Matrix Variate Regressions and Envelope Models

Ding, Shanshan; Cook, R. Dennis

doi:10.1111/rssb.12247

Cited by 56 publications

(41 citation statements)

References 45 publications

(94 reference statements)

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“…. , y j,t−P ) with 1 ≤ j ≤ N ; note that similar formulations can be found in matrix variate regressions such as Zhao and Leng (2014) and Ding and Cook (2018).…”

Section: Multilinear Low-rank Vector Autoregressionmentioning

confidence: 85%

High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

Wang¹,

Lian²,

Zheng

et al. 2019

SSRN Journal

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The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to rearrange the coefficient matrices of the model into a tensor form such that the parameter space can be restricted in three directions simultaneously via tensor decomposition. The proposed method substantially expands the capacity of vector autoregressive modeling for a large number of time series. In contrast, the widely used reduced-rank regression method can restrict the parameter space in only one direction. Moreover, to handle high-dimensional time series, this paper considers imposing sparsity on factor matrices to improve the interpretability and estimation efficiency, which leads to a sparsity-inducing estimator. For the low-dimensional case, we derive asymptotic properties of the proposed least squares estimator and introduce an alternating least squares algorithm. For the high-dimensional case, we establish non-asymptotic properties of the sparsity-inducing estimator and propose an ADMM-based algorithm for regularized estimation. Simulation experiments and a real data example demonstrate the advantages of the proposed approach over various existing methods.

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“…. , y j,t−P ) with 1 ≤ j ≤ N ; note that similar formulations can be found in matrix variate regressions such as Zhao and Leng (2014) and Ding and Cook (2018).…”

Section: Multilinear Low-rank Vector Autoregressionmentioning

confidence: 85%

High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

Wang¹,

Lian²,

Zheng

et al. 2019

SSRN Journal

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“…Rather than vectorizing the DF matrix and treating it as a feature vector for standard classification techniques, we treat the DF as the matrix-valued feature that it is [52]. This allows for the retention of row and column dependence information that would normally be lost in the vectorization process [57].…”

Section: Distribution Fieldmentioning

confidence: 99%

A detection metric designed for O’Connell effect eclipsing binaries

Johnston¹,

Haber²,

Caballero-Nieves³

et al. 2019

Comput. Astrophys.

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We present the construction of a novel time-domain signature extraction methodology and the development of a supporting supervised pattern detection algorithm. We focus on the targeted identification of eclipsing binaries that demonstrate a feature known as the O'Connell effect. Our proposed methodology maps stellar variable observations to a new representation known as distribution fields (DFs). Given this novel representation, we develop a metric learning technique directly on the DF space that is capable of specif-1 arXiv:1911.03543v1 [astro-ph.IM] 8 Nov 2019 ically identifying our stars of interest. The metric is tuned on a set of labeled eclipsing binary data from the Kepler survey, targeting particular systems exhibiting the O'Connell effect. The result is a conservative selection of 124 potential targets of interest out of the Villanova Eclipsing Binary Catalog. Our framework demonstrates favorable performance on Kepler eclipsing binary data, taking a crucial step in preparing the way for large-scale data volumes from next-generation telescopes such as LSST and SKA.

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“…If u = r , then

E_{Σ} false(scriptB false) = R^{r}

, which implies that there is no immaterial information and the envelope model reduces to the standard model. For more intuition on the envelope model, we refer to the review section in Ding and Cook ().…”

Section: Review Of Envelope Modelmentioning

confidence: 99%

“…Khare et al () proposed a comprehensive Bayesian framework for estimation and model selection in envelope models. In addition, Li and Zhang () and Ding and Cook () studied envelope models in matrix‐variate and tensor settings.…”

Section: Introductionmentioning

confidence: 99%

Vector autoregression and envelope model

Wang

Ding

2018

Stat

Self Cite

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Vector autoregression is an important technique for modelling multivariate time series and has been widely used in a variety of applications. Owing to its fast growth of parameters with the dimension of the time series vector, dimension reduction is often desirable in multivariate time series analysis. The envelope model is a new approach to achieve dimension reduction and allows efficient estimation in multivariate analysis. In this paper, we provide the first work to explore the application and extension of envelope models to multivariate time series data. We present the envelope and partial envelope formulations for vector autoregression and elaborate model selection, parameter estimation and asymptotic results. Simulations and real data analysis demonstrate the efficiency gains of the envelope vector autoregression models compared with the standard models in terms of estimation. Meanwhile, the envelope models can excel in prediction improvement.

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Matrix Variate Regressions and Envelope Models

Cited by 56 publications

References 45 publications

High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

A detection metric designed for O’Connell effect eclipsing binaries

Vector autoregression and envelope model

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