Supervised multiway factorization

Lock, Eric F.; Li, Gen

doi:10.1214/18-ejs1421

Cited by 15 publications

(21 citation statements)

References 36 publications

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“…Sun and Li (2016) propose a tensor response regression wherein a multiway outcome is assumed to have a CP factorization, and Li and Zhang (2016) propose a tensor response regression wherein a multiway outcome is assumed to have a Tucker factorization with weights determined by vector-valued predictors. For a similar context Lock and Li (2016) describe a supervised CP factorization, wherein the components of a CP factorization are informed by vector-valued covariates. Hoff (2015) extend a bilinear regression model for matrices to the prediction of an outcome tensor from a predictor tensor with the same number of modes (e.g., 𝕐:N×Q1×⋯×QK and 𝕏:N×P1×⋯×PK) via a Tucker product and describe a Gibbs sampling approach to inference.…”

Section: Introductionmentioning

confidence: 99%

Tensor-on-Tensor Regression

Lock

2018

Journal of Computational and Graphical Statistics

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We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge (L2) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data. An R package is available at https://github.com/lockEF/MultiwayRegression.

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Section: Introductionmentioning

confidence: 99%

Tensor-on-Tensor Regression

Lock

2018

Journal of Computational and Graphical Statistics

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“…Several algorithms to extend SVD to tables with more than two entries have been proposed (Tucker, 1966;Carroll and Chang, 1970;Harshman, 1970;Kroonenberg, 1983;Leibovici, 2010), and development of methods and their applications is still very active (Demšar et al, 2013;Kroonenberg, 2016;Takeuchi et al, 2017;Lock and Li, 2018). Most extensions aim to find an optimum decomposition of a multiway table that allows dimension reduction by looking for a decomposition similar to Eq.…”

Section: Analysing Spatio-temporal Variations In Lsmsmentioning

confidence: 99%

“…This will have multiple societal impacts, not least on the health of animals and humans (IPCC AR5 WG2 A, 2014). The term climate-sensitive infection (CSI) refers to diseases whose epidemiological aspects are driven, at least in part, by climatic factors (McMichael et al, 2006;Ebi et al, 2017;Cayol et al, 2017). In the Arctic, climate change is likely to cause enhanced CSI risk in terms of increased incidence, more frequent outbreaks, geographic spread of existing affected zones, and occurrence of newly affected zones (Pauchard et al, 2016;Sajanti et al, 2017;Waits et al, 2018) The complex ecology of CSI organisms presents a challenge to modelling and predicting their epidemiology (Ostfeld, 2010;Carvalho et al, 2014;Ruscio et al, 2015;Sormunen et al, 2016;Li et al, 2016;White et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal variations and uncertainty in land surface modelling for high latitudes: univariate response analysis

et al. 2020

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Abstract. A range of applications analysing the impact of environmental changes due to climate change, e.g. geographical spread of climate-sensitive infections (CSIs) and agriculture crop modelling, make use of land surface modelling (LSM) to predict future land surface conditions. There are multiple LSMs to choose from that account for land processes in different ways and this may introduce predictive uncertainty when LSM outputs are used as inputs to inform a given application. For useful predictions for a specific application, one must therefore understand the inherent uncertainties in the LSMs and the variations between them, as well as uncertainties arising from variation in the climate data driving the LSMs. This requires methods to analyse multivariate spatio-temporal variations and differences. A methodology is proposed based on multiway data analysis, which extends singular value decomposition (SVD) to multidimensional tables and provides spatio-temporal descriptions of agreements and disagreements between LSMs for both historical simulations and future predictions. The application underlying this paper is prediction of how climate change will affect the spread of CSIs in the Fennoscandian and north-west Russian regions, and the approach is explored by comparing net primary production (NPP) estimates over the period 1998–2013 from versions of leading LSMs (JULES, CLM5 and two versions of ORCHIDEE) that are adapted to high-latitude processes, as well as variations in JULES up to 2100 when driven by 34 global circulation models (GCMs). A single optimal spatio-temporal pattern, with slightly different weights for the four LSMs (up to 14 % maximum difference), provides a good approximation to all their estimates of NPP, capturing between 87 % and 93 % of the variability in the individual models, as well as around 90 % of the variability in the combined LSM dataset. The next best adjustment to this pattern, capturing an extra 4 % of the overall variability, is essentially a spatial correction applied to ORCHIDEE-HLveg that significantly improves the fit to this LSM, with only small improvements for the other LSMs. Subsequent correction terms gradually improve the overall and individual LSM fits but capture at most 1.7 % of the overall variability. Analysis of differences between LSMs provides information on the times and places where the LSMs differ and by how much, but in this case no single spatio-temporal pattern strongly dominates the variability. Hence interpretation of the analysis requires the summation of several such patterns. Nonetheless, the three best principal tensors capture around 76 % of the variability in the LSM differences and to a first approximation successively indicate the times and places where ORCHIDEE-HLveg, CLM5 and ORCHIDEE-MICT differ from the other LSMs. Differences between the climate forcing GCMs had a marginal effect up to 6 % on NPP predictions out to 2100 without specific spatio-temporal GCM interaction.

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“…Several algorithms to extend SVD to tables with more than 2 entries have been proposed (Tucker, 1966;Carroll and Chang, 1970;Harshman, 1970;Kroonenberg, 1983;Leibovici et al, 2007;Leibovici, 2010) and development of methods and their applications is is still very active (Demšar et al, 2013;Kroonenberg, 2016;Takeuchi et al, 2017;Lock and Li, 2018). Most extensions aim to find an optimum decomposition of a multi-way table that allows dimension reduction by looking for a decomposition similar to equation (1) under specific optimisation criteria.…”

Section: Land Surface Model and Data Descriptionmentioning

confidence: 99%

Spatio-Temporal Variations and Uncertainty in Land Surface Modelling for High Latitudes: Univariate Response Analysis

Leibovici¹,

Quegan²,

Comyn‐Platt³

et al. 2019

Preprint

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<p><strong>Abstract.</strong> A range of applications analysing the impact of environmental changes due to climate change, e.g. geographical spread of climate sensitive infections (CSIs), agriculture crop modelling, etc., make use of Land Surface Modelling (LSM) to predict future land surface conditions. There are multiple LSMs to choose from that account for land processes in different ways and, depending on the application, the choice of LSM and its sensitivity will have different impacts. For useful predictions for a specific application, one must therefore understand the inherent uncertainties in the LSMs and the variations between them, as well as uncertainties arising from variation in the climate data driving the LSMs. This requires methods to analyse multivariate spatio-temporal variations and differences. A methodology is proposed based on multi-way data analysis, which extends Singular Value Decomposition (SVD) to multi-dimensional tables, and provides spatio-temporal descriptions of agreements and disagreements between LSMs for both historical simulations and future predictions. The application underlying this paper is prediction of how climate change will affect the spread of CSIs in the Fenno-Scandinavian and north-west Russian regions, and the approach is explored by comparing Net Primary Production (NPP) estimates over the period 1998&#8211;2013 from versions of leading LSMs (JULES, CLM5 and two versions of ORCHIDEE) that are adapted to high latitude processes, as well as variations in JULES up to 2100 when driven by 34 global circulation models (GCMs). A single optimal spatio-temporal pattern, with slightly different weights for the four LSMs (up to 14&#8201;% maximum difference), provides a good approximation to all their estimates of NPP, capturing between 87&#8201;% and 93&#8201;% of the variability in the individual models, as well as around 90&#8201;% of the variability in the combined LSM dataset. The next best adjustment to this pattern, capturing an extra 4&#8201;% of the overall variability, is essentially a spatial correction applied to ORCHIDEE-HLveg that significantly improves the fit to this LSM, with only small improvements for the other LSMs. Subsequent correction terms gradually improve the overall and individual LSM fits, but capture at most 1.7&#8201;% of the overall variability. Analysis of differences between LSMs provides information on the times and places where the LSMs differ and by how much, but in this case no single spatio-temporal pattern strongly dominates the variability. Hence interpretation of the analysis requires the summation of several such patterns. Nonetheless, the three best principal tensors capture around 76&#8201;% of the variability in the LSM differences, and to a first approximation successively indicate the times and places where ORCHIDEE-HLveg, CLM5 and ORCHIDEE-MICT respectively differ from the other LSMs. Differences between the climate forcing GCMs had a marginal effect up to 6&#8201;% on NPP predictions out to 2100 without specific spatio-temporal GCM interaction.</p>

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Supervised multiway factorization

Cited by 15 publications

References 36 publications

Tensor-on-Tensor Regression

Tensor-on-Tensor Regression

Spatio-temporal variations and uncertainty in land surface modelling for high latitudes: univariate response analysis

Spatio-Temporal Variations and Uncertainty in Land Surface Modelling for High Latitudes: Univariate Response Analysis

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