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TMVA - Toolkit for Multivariate Data Analysis

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski, S. Henrot-Versille, M. Jachowski, K. Kraszewski, A. Krasznahorkay, M. Kruk, Y. Mahalalel, R. Ospanov, X. Prudent, A. Robert, D. Schouten, F. Tegenfeldt, A. Voigt, K. Voss, M. Wolter, A. Zemla

arXiv:physics/0703039v5physics.data-an

TL;DR

TMVA addresses the need for accessible, comparable multivariate analysis in high-energy physics by unifying configurable classification and regression methods in ROOT. Its shared interfaces support training, evaluation, and deployment, while TMVA 4 adds flexible method combinations and generalized boosting. The toolkit provides operational methods and standardized performance assessment, with practical limits for some algorithms in memory use and boundary treatment.

  • Problem

    High-energy-physics analyses need to extract information from complex data while comparing and applying many multivariate methods consistently.

  • Method

    TMVA unifies customizable multivariate classification and regression methods through shared Factory and Reader interfaces, with TMVA 4 enabling generalized boosting and method combinations.

  • Results

    TMVA provides fully operational methods for training, testing, evaluation, and application, with standardized outputs and ROOT macros for assessing classification and regression performance.

  • Takeaways & Limitations

    The framework supports convenient use and objective performance assessment of multivariate algorithms in high-energy physics and beyond.

  • Takeaways & Limitations

    PDE-RS requires storing its entire binary tree in memory, limiting the number of training events it can effectively use for multidimensional PDF modeling.

Abstract

from arXiv · show

In high-energy physics, with the search for ever smaller signals in ever larger data sets, it has become essential to extract a maximum of the available information from the data. Multivariate classification methods based on machine learning techniques have become a fundamental ingredient to most analyses. Also the multivariate classifiers themselves have significantly evolved in recent years. Statisticians have found new ways to tune and to combine classifiers to further gain in performance. Integrated into the analysis framework ROOT, TMVA is a toolkit which hosts a large variety of multivariate classification algorithms. Training, testing, performance evaluation and application of all available classifiers is carried out simultaneously via user-friendly interfaces. With version 4, TMVA has been extended to multivariate regression of a real-valued target vector. Regression is invoked through the same user interfaces as classification. TMVA 4 also features more flexible data handling allowing one to arbitrarily form combined MVA methods. A generalised boosting method is the first realisation benefiting from the new framework.

1 Introduction

TMVA is a ROOT-integrated toolkit that provides supervised multivariate classification and, since version 4, regression for high-energy-physics analyses. It unifies many configurable methods with shared training, testing, evaluation, and application interfaces.

  • Scope: TMVA provides ROOT-integrated supervised learning for multivariate classification and, since version 4, multivariate regression.Its methods map input variables to desired outputs using global functions or local models.
  • Available methods: The toolkit includes likelihood estimators, discriminant analyses, neural networks, support vector machines, decision trees, rule ensembles, and a generic boost classifier.These methods cover both established and newer multivariate approaches available through TMVA.
  • Framework: TMVA supplies object-oriented C++/ROOT implementations together with tools for parameter fitting, transformations, training, testing, performance evaluation, and visualisation.User data can be supplied as ROOT trees or text files.
  • Evaluation: The Factory applies common data and evaluation procedures so that all methods use the same training and test data and follow the same prescriptions.It also performs preanalysis and preprocessing, including correlation calculations for input variables.
  • Evaluation: Classification and regression results are reported through benchmark tables, graphical information, ROOT output files, and dedicated display macros.The toolkit compares classifier signal efficiency and background rejection or regression target-estimation variance.
  • Deployment: TMVA offers lightweight Reader and standalone C++ response interfaces, while default configurations provide reasonable performance but require problem-specific tuning for maximum capability.Training results are stored in weight files that can be read from C++, ROOT, or Python applications.

2 TMVA Quick Start

TMVA can be started through example classification or regression jobs that train, test, evaluate, and apply multivariate methods within ROOT-based workflows. Its quick-start setup covers installation, version compatibility, example execution, method selection, result inspection, and visualization.

  • How to download and build TMVA: TMVA requires ROOT and supports ROOT versions v5.08 and above, while newer TMVA releases can be compiled against the local ROOT installation.The appropriate TMVA library must be loaded when using a newer release than the one bundled with ROOT.
  • Running the example: The toolkit can run as a ROOT script, standalone executable, or PyROOT script, with trained methods writing human-readable XML weight files by default.The executable and Python examples are provided in version-specific directories.
  • Running the example: TMVA provides example jobs for classification and regression that train, test, and evaluate methods using academic toy datasets before application to user data.The examples are intended to show how users can customize the workflow for real use cases.
  • Running the example: Users can select which MVA methods to process explicitly, such as running the classification example with only Fisher and likelihood classifiers.The selected method names are passed to the example macro and are predefined in that macro.
  • Displaying the results: Training jobs report input correlations, variable rankings, configurations, method comparisons, benchmark efficiencies, and regression deviations, while ROOT macros visualize training, testing, and evaluation results.TMVA also provides GUIs for launching these visualization macros and supports correlation inspection and linear decorrelation before classification training.

3 Using TMVA

TMVA separates training and application through Factory and Reader objects, supporting variable registration, method booking, evaluation, and response computation. Its workflow also provides classifier probabilities and Rarity representations for comparing methods and inspecting test-background agreement.

  • Training with the TMVA Factory: The training phase uses a Factory to register input and target variables, book methods, and run training, testing, and evaluation.Training outputs include method-specific XML weight files and evaluation histograms.
  • Applying trained methods: The application phase uses a Reader to register variables, load selected methods from weight files, and compute responses during the event loop.For each event, input values are copied into reserved memory locations before responses and, for some methods, errors are calculated.
  • Training with the TMVA Factory: TMVA supports training data from ROOT trees or text files, including separate or shared signal and background trees with optional overall weights.Shared trees use signal and background selection cuts; separate trees can receive distinct weights.
  • Performance representations: Classifier PDFs support probability and Rarity transformations, with Rarity making background responses uniform on [0,1] and signal responses cluster toward 1.In the example, Fisher’s signal Rarity distribution is more strongly peaked toward 1 than Likelihood’s, while background distributions are uniform within statistical fluctuations.
  • Applying trained methods: TMVA also generates standalone C++ response classes, but the supported approach for applying training results is the Reader.Standalone responses can reproduce Reader outputs for a given test event without requiring TMVA or ROOT libraries.

4 Data Preprocessing

TMVA preprocesses input variables transparently before MVA methods see events, supporting normalization, decorrelation, PCA, and Gaussianisation. These transformations can be selected and chained per method, but linear decorrelation is limited for non-Gaussian or highly nonlinear problems.

  • Transformation types: TMVA implements four preprocessing transformations: normalization, covariance-matrix decorrelation, principal component decomposition, and Gaussianisation.Only normalization is available for both classification and regression; the other transformations are currently classification-only.
  • Transformation interface: Preprocessing is applied on the fly through the DataSet and repeated automatically during application using information stored in each method’s weight file.The MVA methods therefore receive transformed events without handling preprocessing directly.
  • Normalization: Normalization linearly scales every input variable between its training-sample minimum and maximum to the interval [−1, 1].This supports direct comparisons between weights and can improve minimization procedures such as neural-network training.
  • Correlation handling: Covariance-based decorrelation and PCA remove linear correlations under assumptions about the input distributions, while Gaussianisation first transforms variables toward Gaussian distributions.The transformations are computed separately for signal and background when their correlation patterns differ.
  • Limitations: For highly nonlinear problems, linear decorrelation can worsen performance, so nonlinear methods without prior decorrelation are recommended.Decorrelation is complete only for linearly correlated, Gaussian-distributed variables and may recover little additional information otherwise.
  • Configuration: Users select transformations with VarTransform and may chain them, such as VarTransform=G,D or VarTransform=G,D,G,D.The available types are Norm, Deco, PCA, and Gauss, with corresponding shorthand letters.

5 Probability Density Functions – the PDF Class

TMVA estimates probability densities using nonparametric methods, including spline interpolation for one-dimensional data and nearest-neighbour approaches for multidimensional PDFs. Smoothing and boundary treatments are configurable, but interpolation and KDE can introduce characteristic distortions.

  • PDF construction: TMVA uses nearest-neighbour estimation for all multidimensional probability densities, while one-dimensional PDFs use nonparametric histograms or unbinned data.One-dimensional binned data are interpolated with polynomial splines, whereas unbinned data use kernel functions.
  • PDF class: The PDF class builds density estimates from source histograms and returns evaluated probabilities through configurable interpolation and smoothing procedures.Its interface supports building a PDF and querying its value at x.
  • Spline PDFs: Adaptive histogram smoothing varies between minimum and maximum iteration counts according to relative statistical errors, preserving significant structures while reducing fluctuations.The reference histogram can use a fixed bin count or a target average number of events per bin.
  • Spline PDFs: Quadratic splines are the default because cubic and higher-order splines can wiggle unexpectedly and lack local control over changes at individual bins.Higher-degree splines provide smooth derivatives but can alter the entire interpolated curve when one control point moves.
  • KDE limitations: Kernel-density estimates can suffer boundary problems, becoming inaccurate near distribution edges when the underlying density has a discontinuity.TMVA exposes KDEborder options to treat these boundary effects.

6 Optimisation and Fitting

TMVA provides a common fitting framework for MVA methods that optimize parameterized estimators. Users can choose among Monte Carlo sampling, Minuit, Genetic Algorithms, and Simulated Annealing, with Minuit favoring robust local minimization rather than global search.

  • Applications: Fitting supports general-purpose optimization of estimators used by methods such as cut optimization and FDA.An example estimator sums deviations of classifier outputs from target values for signal and background events.
  • Fitting framework: TMVA’s fitter base class lets MVA methods select and configure a fitting algorithm through method option strings.Four fitters are implemented: Monte Carlo sampling, Minuit minimization, a Genetic Algorithm, and Simulated Annealing.
  • Monte Carlo sampling: Monte Carlo fitting randomly samples parameters within limits and retains the sample that optimizes the estimator.Sampling can use uniform or Gaussian priors, with optional Gaussian proposals around the current best value.
  • Minuit minimization: Minuit searches for a minimum along gradient directions and analyzes the estimator near that minimum, but it accepts local minima rather than seeking a global solution.For multiple local or global solutions, the paper suggests using another fitter designed for such problems.
  • Genetic Algorithm: The Genetic Algorithm evolves a population through fitness evaluation, selection, crossover, mutation, and repeated generations until convergence or a stopping criterion.The best individual is selected as the solution after the evolutionary cycles terminate.

7 Boosting and Bagging

TMVA implements boosting and bagging to combine weak or unstable MVA methods, extending the approach to classification and regression. GradientBoost addresses AdaBoost’s sensitivity to outliers through alternative loss functions and gradient-based tree fitting.

  • Boosting: Boosting sequentially trains MVA algorithms on reweighted data and combines them through a weighted majority vote to improve performance and stability.TMVA can boost any MVA method, although decision trees are the most commonly boosted.
  • Adaptive Boost (AdaBoost): AdaBoost increases the weights of events misclassified by the previous decision tree before training the next tree.The subsequent tree uses modified event weights, with the weights renormalised to preserve the total event count.
  • Regression Boosting: For regression, TMVA uses AdaBoost.R2, which reweights every event according to its individual prediction loss rather than a binary classification error.The boosted regressor combines methods using a weighted median.
  • Gradient Boost: GradientBoost minimises a chosen loss through steepest descent, fitting regression-tree leaf values to the mean loss gradient in each tree-defined region.The method currently uses binomial log-likelihood loss for classification and can accommodate any loss whose gradient is calculable.
  • Gradient Boost: GradientBoost gives good results with 5–10-leaf trees and is typically less susceptible to overtraining; shrinkage values of 0.1–0.3 can improve difficult predictions.Smaller shrinkage requires more trees but can significantly improve accuracy in difficult settings.
  • Bagging: Bagging repeatedly trains classifiers on resampled events and averages them, primarily stabilising statistical representations rather than enhancing weak classifiers.TMVA implements resampling with random Poisson weights, including sampling with replacement.

8 The TMVA Methods

TMVA’s method layer provides common infrastructure for configuring, training, evaluating, and applying diverse classifiers. The methods have distinct operating boundaries: cuts can be competitive with strong variables, likelihood is optimal under modelling assumptions, and PDE-based methods trade flexibility against speed or data requirements.

  • Common Infrastructure: All TMVA methods inherit shared data, configuration, I/O, and performance-evaluation functionality while implementing method-specific interfaces.The package also supports classifier-output PDFs and configurable PDF controls.
  • Common Infrastructure: TMVA documents each method’s introduction, configuration options, implementation, variable ranking, and performance characteristics for classification and available regression tasks.Training and application can recreate methods from configuration or weight files.
  • Rectangular Cut Optimisation: Rectangular cut optimisation returns binary signal/background responses and maximises background rejection across the scanned signal-efficiency range.The optimisation is a sequence of univariate cuts, not a multivariate combination of variables.
  • Rectangular Cut Optimisation: The Genetic Algorithm currently provides the best cut-optimisation convergence, but solution quality deteriorates quickly as the number of discriminating variables rises.TMVA therefore recommends restricting rectangular cut optimisation to the variables with the largest discriminating power.
  • Performance Boundaries: Cuts can be competitive when variables separate signal from background well, but underperform with strong nonlinear correlations or many weakly discriminating variables.The likelihood ratio is optimal for the supplied variables when model inaccuracies, including residual correlations and inaccurate PDFs, are absent.
  • PDE Methods: PDE-RS can model complex nonlinear correlations and achieve competitive performance with sufficiently few variables and ample training statistics, but it responds slowly and requires storing the full binary tree.Its memory requirement limits the number of training events that can effectively model the multidimensional PDF.
  • PDE Methods: Gaussian kernels remove foam-cell boundary discontinuities and often improve separation, while increasing classification time; PDE-Foam performance is stable across most parameter variations.For small samples with many observables, VolFrac requires tuning; for large samples, increasing nActiveCells can improve performance when training time is not critical.

1) Separate signal and background foams

With separate signal and background foams, PDE-Foam models each class distribution independently and evaluates an event using the corresponding cell contents and volumes. This lets the foam geometries adapt to differing distribution shapes while keeping testing cost independent of training-sample size.

  • Separate Signal and Background Foams: When SigBgSeparate=True, PDE-Foam constructs independent signal and background foams from separate multidimensional training-event trees.The foams are initialised and grown independently so their geometries reflect the respective distributions.
  • Separate Signal and Background Foams: Each active foam cell is filled with the weighted number of signal or background training events contained in its volume.The event weights are incorporated separately into the signal and background cell counts.
  • Separate Signal and Background Foams: During evaluation, PDE-Foam finds the two cells containing an event and computes its estimator from their event counts and respective cell volumes.The testing phase uses the stored cell statistics rather than revisiting the full training sample.
  • Separate Signal and Background Foams: With equal normalised total signal and background weights, the PDE-Foam discriminant approximates the probability that an event within a cell is signal.The EqualNumEvents normalisation mode enforces this condition.
  • Performance: Separate foams adapt their geometries to the individual signal and background distributions, making the algorithm well suited to substantially different distribution shapes.Training comprises steps 1–4, while testing performs step 5; testing memory and computation do not depend on the number of training events.

2) Single signal and background foam

PDE-Foam supports classification and both mono-target and multi-target regression by storing estimators or target information in adaptive foam cells. Its cell-based evaluation enables fast responses and comparable performance across implementations, while multi-target regression extends the foam into additional target dimensions.

  • Classification: PDE-Foam can use one foam containing an estimator for both signal and background events.The foam is grown from signal-to-background estimator density and each cell stores the corresponding discriminator.
  • Classification: Each test event receives the discriminator stored in the foam cell containing that event.
  • Classification: The two foam implementations show similar performance when they use the same total number of foam cells.
  • Regression: Multi-target regression forms an (nvar + ntar)-dimensional foam, storing target information in additional foam dimensions.
  • Regression: Mono-target regression stores average target values in nvar-dimensional foam cells and reads the corresponding cell average for each test event.
  • Regression: The kernel weighting methods also support regression, including the modified foam structure used for multi-target regression.
  • Performance: PDE-Foam is fast because its response depends on a limited number of cells rather than the training-sample size, and it targets highly nonlinear correlations.

8.10 Artificial Neural Networks (nonlinear discriminant analysis)

TMVA provides three feed-forward multilayer perceptron implementations, including a newly developed MLP recommended for its flexibility and speed. The networks support configurable architectures, training procedures, sampling, convergence checks, normalization, and regression-related use cases.

  • Implementations: TMVA offers three feed-forward multilayer perceptron implementations, with the newly developed MLP recommended for greater speed and flexibility.
  • MLP configuration: The MLP supports configurable hidden-layer architecture, neuron functions, training methods, learning parameters, sampling, and batch settings.
  • Training controls: Event sampling uses only a fraction of training events for an initial number of epochs and can be configured separately for training and testing.
  • Training controls: Sampling is intended primarily to speed training on large samples and may also improve robustness against convergence in a local minimum.
  • Training controls: Convergence testing can stop training after successive tests show insufficient improvement, while VarTransform=Norm normalizes inputs and regression outputs to [−1, 1].
  • MLP configuration: MLP training can use back-propagation, BFGS, or a genetic algorithm, with the genetic algorithm described as slower and worse.
  • Performance: In the reported tests, MLP and ROOT networks performed equally well, but MLP had a clear speed advantage; the Clermont-Ferrand network performed worse and required at least 10k cycles for competitive results.

8.12 Boosted Decision and Regression Trees

TMVA implements decision and regression trees as interpretable binary partitioning models, and combines them into forests using boosting, bagging, or randomized-tree strategies. These ensembles improve stability, while pruning addresses overtraining and configuration options control tree construction.

  • Tree structure: Decision trees repeatedly split one variable at a time until stopping, assigning classification leaves by majority signal/background or regression leaves a constant target value.The regression output is the average target value of training events in the corresponding leaf.
  • Tree structure: Each split selects the variable and cut providing the best local signal-background separation, while regression splitting maximizes the decrease in average squared error.The same variable may be reused at multiple nodes, and some variables may never be selected.
  • Tree structure: Decision trees partition phase space into many hypercubes, with each classification path representing a distinct sequence of cuts and each regression leaf carrying a target value.This gives trees a more flexible partition than selecting a single cut-defined hypercube.
  • Ensembles: A forest mitigates tree instability by combining trees through majority voting, while boosting modifies event weights and typically improves statistical stability and separation performance.Instability can arise when statistically similar variables compete for a split, changing the structure below that node.
  • Ensembles: TMVA supports AdaBoost, AdaBoostR2, gradient boost, bagging, and randomized trees, with randomized trees considering variable and event subsets when growing each tree.The available boosting options and applicability depend on whether the task is classification or regression.
  • Performance and trade-offs: Decision trees are simple, insensitive to poorly discriminating inputs, and require little tuning, but their theoretical best performance can be inferior to methods such as neural networks.The paper notes limited HEP experience with boosted decision trees at the time of discussion.

9 Combining MVA Methods

TMVA supports combining multivariate methods for intricate problems or variable spaces with strongly varying properties. Its generalized boosting framework combines classifiers through weighted responses, while category methods train specialized models in distinct subpopulations.

  • Motivation and combination classes: Combining MVA methods is intended for intricate classification or regression problems requiring substantial optimization or involving variable spaces with strongly varying properties.TMVA distinguishes categorizing methods, committees of methods, and a general MVA booster.
  • Category methods: Category methods divide variable space into zones and independently train the most appropriate method and variables for each resulting subpopulation.The category assignment is defined by requirements on input variables.
  • Boosted classifiers: A boosted classifier combines same-type classifiers trained on the same sample with different event weights, producing a weighted final response.The Boost method is currently applicable only to classification problems.
  • Boost configuration: TMVA books boosting by adding boost options to a classifier option string, with Boost Num controlling iterations and Boost Type selecting the algorithm.AdaBoost may stop at an error rate of 0.5 or after the configured maximum number of iterations.
  • Boost configuration: By default, boosted classifiers use a weighted average whose weights derive from misclassification error, although arithmetic averaging is also available.The weighting behavior is controlled by Boost MethodWeightType.
  • Output transformations: Boosting can apply linear, step, or logarithmic transformations to classifier outputs, with the step transformation producing −1 below and +1 above its threshold.The step transformation is the default setting.
  • Monitoring and limitations: Boost monitoring records event weights, classifier weights, error rates, and optional per-classifier histograms to help inspect ensemble behavior.The monitoring histograms are enabled with Boost MonitorMethod=T.
  • Monitoring and limitations: The boosted-classifier implementation does not provide input-variable rankings, and careless AdaBoost tuning can reduce performance for arbitrary classifiers.The paper emphasizes that performance depends on classifier characteristics and input data.

10 Which MVA method should I use for my problem?

TMVA offers no universally best MVA method: the choice depends on discrimination power, robustness, sample size, dimensionality, and correlation structure. Simple methods can suffice for linear structure, whereas nonlinear methods suit demanding optimization and strongly correlated variables.

  • Selection criteria: TMVA gives no general answer about which MVA method to use, because simplicity matters only when it does not substantially reduce discrimination power.Robustness to overtraining is especially relevant when the training sample is scarce.
  • Robustness: Boosted decision trees are particularly vulnerable to overtraining without care, requiring problem-specific pruning-strength adjustment, although observed performance can remain robust for strongly overtrained trees.These statements describe both the stated risk and an empirical robustness observation.
  • Linear structure: For linearly correlated variables with shifted signal and background means, a single Fisher discriminant already provides theoretically maximum separation, so boosting adds no gain.The paper presents this as an academic training-sample example.
  • Linear structure: Linear discriminant analysis can reduce parameter tuning and support smaller training samples when variable relationships are adequately assessed through scatter and profile plots.Printing linear correlation coefficients alone is insufficient because they do not capture nonlinear relationships.
  • Nonlinear methods: Neural networks, support vector machines, boosted decision trees, and RuleFit are recommended for highly optimized problems with many input variables.The recommendation is conditional on the problem requiring substantial optimization and permitting many inputs.
  • Nonlinear methods: Multidimensional probability-density estimators such as PDE-RS, k-NN, and PDEFoam suit strong nonlinearities and intricate correlations but generally require relatively few input variables.Their applicability is constrained by the dimensionality of the input space.

11 TMVA implementation status summary for classification and regression

TMVA’s classification and regression methods are broadly operational for user analyses, including training, testing, evaluation, and application. Feature support remains uneven, especially for multi-target regression, variable ranking, standalone regression response classes, and some event-weight cases.

  • Overall status: All TMVA methods are operational for user analyses covering training, testing, evaluation, and application to unknown data samples.Additional features are optional and not uniformly available across methods.
  • Output support: Although TMVA 4 supports multidimensional MVA outputs, classification does not yet implement them, and only a few regression methods support multiple targets.This limits multi-output functionality differently across classification and regression.
  • Event-weight support: Individual event-weight support is common, but it is absent for CFMlpANN, while negative-weight support still requires further scrutiny.Negative event weights can arise in next-to-leading-order Monte Carlo simulations.
  • Variable ranking: Input-variable ranking is not straightforward for every MVA method, and objective ranking by successive variable elimination is only realized for the naive-Bayes likelihood classifier.A broader transparent ranking approach remains under consideration.
  • Application support: Standalone C++ response classes are generated by most classifiers but are not yet available for regression analysis or several listed methods.The missing methods include PDE-RS, PDE-Foam, k-NN, Cuts, and CFMlpANN.
  • User support: TMVA provides complete help messages for performance tuning and custom analysis macros for selected method-specific properties.Additional macros can be added upon user request.

12 Conclusions and Plans

TMVA unifies customizable multivariate classification and regression methods in ROOT, with standardized evaluation and flexible method combination. TMVA 4 adds generalized boosting and supports future committee-method designs.

  • Design and workflow: TMVA unifies customizable multivariate classification and regression algorithms in one ROOT-integrated framework with objective performance assessment.The toolkit supports training, testing, evaluation, visualization, and application through common interfaces.
  • Design and workflow: TMVA’s transparent Factory gives every method the same training and test data and evaluation prescriptions for unbiased comparison.A complete analysis separates training and application, with standardized outputs and ROOT macros supporting performance assessment.
  • Available methods: TMVA includes mature classification and regression methods spanning adaptive density estimation, nearest neighbours, discriminants, neural networks, support vector machines, boosted trees, and rule ensembles.Several methods support regression, including PDE-RS, PDE-Foam, k-NN, LD, MLP, and boosted decision trees.
  • Combination methods: TMVA 4’s framework can combine MVA methods, with generalized boosting allowing any classifier to be boosted through configuration options.The resulting committee method combines boosting with already optimized MVA algorithms.
  • Combination methods: Planned committee methods would assign different methods and variables to input-space regions or feed one MVA method’s output into another.These extensions go beyond boosting to categorized and sequential combinations.

A More Classifier Booking Examples

TMVA provides code examples for booking a broad range of classification methods and, where available, regression methods. Each booking specifies a method type, unique name, and classifier-specific options.

  • Cut and density methods: TMVA examples cover cut optimization using Monte Carlo sampling, genetic algorithms, and simulated annealing.The examples illustrate multiple optimization strategies for the cut-based method.
  • Cut and density methods: The booking examples include likelihood classifiers with spline, decorrelated, and unbinned-kernel probability-density options.Unspecified options use classifier defaults.
  • Multivariate methods: TMVA examples include multidimensional PDE range search, self-adapting PDE-Foam, k-nearest neighbours, and H-matrix methods.These represent density-estimation and distance- or matrix-based approaches available for booking.
  • Discriminant methods: The examples also cover Fisher variants, boosted Fisher, linear discriminant, and function discriminant analysis methods.Configuration strings can request input transformations such as Gaussian or principal-component transformations.
  • Neural networks: Neural-network examples include TMVA, BFGS, ROOT, and ALEPH multilayer perceptron variants.The examples identify distinct implementations and optimization choices.
  • Ensembles: The examples include adaptive, gradient, and bagged boosted decision trees together with RuleFit predictive rule ensembles.Each method is booked through a type enumerator, a unique user-defined name, and an option string.

Index

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