Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data. / Cordoba, Irene; Bielza, Concha; Larranaga, Pedro; Varando, Gherardo.

In: IEEE Access, Vol. 8, 01.01.2020, p. 154614-154624.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Cordoba, I, Bielza, C, Larranaga, P & Varando, G 2020, 'Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data', IEEE Access, vol. 8, pp. 154614-154624. https://doi.org/10.1109/ACCESS.2020.3018593

APA

Cordoba, I., Bielza, C., Larranaga, P., & Varando, G. (2020). Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data. IEEE Access, 8, 154614-154624. https://doi.org/10.1109/ACCESS.2020.3018593

Vancouver

Cordoba I, Bielza C, Larranaga P, Varando G. Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data. IEEE Access. 2020 Jan 1;8:154614-154624. https://doi.org/10.1109/ACCESS.2020.3018593

Author

Cordoba, Irene ; Bielza, Concha ; Larranaga, Pedro ; Varando, Gherardo. / Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data. In: IEEE Access. 2020 ; Vol. 8. pp. 154614-154624.

Bibtex

@article{ac20bc0e33034955a67c7d6a29af0c45,
title = "Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data",
abstract = "The sparse Cholesky parametrization of the inverse covariance matrix is directly related to Gaussian Bayesian networks. Its counterpart, the covariance Cholesky factorization model, has a natural interpretation as a hidden variable model for ordered signal data. Despite this, it has received little attention so far, with few notable exceptions. To fill this gap, in this paper we focus on arbitrary zero patterns in the Cholesky factor of a covariance matrix. We discuss how these models can also be extended, in analogy with Gaussian Bayesian networks, to data where no apparent order is available. For the ordered scenario, we propose a novel estimation method that is based on matrix loss penalization, as opposed to the existing regression-based approaches. The performance of this sparse model for the Cholesky factor, together with our novel estimator,is assessed in a simulation setting, as well as over spatial and temporal real data where a natural ordering arises among the variables. We give guidelines, based on the empirical results, about which of the methods analysed is more appropriate for each setting.",
author = "Irene Cordoba and Concha Bielza and Pedro Larranaga and Gherardo Varando",
year = "2020",
month = jan,
day = "1",
doi = "10.1109/ACCESS.2020.3018593",
language = "English",
volume = "8",
pages = "154614--154624",
journal = "IEEE Access",
issn = "2169-3536",
publisher = "Institute of Electrical and Electronics Engineers",

}

RIS

TY - JOUR

T1 - Sparse Cholesky Covariance Parametrization for Recovering Latent Structure in Ordered Data

AU - Cordoba, Irene

AU - Bielza, Concha

AU - Larranaga, Pedro

AU - Varando, Gherardo

PY - 2020/1/1

Y1 - 2020/1/1

N2 - The sparse Cholesky parametrization of the inverse covariance matrix is directly related to Gaussian Bayesian networks. Its counterpart, the covariance Cholesky factorization model, has a natural interpretation as a hidden variable model for ordered signal data. Despite this, it has received little attention so far, with few notable exceptions. To fill this gap, in this paper we focus on arbitrary zero patterns in the Cholesky factor of a covariance matrix. We discuss how these models can also be extended, in analogy with Gaussian Bayesian networks, to data where no apparent order is available. For the ordered scenario, we propose a novel estimation method that is based on matrix loss penalization, as opposed to the existing regression-based approaches. The performance of this sparse model for the Cholesky factor, together with our novel estimator,is assessed in a simulation setting, as well as over spatial and temporal real data where a natural ordering arises among the variables. We give guidelines, based on the empirical results, about which of the methods analysed is more appropriate for each setting.

AB - The sparse Cholesky parametrization of the inverse covariance matrix is directly related to Gaussian Bayesian networks. Its counterpart, the covariance Cholesky factorization model, has a natural interpretation as a hidden variable model for ordered signal data. Despite this, it has received little attention so far, with few notable exceptions. To fill this gap, in this paper we focus on arbitrary zero patterns in the Cholesky factor of a covariance matrix. We discuss how these models can also be extended, in analogy with Gaussian Bayesian networks, to data where no apparent order is available. For the ordered scenario, we propose a novel estimation method that is based on matrix loss penalization, as opposed to the existing regression-based approaches. The performance of this sparse model for the Cholesky factor, together with our novel estimator,is assessed in a simulation setting, as well as over spatial and temporal real data where a natural ordering arises among the variables. We give guidelines, based on the empirical results, about which of the methods analysed is more appropriate for each setting.

U2 - 10.1109/ACCESS.2020.3018593

DO - 10.1109/ACCESS.2020.3018593

M3 - Journal article

VL - 8

SP - 154614

EP - 154624

JO - IEEE Access

JF - IEEE Access

SN - 2169-3536

ER -

ID: 248192497