logger.debug("Sampling from parameter point %s / %s", i_set + 1, n_sets) x, thetas, nus, augmented_data, eff_n_samples, n_stats_warnings, n_neg_weights_warnings, n_too_large_weights_warnings = self._sample_set( set_, n_samples=n_samples_per_set, augmented_data_definitions=augmented_data_definitions, sampling_index=sampling_index, needs_gradients=needs_gradients, use_train_events=use_train_events, test_split=test_split, nuisance_score=nuisance_score, n_stats_warnings=n_stats_warnings, n_too_large_weights_warnings=n_too_large_weights_warnings, n_neg_weights_warnings=n_neg_weights_warnings, sample_only_from_closest_benchmark=sample_only_from_closest_benchmark, n_eff_forced=n_eff_forced, ) all_x.append(x) for i, values in enumerate(augmented_data): all_augmented_data[i].append(values) for i, values in enumerate(thetas): all_thetas[i].append(values) for i, values in enumerate(nus): all_nus[i].append(values) all_effective_n_samples.append(eff_n_samples) # Combine and return results all_x = np.vstack(all_x) for i, values in enumerate(all_thetas): all_thetas[i] = np.vstack(values) for i, values in enumerate(all_nus): all_nus[i] = np.vstack(values) for i, values in enumerate(all_augmented_data): all_augmented_data[i] = np.vstack(values) all_effective_n_samples = np.hstack(all_effective_n_samples) all_thetas = self._combine_thetas_nus(all_thetas, all_nus) # Report effective number of samples self._report_effective_n_samples(all_effective_n_samples) return all_x, all_augmented_data, all_thetas, all_effective_n_samples @staticmethod def _check_sets(sets): n_sets = len(sets) n_params = None for set_ in sets: if n_params is None: n_params = len(set_) assert len(set_) == n_params for param_point in set_: assert len(param_point) == 2 return n_sets, n_params @staticmethod def _check_gradient_need(augmented_data_definitions): for definition in augmented_data_definitions: if definition[0] == "score": return True return False def _sample_set( self, set_, n_samples, sample_only_from_closest_benchmark, augmented_data_definitions, sampling_index=0, needs_gradients=True, nuisance_score=True, use_train_events=True, test_split=0.2, n_stats_warnings=0, n_neg_weights_warnings=0, n_too_large_weights_warnings=0, n_eff_forced=None, ): # Parse thetas and nus thetas, nus = [], [] theta_values, nu_values = [], [] theta_matrices, theta_gradient_matrices = [], [] logger.debug("Drawing %s events for the following parameter points:", n_samples) for i_param, (theta, nu) in enumerate(set_): thetas.append(theta) nus.append(nu) theta_value = self._get_theta_value(theta) theta_value = np.broadcast_to(theta_value, (n_samples, theta_value.size)) theta_values.append(theta_value) if nu is None: nu_value = None nu_values.append([[None] for _ in range(n_samples)]) else: nu_value = self._get_nu_value(nu) nu_values.append(np.broadcast_to(nu_value, (n_samples, nu_value.size))) theta_matrices.append(self._get_theta_benchmark_matrix(theta)) if needs_gradients: theta_gradient_matrices.append(self._get_dtheta_benchmark_matrix(theta)) if i_param == sampling_index: logger.debug(" %s: theta = %s, nu = %s (sampling)", i_param, theta_value[0, :], nu_value) else: logger.debug(" %s: theta = %s, nu = %s", i_param, theta_value[0, :], nu_value) theta_value_sampling = theta_values[sampling_index][0, :] # Cross sections xsecs, xsec_uncertainties = self.xsecs( thetas, nus, events="train" if use_train_events else "test", test_split=test_split, generated_close_to=None if not sample_only_from_closest_benchmark else theta_value_sampling, ) if needs_gradients: xsec_gradients = self.xsec_gradients( thetas, nus, gradients="all" if nuisance_score else "theta", events="train" if use_train_events else "test", test_split=test_split, generated_close_to=None if not sample_only_from_closest_benchmark else theta_value_sampling, ) else: xsec_gradients = None # Report large uncertainties if xsec_uncertainties[sampling_index] > 0.1 * xsecs[sampling_index]: n_stats_warnings += 1 if n_stats_warnings <= 1: logger.warning( "Large statistical uncertainty on the total cross section when sampling from theta = %s: " "(%4f +/- %4f) pb (%s %%). Skipping these warnings in the future...", theta_values[sampling_index][0], xsecs[sampling_index], xsec_uncertainties[sampling_index], 100.0 * xsec_uncertainties[sampling_index] / xsecs[sampling_index], ) # Prepare output done = np.zeros(n_samples, dtype=np.bool) x = np.zeros((n_samples, self.n_observables)) augmented_data = [] for definition in augmented_data_definitions: if definition[0] == "ratio": augmented_data.append(np.zeros((n_samples, 1))) elif definition[0] == "score": if nuisance_score: augmented_data.append(np.zeros((n_samples, self.n_parameters + self.n_nuisance_parameters))) else: augmented_data.append(np.zeros((n_samples, self.n_parameters))) largest_event_probability = 0.0 # Main sampling loop start_event, end_event, correction_factor = self._train_test_split(use_train_events, test_split) while not np.all(done): # Draw random numbers in [0, 1] u = np.random.rand(n_samples) # Shape: (n_samples,) cumulative_p = np.array([0.0]) # Loop over weighted events for x_batch, weights_benchmarks_batch in self.event_loader( start=start_event, end=end_event, generated_close_to=None if not sample_only_from_closest_benchmark else theta_value_sampling, ): weights_benchmarks_batch *= correction_factor # Weights weights = self._weights(thetas, nus, weights_benchmarks_batch, theta_matrices) if needs_gradients: weight_gradients = self._weight_gradients( thetas, nus, weights_benchmarks_batch, gradients="all" if nuisance_score else "theta", theta_matrices=theta_matrices, theta_gradient_matrices=theta_gradient_matrices, ) else: weight_gradients = None # Evaluate p(x | sampling theta) p_sampling = weights[sampling_index] / xsecs[sampling_index] # Shape: (n_batch_size,) # Handle negative weights (should be rare) n_negative_weights = np.sum(p_sampling < 0.0) if n_negative_weights > 0: n_neg_weights_warnings += 1 if n_neg_weights_warnings <= 3: logger.warning( "For this value of theta, %s / %s events have negative weight and will be ignored", n_negative_weights, p_sampling.size, ) if n_neg_weights_warnings == 3: logger.warning("Skipping warnings about negative weights in the future...") p_sampling[p_sampling < 0.0] = 0.0 # Remove events with too large weights if n_eff_forced is not None: n_too_large_weights = np.sum(p_sampling > 1.0 / n_eff_forced) if n_too_large_weights > 0: n_too_large_weights_warnings += 1 if n_too_large_weights_warnings <= 1: logger.warning( "For this value of theta, %s / %s events have too large weight and will be ignored", n_too_large_weights, p_sampling.size, ) if n_too_large_weights_warnings == 1: logger.warning("Skipping warnings about too large weights in the future...") p_sampling[p_sampling > 1.0 / n_eff_forced] = 0.0 # Remember largest weights (to calculate effective number of samples) largest_event_probability = max(largest_event_probability, np.max(p_sampling)) # Calculate cumulative p (summing up all events until here) cumulative_p = cumulative_p.flatten()[-1] + np.cumsum(p_sampling) # Shape: (n_batch_size,) # When cumulative_p hits u, we store the events indices = np.searchsorted(cumulative_p, u, side="left").flatten() # Shape: (n_samples,), values: [0, ..., n_batch_size] found_now = np.invert(done) & (indices < len(cumulative_p)) # Shape: (n_samples,) x[found_now] = x_batch[indices[found_now]] done[found_now] = True # Extract augmented data relevant_augmented_data = self._calculate_augmented_data( augmented_data_definitions=augmented_data_definitions, weights=weights[:, indices[found_now]], weight_gradients=None if weight_gradients is None else weight_gradients[:, :, indices[found_now]], xsecs=xsecs, xsec_gradients=xsec_gradients, ) for i, this_relevant_augmented_data in enumerate(relevant_augmented_data): augmented_data[i][found_now] = this_relevant_augmented_data # Finished? if np.all(done): break # Cross-check cumulative probabilities at end logger.debug(" Cumulative probability (should be close to 1): %s", cumulative_p[-1]) # Check that we got 'em all, otherwise repeat if not np.all(done): logger.debug( " After full pass through event files, {} / {} samples not found, with u = {}".format( np.sum(np.invert(done)), done.size, u[np.invert(done)] ) ) n_eff_samples = 1.0 / max(1.0e-12, largest_event_probability) n_eff_samples = [n_eff_samples for _ in range(n_samples)] return ( x, theta_values, nu_values, augmented_data, n_eff_samples, n_stats_warnings, n_neg_weights_warnings, n_too_large_weights_warnings, ) @staticmethod def _calculate_augmented_data( augmented_data_definitions, weights, # shape (n_thetas, n_events) weight_gradients, # grad_theta dsigma(theta, nu) with shape (n_thetas, n_gradients, n_events) xsecs, # shape (n_thetas,) xsec_gradients, # grad_theta sigma(theta, nu) with shape (n_params, n_gradients) ): augmented_data = [] for definition in augmented_data_definitions: if definition[0] == "ratio": _, i_num, i_den = definition ratio = (weights[i_num] / xsecs[i_num]) / (weights[i_den] / xsecs[i_den]) ratio = ratio.reshape((-1, 1)) # (n_samples, 1) augmented_data.append(ratio) elif definition[0] == "score": _, i = definition score = weight_gradients[i, :, :] / weights[i, np.newaxis, :] # (n_gradients, n_samples) score = score - xsec_gradients[i, :, np.newaxis] / xsecs[i, np.newaxis, np.newaxis] score = score.T # (n_samples, n_gradients) augmented_data.append(score) else: raise ValueError("Unknown augmented data type {}".format(definition[0])) return augmented_data def _combine_thetas_nus(self, all_thetas, all_nus): n_thetas = len(all_thetas) assert n_thetas == len(all_nus) # all_nus is a list of a list of (None or ndarray) # Figure out if there's anything nontrivial in there add_nuisance_params = False for nus in all_nus: if self._any_nontrivial_nus(nus): add_nuisance_params = True # No nuisance params? if not add_nuisance_params or self.nuisance_morpher is None or self.n_nuisance_parameters == 0: return all_thetas all_combined = [] for thetas, nus in zip(all_thetas, all_nus): combined = [] if nus is None: nus = [None for _ in range(thetas)] for theta, nu in zip(thetas, nus): if nu is None or None in nu: nu = np.zeros(self.n_nuisance_parameters) combined.append(np.hstack((theta, nu))) all_combined.append(np.asarray(combined)) return all_combined @staticmethod def _report_effective_n_samples(all_effective_n_samples): if len(all_effective_n_samples) > 1: logger.info( "Effective number of samples: mean %s, with individual thetas ranging from %s to %s", np.mean(all_effective_n_samples), np.min(all_effective_n_samples), np.max(all_effective_n_samples), ) logger.debug("Effective number of samples for all thetas: %s", all_effective_n_samples) else: logger.info("Effective number of samples: %s", all_effective_n_samples[0]) @staticmethod def _parse_theta(theta, n_samples): theta_type_in = theta[0] theta_value_in = theta[1] if theta_type_in == "benchmark": thetas_out = [theta_value_in] if n_samples is None: n_samples_per_theta = 1 else: n_samples_per_theta = n_samples elif theta_type_in == "benchmarks": n_benchmarks = len(theta_value_in) if n_samples is None: n_samples_per_theta = 1 else: n_samples_per_theta = max(int(round(n_samples / n_benchmarks, 0)), 1) thetas_out = theta_value_in elif theta_type_in == "morphing_point": thetas_out = [np.asarray(theta_value_in)] if n_samples is None: n_samples_per_theta = 1 else: n_samples_per_theta = n_samples elif theta_type_in == "morphing_points": n_benchmarks = len(theta_value_in) if n_samples is None: n_samples_per_theta = 1 else: n_samples_per_theta = max(int(round(n_samples / n_benchmarks, 0)), 1) thetas_out = theta_value_in elif theta_type_in == "random_morphing_points": n_benchmarks, priors = theta_value_in if n_benchmarks is None or n_benchmarks <= 0 or (n_samples is not None and n_benchmarks > n_samples): n_benchmarks = max(n_samples, 1) if n_samples is None: n_samples_per_theta = 1 else: n_samples_per_theta = max(int(round(n_samples / n_benchmarks, 0)), 1) thetas_out = [] for prior in priors: if prior[0] == "flat": prior_min = prior[1] prior_max = prior[2] thetas_out.append(prior_min + (prior_max - prior_min) * np.random.rand(n_benchmarks)) elif prior[0] == "gaussian": prior_mean = prior[1] prior_std = prior[2] thetas_out.append(np.random.normal(loc=prior_mean, scale=prior_std, size=n_benchmarks)) else: raise ValueError("Unknown prior {}".format(prior)) thetas_out = np.array(thetas_out).T else: raise ValueError("Unknown theta specification {}".format(theta)) return thetas_out, n_samples_per_theta def _parse_nu(self, nu, n_thetas): if nu is None: nu_type_in = "nominal" nu_value_in = None else: nu_type_in = nu[0] nu_value_in = nu[1] if n_thetas < 1: n_thetas = 1 if nu_type_in == "nominal" or self.n_nuisance_parameters == 0: nu_out = [None for _ in range(n_thetas)] elif nu_type_in == "iid": priors = [nu_value_in for _ in range(self.n_nuisance_parameters)] return self._parse_nu(("random_morphing_points", (None, priors)), n_thetas) elif nu_type_in == "morphing_point": nu_out = np.asarray([nu_value_in for _ in range(n_thetas)]) elif nu_type_in == "morphing_points": n_nus = len(nu_value_in) nu_out = np.asarray([nu_value_in[i % n_nus] for i in range(n_thetas)]) elif nu_type_in == "random_morphing_points": _, priors = nu_value_in nu_out = [] for prior in priors: if prior[0] == "flat": prior_min = prior[1] prior_max = prior[2] nu_out.append(prior_min + (prior_max - prior_min) * np.random.rand(n_thetas)) elif prior[0] == "gaussian": prior_mean = prior[1] prior_std = prior[2] nu_out.append(np.random.normal(loc=prior_mean, scale=prior_std, size=n_thetas)) else: raise ValueError("Unknown prior {}".format(prior)) nu_out = np.array(nu_out).T else: raise ValueError("Unknown nu specification {}".format(nu)) return nu_out @staticmethod def _build_sets(thetas, nus): if len(nus) != len(thetas): raise RuntimeError("Mismatching thetas and nus: {} vs {}".format(len(thetas), len(nus))) n_sets = max([len(param) for param in thetas + nus]) sets = [[] for _ in range(n_sets)] for (theta, nu) in zip(thetas, nus): n_theta_sets_before = len(theta) n_nu_sets_before = len(nu) if n_theta_sets_before <= 0 or n_nu_sets_before <= 0: raise RuntimeError( ( "Inconsistent number of sets in _build_sets: thetas = {}, nus = {}, theta = {}, " "nu = {}" ).format(thetas, nus, theta, nu) ) for i_set in range(n_sets): sets[i_set].append((theta[i_set % n_theta_sets_before], nu[i_set % n_nu_sets_before])) return sets @staticmethod def _format_sampling(theta): if theta[0] == "benchmark": return str(theta[1]) elif theta[0] == "morphing_point": return str(theta[1]) elif theta[0] == "benchmarks": return "{} benchmarks, starting with {}".format(len(theta[1]), theta[1][:3]) elif theta[0] == "morphing_points": return "{} morphing points, starting with {}".format(len(theta[1]), theta[1][:3]) elif theta[0] == "random_morphing_points": prior_str = "" for i, (type, arg0, arg1) in enumerate(theta[1][1]): prior_str += "\n" if type == "gaussian": prior_str += " theta_{} ~ Gaussian with mean {} and std {}".format(i, arg0, arg1) elif type == "flat": prior_str += " theta_{} ~ flat from {} to {}".format(i, arg0, arg1) if theta[1][0] is None: return "Maximally many random morphing points, drawn from the following priors:{}".format(prior_str) else: return "{} random morphing points, drawn from the following priors:{}".format(theta[1][0], prior_str)
[docs]def combine_and_shuffle(input_filenames, output_filename, k_factors=None, overwrite_existing_file=True): """ Combines multiple MadMiner files into one, and shuffles the order of the events. Note that this function assumes that all samples are generated with the same setup, including identical benchmarks (and thus morphing setup). If it is used with samples with different settings, there will be wrong results! There are no explicit cross checks in place yet! Parameters ---------- input_filenames : list of str List of paths to the input MadMiner files. output_filename : str Path to the combined MadMiner file. k_factors : float or list of float, optional Multiplies the weights in input_filenames with a universal factor (if k_factors is a float) or with independent factors (if it is a list of float). Default value: None. overwrite_existing_file : bool, optional If True and if the output file exists, it is overwritten. Default value: True. Returns ------- None """ logger.debug("Combining and shuffling samples") if len(input_filenames) > 1: logger.warning( "Careful: this tool assumes that all samples are generated with the same setup, including" " identical benchmarks (and thus morphing setup). If it is used with samples with different" " settings, there will be wrong results! There are no explicit cross checks in place yet." ) # k factors if k_factors is None: k_factors = [1.0 for _ in input_filenames] elif isinstance(k_factors, float): k_factors = [k_factors for _ in input_filenames] # Copy first file to output_filename logger.info("Copying setup from %s to %s", input_filenames[0], output_filename) # TODO: More memory efficient strategy # Load events all_observations = None all_weights = None all_sampling_ids = None all_n_events_background = 0 all_n_events_signal_per_benchmark = 0 for i, (filename, k_factor) in enumerate(zip(input_filenames, k_factors)): logger.info( "Loading samples from file %s / %s at %s, multiplying weights with k factor %s", i + 1, len(input_filenames), filename, k_factor, ) ( _, _, _, _, _, _, _, _, _, _, n_signal_events_generated_per_benchmark, n_background_events, ) = load_madminer_settings(filename) if n_signal_events_generated_per_benchmark is not None and n_background_events is not None: all_n_events_signal_per_benchmark += n_signal_events_generated_per_benchmark all_n_events_background += n_background_events for observations, weights, sampling_ids in madminer_event_loader(filename, return_sampling_ids=True): logger.debug("Sampling benchmarks: %s", sampling_ids) if all_observations is None: all_observations = observations all_weights = k_factor * weights else: all_observations = np.vstack((all_observations, observations)) all_weights = np.vstack((all_weights, k_factor * weights)) if all_sampling_ids is None: all_sampling_ids = sampling_ids elif sampling_ids is not None: all_sampling_ids = np.hstack((all_sampling_ids, sampling_ids)) logger.debug("Combined sampling benchmarks: %s", all_sampling_ids) # Shuffle all_observations, all_weights, all_sampling_ids = shuffle(all_observations, all_weights, all_sampling_ids) # Save result save_preformatted_events_to_madminer_file( filename=output_filename, observations=all_observations, weights=all_weights, sampling_benchmarks=all_sampling_ids, copy_setup_from=input_filenames[0], overwrite_existing_samples=overwrite_existing_file, ) if all_n_events_background + np.sum(all_n_events_signal_per_benchmark) > 0: save_sample_summary_to_madminer_file( filename=output_filename, n_events_background=all_n_events_background, n_events_per_sampling_benchmark=all_n_events_signal_per_benchmark, )
[docs]def benchmark(benchmark_name): """ Utility function to be used as input to various SampleAugmenter functions, specifying a single parameter benchmark. Parameters ---------- benchmark_name : str Name of the benchmark (as in `madminer.core.MadMiner.add_benchmark`) Returns ------- output : tuple Input to various SampleAugmenter functions """ return "benchmark", benchmark_name
[docs]def benchmarks(benchmark_names): """ Utility function to be used as input to various SampleAugmenter functions, specifying multiple parameter benchmarks. Parameters ---------- benchmark_names : list of str List of names of the benchmarks (as in `madminer.core.MadMiner.add_benchmark`) Returns ------- output : tuple Input to various SampleAugmenter functions """ return "benchmarks", benchmark_names
[docs]def morphing_point(theta): """ Utility function to be used as input to various SampleAugmenter functions, specifying a single parameter point theta in a morphing setup. Parameters ---------- theta : ndarray or list Parameter point with shape `(n_parameters,)` Returns ------- output : tuple Input to various SampleAugmenter functions """ return "morphing_point", np.asarray(theta)
[docs]def morphing_points(thetas): """ Utility function to be used as input to various SampleAugmenter functions, specifying multiple parameter points theta in a morphing setup. Parameters ---------- thetas : ndarray or list of lists or list of ndarrays Parameter points with shape `(n_thetas, n_parameters)` Returns ------- output : tuple Input to various SampleAugmenter functions """ return "morphing_points", [np.asarray(theta) for theta in thetas]
[docs]def random_morphing_points(n_thetas, priors): """ Utility function to be used as input to various SampleAugmenter functions, specifying random parameter points sampled from a prior in a morphing setup. Parameters ---------- n_thetas : int Number of parameter points to be sampled priors : list of tuples Priors for each parameter is characterized by a tuple of the form `(prior_shape, prior_param_0, prior_param_1)`. Currently, the supported prior_shapes are `flat`, in which case the two other parameters are the lower and upper bound of the flat prior, and `gaussian`, in which case they are the mean and standard deviation of a Gaussian. Returns ------- output : tuple Input to various SampleAugmenter functions """ return "random_morphing_points", (n_thetas, priors)
[docs]def iid_nuisance_parameters(shape="gaussian", param0=0.0, param1=1.0): """ Utility function to be used as input to various SampleAugmenter functions, specifying that nuisance parameters are fixed at their nominal valuees. Parameters ---------- prior : tuple Prior for all nuisance parameters with form `(prior_shape, prior_param_0, prior_param_1)`. Currently, the supported prior_shapes are `flat`, in which case the two other parameters are the lower and upper bound of the flat prior, and `gaussian`, in which case they are the mean and standard deviation of a Gaussian. Returns ------- output : tuple Input to various SampleAugmenter functions """ return "iid", (shape, param0, param1)
[docs]def nominal_nuisance_parameters(): """ Utility function to be used as input to various SampleAugmenter functions, specifying that nuisance parameters are fixed at their nominal valuees. Returns ------- output : tuple Input to various SampleAugmenter functions """ return "nominal", None