Abstract
Artificial neural networks(ANN) have been found to be an effective nonparametric method in many predictive applications. However, they have not been discussed much in the literature for angular data. In this article, we present two separate ANN models for angular-angular and linear-angular regression. We compare the performance of these ANN models with other regression models used in these contexts available in the literature. We find that the presented ANN models perform competitively and sometimes better as a predictive tool. We also propose two new methods for generating prediction intervals for ANN models. We find these prediction intervals provide good coverage probabilities on the Test dataset.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Agostinelli, C., Lund, U.: R package circular: Circular Statistics (version 0.4-93).CA: Department of Environmental Sciences, Informatics and Statistics, Ca’ Foscari University, Venice, Italy. UL: Department of Statistics, California Polytechnic State University, San Luis Obispo, California, USA (2017). https://r-forge.r-project.org/projects/circular/
Arnold V.I.: On the representation of functions of several variables as a superposition of functions of a smaller number of variables. In: Collected Works: Representations of Functions, Celestial Mechanics and KAM Theory, 1957–1965, pp. 25–46 (2009)
Grant, B.J., et al.: Bio3D: an R package for the comparative analysis of protein structures. Bioinformatics 22, 2695–2696 (2006)
Bhattacharya, S., Sengupta, A.: Bayesian analysis of semiparametric linear-circular models. J. Agric. Biol. Environ. Stat. 14(1), 33 (2009)
Chakraborty, S., Wong, S.W.K.: BAMBI: an R package for fitting bivariate angular mixture models. ArXiv preprint arXiv:1708.07804 (2017)
Cox, D.R., Snell, E.J.: Applied Statistics-Principles and Examples, vol. 2. CRC Press (1981)
Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math. Cont. Sig. Syst. 2(4), 303–314 (1989)
Di Marzio, M., Panzera, A., Taylor, C.C.: Non-parametric regression for circular responses. Scandinavian J. Stat. 40(2), 238–255 (2013)
Downs, T.D., Mardia, K.V.: Circular regression. Biometrika 89(3), 683–698 (2002)
Fisher, N.I.: Statistical Analysis of Circular Data. Cambridge University Press (1995)
Fisher, N.I., Lee, A.J.: Regression models for an angular response. Biometrics 665–677 (1992)
Goodfellow, I., et al.: Deep Learning, vol. 1. 2. MIT Press Cambridge (2016)
Gould, A.L.: A regression technique for angular variates. Biometrics, 683–700 (1969)
Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural Netw. 4(2), 251–257 (1991)
Jammalamadaka, S., Sengupta, A.: Topics in Circular Statistics, vol. 5. World Scientific (2001)
Johnson, R.A., Wehrly, T.E.: Some angular-linear distributions and related regression models. J. Am. Stat. Assoc. 73(363), 602–606 (1978)
Kato, S., Shimizu, K., Shieh, G.S.: A circular-circular regression model. Stat. Sinica 633–645 (2008)
Kemp, M., et al.: RNCEP: global weather and climate data at your fingertips. Methods Ecol. Evol. 3(1 2012). R package version 1.0.10, pp. 65–70. ISSN: 2041-210X. https://doi.org/10.1111/j.2041-210X.2011.00138.x
Li, H., et al.: Deep learning methods for protein torsion angle prediction. BMC Bioinf. 18(1), 417 (2017)
Lu, Z., et al.: The expressive power of neural networks: a view from the width. Advances in neural information processing systems, pp. 6231–6239 (2017)
Lund, U., Agostinelli, C.: CircStats: circular statistics, from topics in circular statistics (2001). R package version 0.2-6. 2018. https://CRAN.R-project.org/package=CircStats
Panaretos, V.M., Zemel, Y.: Statistical aspects of Wasserstein distances. Ann. Rev. Stat. Appl. 6, 405–431 (2019)
Presnell, B., Morrison, S.P., Littell, R.C.: Projected multivariate linear models for directional data. J. Am. Stat. Assoc. 93(443), 1068–1077 (1998)
Rivest, L.-P.: A decentered predictor for circular-circular regression. Biometrika 84(3), 717–726 (1997)
Rosenblatt, F.: The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65(6), 386 (1958)
Sarma, Y., Jammalamadaka, S.: Circular regression. In: Statistical Science and Data Analysis. Proceedings of the Third Pacific Area Statistical Conference, pp. 109–128 (1993)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Laha, A.K., Majumdar, S. (2022). Angular-Angular and Linear-Angular Regression Using ANN. In: SenGupta, A., Arnold, B.C. (eds) Directional Statistics for Innovative Applications. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-1044-9_24
Download citation
DOI: https://doi.org/10.1007/978-981-19-1044-9_24
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-1043-2
Online ISBN: 978-981-19-1044-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)