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Subsampling and Aggregation: A Solution to the Scalability Problem in Distance-Based Prediction for Mixed-Type Data

Author

Listed:
  • Amparo Baíllo

    (Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
    These authors contributed equally to this work.)

  • Aurea Grané

    (Statistics Department, Universidad Carlos III de Madrid, 28903 Getafe, Spain
    These authors contributed equally to this work.)

Abstract

The distance-based linear model (DB-LM) extends the classical linear regression to the framework of mixed-type predictors or when the only available information is a distance matrix between regressors (as it sometimes happens with big data). The main drawback of these DB methods is their computational cost, particularly due to the eigendecomposition of the Gram matrix. In this context, ensemble regression techniques provide a useful alternative to fitting the model to the whole sample. This work analyzes the performance of three subsampling and aggregation techniques in DB regression on two specific large, real datasets. We also analyze, via simulations, the performance of bagging and DB logistic regression in the classification problem with mixed-type features and large sample sizes.

Suggested Citation

  • Amparo Baíllo & Aurea Grané, 2021. "Subsampling and Aggregation: A Solution to the Scalability Problem in Distance-Based Prediction for Mixed-Type Data," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2247-:d:634318
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    References listed on IDEAS

    as
    1. A. R. de Leon & A. Soo & T. Williamson, 2011. "Classification with discrete and continuous variables via general mixed-data models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1021-1032, February.
    2. Grané, Aurea & Salini, Silvia & Verdolini, Elena, 2021. "Robust multivariate analysis for mixed-type data: Novel algorithm and its practical application in socio-economic research," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    3. Eva Boj & Adrià Caballé & Pedro Delicado & Anna Esteve & Josep Fortiana, 2016. "Global and local distance-based generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 170-195, March.
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