A program for the Bayesian Neural Network in the ROOT framework

We present a Bayesian Neural Network algorithm implemented in the TMVA package (Hoecker et al., 2007 [1]), within the ROOT framework (Brun and Rademakers, 1997 [2]). Comparing to the conventional utilization of Neural Network as discriminator, this new implementation has more advantages as a non-parametric regression tool, particularly for fitting probabilities. It provides functionalities including cost function selection, complexity control and uncertainty estimation. An example of such application in High Energy Physics is shown. The algorithm is available with ROOT release later than 5.29.Program summaryProgram title: TMVA-BNNCatalogue identifier: AEJX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJX_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: BSD licenseNo. of lines in distributed program, including test data, etc.: 5094No. of bytes in distributed program, including test data, etc.: 1,320,987Distribution format: tar.gzProgramming language: C++Computer: Any computer system or cluster with C++ compiler and UNIX-like operating systemOperating system: Most UNIX/Linux systems. The application programs were thoroughly tested under Fedora and Scientific Linux CERN.Classification: 11.9External routines: ROOT package version 5.29 or higher (http://root.cern.ch)Nature of problem: Non-parametric fitting of multivariate distributionsSolution method: An implementation of Neural Network following the Bayesian statistical interpretation. Uses Laplace approximation for the Bayesian marginalizations. Provides the functionalities of automatic complexity control and uncertainty estimation.Running time: Time consumption for the training depends substantially on the size of input sample, the NN topology, the number of training iterations, etc. For the example in this manuscript, about 7 min was used on a PC/Linux with 2.0 GHz processors.

► A Bayesian Neural Network (BNN) is implemented in TMVA, within the ROOT framework.
► The Neural Network can be used as a non-parametric regression tool.
► The training and prediction procedure can be interpreted as Bayesian inference.
► A demonstration of BNN to fit the false identification rate of isolated muons.