publication . Preprint . Article . 2015

Approximating Likelihood Ratios with Calibrated Discriminative Classifiers

Kyle Cranmer; Pavez, Juan; Louppe, Gilles;
Open Access English
  • Published: 06 Jun 2015
  • Country: Belgium
Abstract
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes that tie parameters $\theta$ of an underlying theory and measurement apparatus to high-dimensional observations $\mathbf{x}\in \mathbb{R}^p$. However, simulator often do not provide a way to evaluate the likelihood function for a given observation $\mathbf{x}$, which motivates a new class of likelihood-free inference algorithms. In this paper, we show that likelihood ratios are invariant under a specific class of dimensionalit...
Subjects
free text keywords: Statistics - Applications, Physics - Data Analysis, Statistics and Probability, Statistics - Machine Learning, 62P35, 62F99, 62H30, : Physics [Physical, chemical, mathematical & earth Sciences], : Physique [Physique, chimie, mathématiques & sciences de la terre], : Computer science [Engineering, computing & technology], : Sciences informatiques [Ingénierie, informatique & technologie], Physics - Data Analysis, Statistics and Probability, 62P35, 62F99, 62H30
Funded by
NSF| Elementary Particle Physics with ATLAS
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1505463
,
NSF| Elementary Particle Physics with ATLAS
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1205376
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Physics
,
NSF| Collaborative Research: SI2-SSI: Data-Intensive Analysis for High Energy Physics (DIANA/HEP)
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1450310
24 references, page 1 of 2

Agostinelli, S. et al. (2003). A506:250{303.

Allanach, B., Lester, C., Parker, M. A., and Webber, B. (2000). Measuring sparticle masses in nonuniversal string inspired models at the LHC. JHEP, 0009:004. [OpenAIRE]

Baak, M., Gadatsch, S., Harrington, R., and Verkerke, W. (2015). Interpolation between multi-dimensional histograms using a new non-linear moment morphing method. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 771:39{48. [OpenAIRE]

Baldi, P., Cranmer, K., Faucett, T., Sadowski, P., and Whiteson, D. (2016). Parameterized Machine Learning for High-Energy Physics. arXiv preprint arXiv:1601.07913.

Beaumont, M. A., Zhang, W., and Balding, D. J. (2002). Approximate bayesian computation in population genetics. Genetics, 162(4):2025{2035. [OpenAIRE]

Bickel, S., Bruckner, M., and Sche er, T. (2009). Discriminative learning under covariate shift. The Journal of Machine Learning Research, 10:2137{2155.

Brochu, E., Cora, V. M., and De Freitas, N. (2010). A tutorial on bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv preprint arXiv:1012.2599.

Chen, Y., Di Marco, E., Lykken, J., Spiropulu, M., Vega-Morales, R., et al. (2015). 8D likelihood e ective Higgs couplings extraction framework in h ! 4`. JHEP, 1501:125.

Cowan, G., Cranmer, K., Gross, E., and Vitells, O. (2010). Asymptotic formulae for likelihood-based tests of new physics. Eur.Phys.J., C71:1554.

Cranmer, K., Lewis, G., Moneta, L., Shibata, A., and Verkerke, W. (2012). HistFactory: A tool for creating statistical models for use with RooFit and RooStats. CERN-OPEN2012-016.

Friedman, J., Hastie, T., Tibshirani, R., et al. (2000). Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors). The annals of statistics, 28(2):337{407. [OpenAIRE]

Louppe, G., Cranmer, K., and Pavez, J. (2016). carl: a likelihood-free inference toolbox. http://dx.doi.org/10.5281/zenodo.47798, https://github.com/diana-hep/carl. [OpenAIRE]

Neal, R. M. (2007). Computing likelihood functions for high-energy physics experiments when distributions are de ned by simulators with nuisance parameters. In Proceedings of PhyStat2007, CERN-2008-001, pages 111{118.

Nguyen, X., Wainwright, M. J., Jordan, M., et al. (2010). Estimating divergence functionals and the likelihood ratio by convex risk minimization. Information Theory, IEEE Transactions on, 56(11):5847{5861.

Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825{2830. [OpenAIRE]

24 references, page 1 of 2
Abstract
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes that tie parameters $\theta$ of an underlying theory and measurement apparatus to high-dimensional observations $\mathbf{x}\in \mathbb{R}^p$. However, simulator often do not provide a way to evaluate the likelihood function for a given observation $\mathbf{x}$, which motivates a new class of likelihood-free inference algorithms. In this paper, we show that likelihood ratios are invariant under a specific class of dimensionalit...
Subjects
free text keywords: Statistics - Applications, Physics - Data Analysis, Statistics and Probability, Statistics - Machine Learning, 62P35, 62F99, 62H30, : Physics [Physical, chemical, mathematical & earth Sciences], : Physique [Physique, chimie, mathématiques & sciences de la terre], : Computer science [Engineering, computing & technology], : Sciences informatiques [Ingénierie, informatique & technologie], Physics - Data Analysis, Statistics and Probability, 62P35, 62F99, 62H30
Funded by
NSF| Elementary Particle Physics with ATLAS
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1505463
,
NSF| Elementary Particle Physics with ATLAS
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1205376
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Physics
,
NSF| Collaborative Research: SI2-SSI: Data-Intensive Analysis for High Energy Physics (DIANA/HEP)
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1450310
24 references, page 1 of 2

Agostinelli, S. et al. (2003). A506:250{303.

Allanach, B., Lester, C., Parker, M. A., and Webber, B. (2000). Measuring sparticle masses in nonuniversal string inspired models at the LHC. JHEP, 0009:004. [OpenAIRE]

Baak, M., Gadatsch, S., Harrington, R., and Verkerke, W. (2015). Interpolation between multi-dimensional histograms using a new non-linear moment morphing method. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 771:39{48. [OpenAIRE]

Baldi, P., Cranmer, K., Faucett, T., Sadowski, P., and Whiteson, D. (2016). Parameterized Machine Learning for High-Energy Physics. arXiv preprint arXiv:1601.07913.

Beaumont, M. A., Zhang, W., and Balding, D. J. (2002). Approximate bayesian computation in population genetics. Genetics, 162(4):2025{2035. [OpenAIRE]

Bickel, S., Bruckner, M., and Sche er, T. (2009). Discriminative learning under covariate shift. The Journal of Machine Learning Research, 10:2137{2155.

Brochu, E., Cora, V. M., and De Freitas, N. (2010). A tutorial on bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. arXiv preprint arXiv:1012.2599.

Chen, Y., Di Marco, E., Lykken, J., Spiropulu, M., Vega-Morales, R., et al. (2015). 8D likelihood e ective Higgs couplings extraction framework in h ! 4`. JHEP, 1501:125.

Cowan, G., Cranmer, K., Gross, E., and Vitells, O. (2010). Asymptotic formulae for likelihood-based tests of new physics. Eur.Phys.J., C71:1554.

Cranmer, K., Lewis, G., Moneta, L., Shibata, A., and Verkerke, W. (2012). HistFactory: A tool for creating statistical models for use with RooFit and RooStats. CERN-OPEN2012-016.

Friedman, J., Hastie, T., Tibshirani, R., et al. (2000). Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors). The annals of statistics, 28(2):337{407. [OpenAIRE]

Louppe, G., Cranmer, K., and Pavez, J. (2016). carl: a likelihood-free inference toolbox. http://dx.doi.org/10.5281/zenodo.47798, https://github.com/diana-hep/carl. [OpenAIRE]

Neal, R. M. (2007). Computing likelihood functions for high-energy physics experiments when distributions are de ned by simulators with nuisance parameters. In Proceedings of PhyStat2007, CERN-2008-001, pages 111{118.

Nguyen, X., Wainwright, M. J., Jordan, M., et al. (2010). Estimating divergence functionals and the likelihood ratio by convex risk minimization. Information Theory, IEEE Transactions on, 56(11):5847{5861.

Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825{2830. [OpenAIRE]

24 references, page 1 of 2
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publication . Preprint . Article . 2015

Approximating Likelihood Ratios with Calibrated Discriminative Classifiers

Kyle Cranmer; Pavez, Juan; Louppe, Gilles;