Covariance Inference and Decompositions for Tensor Datasets
A collection of functions for Kronecker structured covariance
estimation and testing under the array normal model. For estimation,
maximum likelihood and Bayesian equivariant estimation procedures are
implemented. For testing, a likelihood ratio testing procedure is
available. This package also contains additional functions for manipulating
and decomposing tensor data sets. This work was partially supported by NSF
grant DMS-1505136. Details of the methods are described in
Gerard and Hoff (2015) <10.1016> and
Gerard and Hoff (2016) <10.1016>.10.1016>10.1016>
This package contains a collection of functions for statistical analysis
with tensor(array)-variate data sets. In particular,
tensr has the
- Basic functions for handling arrays, such as vectorization, matrix
unfolding, and multilinear multiplication.
- Functions for calculating (Tucker) tensor decompositions, such as
the incredible higher-order LQ decomposition (incredible HOLQ), the
incredible singular value decomposition (ISVD), the incredible
higher-order polar decomposition (IHOP), the higher-order singular
value decomposition (HOSVD), and the low multilinear rank
approximation using the higher-order orthogonal iteration (HOOI).
- Perform likelihood inference in mean-zero Kronecker structured
covariance models, such as
- Derive the maximum likelihood estimates of the covariance
matrices under the array normal model,
- Run a likelihood ratio test in separable covariance models, and
- Calculate AIC’s and BIC’s for separable covariance models.
- Run a Gibbs sampler to draw from the posterior distribution of the
Kronecker structured covariance matrix in the array normal model.
This posterior is with respect to a (non-informative) prior induced
by the right Haar measure over a product group of lower triangular
matrices acting on the space of Kronecker structured covariance
matrices. For any invariant loss function, any Bayes rule with
respect to this prior will be the uniformly minimum risk equivariant
estimator (UMREE) with respect to that loss.
- Calculate the UMREE under a multiway generalization of Stein’s loss.
This estimator dominates the maximum likelihood estimator uniformly
over the entire parameter space of Kronecker structured covariance
- Calculate a (randomized) orthogonally invariant estimator of the
Kronecker structured covariance matrix. This estimator dominates the
UMREE under the product group of lower triangular matrices.
This package is also published on
Vignettes are available on Equivariant
To install from CRAN, run in
To install the latest version from Github, run in
Gerard, D., & Hoff, P. (2016). A higher-order LQ decomposition for
separable covariance models. Linear Algebra and its Applications, 505,
57-84. [Link to LAA]
[Link to arXiv]
Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the
MLE in the array normal model. Journal of Multivariate Analysis, 137,
32-49. [Link to JMVA]
[Link to arXiv]