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Can the Compositional Nature of Compositional Data Be Ignored by Using Deep Learning Approaches?

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Studies in Theoretical and Applied Statistics (SIS 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 406))

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Abstract

The application of non-compositional methods to compositional data representing parts of a whole should be avoided from a theoretical point of view. For example, one can show that Pearson correlations applied to compositional data are biased to be negative. Moreover, almost all statistical methods lead to biased estimates when applied to compositional data. One way out is to analyze data after representing them in log-ratio coordinates. However, several implications arise, such as interpretation in log-ratios and dealing with zeros and non-detects where log-ratios are undefined. When focusing on settings where only the prediction and classification error is important rather than an interpretation of results, one might argue to rather use non-linear methods to avoid those implications. Generally, it is known that misclassification and prediction errors are lower with a log-ratio approach when using machine learning methods that model the linear relationship between variables. However, is this also true when training a neural network who may learn the inner relationships between parts of a whole also without representing the data in log-ratios? This paper gives an answer of this matter based on applications with multiple real data sets, leading to the recommendation to use a compositional treatment of compositional data in any case. Misclassification and prediction errors are lower when nonlinear methods, and in particular deep learning methods, are applied together with a compositional treatment of compositional data. The compositional treatment of compositional data therefore remains very important even in the context of focusing on prediction errors using deep artificial neural networks or other nonlinear methods.

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Authors and Affiliations

  1. Institute of Data Analysis and Process Design, Zurich University of Applied Sciences, Rosenstrasse 3, 8404, Winterthur, Switzerland

    Matthias Templ

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  1. Matthias Templ
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Correspondence to Matthias Templ .

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Editors and Affiliations

  1. Department of Economics and Management, University of Pisa, Pisa, Italy

    Nicola Salvati

  2. Department of Economics and Statistics, University of Salerno, Fisciano, Salerno, Italy

    Cira Perna

  3. Department of Economics and Management, University of Pisa, Pisa, Italy

    Stefano Marchetti

  4. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia

    Raymond Chambers

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Templ, M. (2022). Can the Compositional Nature of Compositional Data Be Ignored by Using Deep Learning Approaches?. In: Salvati, N., Perna, C., Marchetti, S., Chambers, R. (eds) Studies in Theoretical and Applied Statistics . SIS 2021. Springer Proceedings in Mathematics & Statistics, vol 406. Springer, Cham. https://doi.org/10.1007/978-3-031-16609-9_11

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