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Comparative Study Between Ensemble Learning and Evolutionary Learning to Solve the Higgs Boson Detection

Authors:

  • Ahmed Maaloul

Environment:

  • Google Colab with GPU enabled (T4) for accelerated computation.

Dataset Description and Aim

Dataset Description

Title: Dataset from the ATLAS Higgs Boson Machine Learning Challenge 2014 Source: ATLAS Collaboration, CERN Open Data Portal

This dataset was created for the ATLAS Higgs Boson Machine Learning Challenge and is derived from official ATLAS full-detector simulations. It contains events representing "Higgs to tau-tau" signals mixed with various background processes. The events are simulated to mimic real detector data, leveraging our knowledge of particle physics. Each event includes detailed properties such as transverse momentum, invariant mass, and pseudorapidity, among others, which are crucial for classification tasks.

Key Characteristics:

  • Number of events: 818,238
  • File size: 186.5 MiB
  • Evaluation Metric: Approximate Median Significance (AMS)

Simulation Process:

  1. Random proton-proton collisions are simulated based on existing particle physics knowledge.
  2. Resulting particles are tracked through a virtual model of the detector, yielding simulated events with properties mimicking real-world collisions.

Signal and Background:

  • Signal Events: Events in which Higgs bosons (with a fixed mass of 125 GeV) are produced.
  • Background Events: Other known processes producing similar signatures, including:
    • Decay of Z bosons into two taus.
    • Events with top quark pairs producing leptons and hadronic taus.
    • W boson decays producing electrons or muons with hadronic taus (due to particle identification imperfections).

Weights:

Each simulated event has a weight proportional to its conditional density. These weights are crucial for accurate evaluation of the AMS metric but are excluded as inputs to the classifier.

Aim of the Analysis

The goal is to develop and compare machine learning models for detecting Higgs boson events based on the dataset’s features. Specifically, the objectives are:

  1. Preprocessing: Handle missing values, normalize features, and prepare the data for modeling.
  2. Model Implementation:
    • Apply ensemble learning methods (e.g., Random Forest, Gradient Boosting).
    • Use evolutionary learning techniques to optimize performance.
  3. Performance Evaluation:
    • Assess models using metrics such as AMS, accuracy, precision, recall, and F1-score.
    • Compare ensemble and evolutionary learning approaches in terms of performance and computational efficiency.

Feature Descriptions

Variable Description
EventId Unique identifier for the event.
DER_mass_MMC Estimated mass of the Higgs boson candidate.
DER_mass_transverse_met_lep Transverse mass between missing transverse energy and the lepton.
DER_mass_vis Invariant mass of the hadronic tau and the lepton.
DER_pt_h Modulus of the vector sum of transverse momenta (hadronic tau, lepton, missing energy).
DER_deltaeta_jet_jet Pseudorapidity separation between the two jets. Undefined if PRI_jet_num ≤ 1.
DER_mass_jet_jet Invariant mass of the two jets. Undefined if PRI_jet_num ≤ 1.
DER_prodeta_jet_jet Product of pseudorapidities of the two jets. Undefined if PRI_jet_num ≤ 1.
DER_deltar_tau_lep R separation between the hadronic tau and the lepton.
DER_pt_tot Modulus of the vector sum of transverse momenta of key particles.
DER_sum_pt Sum of transverse momenta of all key particles and additional jets.
DER_pt_ratio_lep_tau Ratio of transverse momenta of the lepton and the hadronic tau.
DER_met_phi_centrality Centrality of the azimuthal angle of missing transverse energy relative to the tau and lepton.
DER_lep_eta_centrality Centrality of the pseudorapidity of the lepton relative to the two jets. Undefined if PRI_jet_num ≤ 1.
PRI_tau_pt Transverse momentum of the hadronic tau.
PRI_tau_eta Pseudorapidity of the hadronic tau.
PRI_tau_phi Azimuth angle of the hadronic tau.
PRI_lep_pt Transverse momentum of the lepton.
PRI_lep_eta Pseudorapidity of the lepton.
PRI_lep_phi Azimuth angle of the lepton.
PRI_met Missing transverse energy.
PRI_met_phi Azimuth angle of the missing transverse energy.
PRI_met_sumet Total transverse energy in the detector.
PRI_jet_num Number of jets. Possible values: 0, 1, 2, or 3.
PRI_jet_leading_pt Transverse momentum of the leading jet. Undefined if PRI_jet_num = 0.
PRI_jet_leading_eta Pseudorapidity of the leading jet. Undefined if PRI_jet_num = 0.
PRI_jet_leading_phi Azimuth angle of the leading jet. Undefined if PRI_jet_num = 0.
PRI_jet_subleading_pt Transverse momentum of the subleading jet. Undefined if PRI_jet_num ≤ 1.
PRI_jet_subleading_eta Pseudorapidity of the subleading jet. Undefined if PRI_jet_num ≤ 1.
PRI_jet_subleading_phi Azimuth angle of the subleading jet. Undefined if PRI_jet_num ≤ 1.
PRI_jet_all_pt Scalar sum of transverse momentum of all jets in the event.
Weight Event weight proportional to the conditional density.
Label Event label: ‘s’ for signal and ‘b’ for background.
KaggleSet Specifies the Kaggle dataset: training, public leaderboard, or private leaderboard.
KaggleWeight Weight normalized within each Kaggle dataset.

Data Visualization and Preprocessing

Removing Unnecessary Columns

  • EventId: Unique identifier for each event.
  • KaggleSet: Indicates the subset of the data (e.g., training, public leaderboard, private leaderboard).
  • KaggleWeight: Normalized weights within each Kaggle dataset.

Random Sampling

We perform random sampling to create a representative subset of the dataset, allowing for faster preprocessing.

Mapping the Label to Numerical Values

The Label column is mapped to numerical values (s to 1 and b to 0).

Dealing with Missing Values

Missing values, represented by -999, are imputed using the SimpleImputer class with a mean strategy.

Outliers

Outliers are checked using boxplots for all columns.

Feature Scaling

Given the significant number of outliers, StandardScaler is used for feature scaling.

Crossing Certain Pairs of Columns

Scatter plots are generated for selected pairs of columns to visualize the distribution of signal and background events.

Unbalance Ratio

The dataset contains significantly more background (0) events than signal (1) events, indicating a class imbalance.

Feature Selection

A correlation matrix is used to identify highly correlated features, indicating redundancy in the dataset. Principal Component Analysis (PCA) is applied to retain 95% variance.

Split the Data

The dataset is split into training and testing sets, maintaining the class distribution.

Ensemble Learning

Ensemble Learning Methods

  • Bagging (Bootstrap Aggregating): Combines multiple individual models (often decision trees) to produce a more robust final prediction.
  • Boosting: Trains models sequentially, where each new model focuses on correcting the errors of the previous ensemble.

Classifier Candidates

  • RandomForestClassifier (Bagging)
  • XGBClassifier (Boosting)
  • GradientBoostingClassifier (Boosting)
  • GaussianNB (Naive Bayes)

Training, Predicting, and Storing Results

The models are trained and evaluated using different sampling methods (None, UnderSampling, OverSampling, SMOTE). The results are stored in a DataFrame.

Evolutionary Learning Implementation with DEAP

Genetic Programming Framework

  • Primitive Set: Defines the basic operations and functions.
  • Fitness and Individual Classes: Defines the fitness function and individual representation.
  • Toolbox Setup: Sets up the genetic operators and evaluation functions.

Training and Storing Metrics

The genetic programming models are trained using eaSimple and eaMuPlusLambda algorithms. The results are stored in a DataFrame.

Bonus: Voting Classifier with the Final Population GP

A voting classifier is created from the top individuals in the final population and evaluated on the test set.

Comparative Analysis

Performance

  • Accuracy & F1-Score: XGBoost consistently attains the highest accuracy and F1-score, followed by Random Forest and Gradient Boosting. GP methods achieve moderate performance.
  • Precision & Recall: Ensemble methods dominate in precision and recall, with GP methods achieving moderate performance.

Efficiency

  • Training Time: Gradient Boosting and GP methods incur higher training times. XGBoost benefits from GPU support and achieves faster training times.
  • Testing Time: GP Voting Ensemble has the highest inference cost. XGBoost maintains fast prediction times.

Model Complexity

  • Interpretability: Ensemble methods are seen as "black box" approaches, while GP solutions can be more transparent if they remain shallow.
  • Evolved Models vs. Ensemble Methods: Both ensembles and GP can grow complex, with actual simplicity depending on hyperparameter constraints.

Advantages and Disadvantages

  • Ensemble Learning: Excellent predictive performance, scalable to large data, but limited global interpretability.
  • Evolutionary Learning: Flexible approach for discovering novel model structures, but computationally costly and less accurate than top ensembles.
  • GP Voting Ensembles: Can bolster GP performance but incurs high inference costs.

Conclusion

XGBoost emerges as the optimal method for Higgs Boson detection, excelling in accuracy, speed, and predictive robustness. GP approaches, particularly eaMuPlusLambda, demonstrate greater effectiveness than eaSimple but remain slower and less accurate compared to leading ensemble methods.