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Exact dimensionality selection for Bayesian PCA

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  • Charles Bouveyron
  • Pierre Latouche
  • Pierre‐Alexandre Mattei

Abstract

We present a Bayesian model selection approach to estimate the intrinsic dimensionality of a high‐dimensional dataset. To this end, we introduce a novel formulation of the probabilisitic principal component analysis model based on a normal‐gamma prior distribution. In this context, we exhibit a closed‐form expression of the marginal likelihood which allows to infer an optimal number of components. We also propose a heuristic based on the expected shape of the marginal likelihood curve in order to choose the hyperparameters. In nonasymptotic frameworks, we show on simulated data that this exact dimensionality selection approach is competitive with both Bayesian and frequentist state‐of‐the‐art methods.

Suggested Citation

  • Charles Bouveyron & Pierre Latouche & Pierre‐Alexandre Mattei, 2020. "Exact dimensionality selection for Bayesian PCA," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(1), pages 196-211, March.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:1:p:196-211
    DOI: 10.1111/sjos.12424
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    1. Kellard, Neil M. & Kontonikas, Alexandros & Lamla, Michael J. & Maiani, Stefano & Wood, Geoffrey, 2023. "Institutional settings and financing green innovation," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 89(C).
    2. Qi Li & Yong Huang & Jiahui Chen & Xiaohui Liu & Xianghao Meng & Chao Lin, 2023. "Feature Selection and Damage Identification for Urban Railway Track Using Bayesian Globally Sparse Principal Component Analysis," Sustainability, MDPI, vol. 15(6), pages 1-17, March.
    3. Rahman, Khalil Ur & Ejaz, Nuaman & Shang, Songhao & Balkhair, Khaled S. & Alghamdi, Khalid Mohammad & Zaman, Kifayat & Khan, Mahmood Alam & Hussain, Anwar, 2024. "A robust integrated agricultural drought index under climate and land use variations at the local scale in Pakistan," Agricultural Water Management, Elsevier, vol. 295(C).

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