rrrBayes: Bayesian inference for reduced rank regression

In lockEF/MultiwayRegression: Perform tensor-on-tensor regression

Description

Performs Bayesian inference for a linear model to estimate one multi-way array from another, under the restriction that the coefficient array has given PARAFAC rank.

Usage

rrrBayes(X,Y,Inits,Xmat.new,R=1,lambda=0,Samples=1000, thin=1,seed=0)

Arguments

X	A predictor array of dimension N x P_1 x ... x P_L for the training data.
Y	An outcome array of dimension N x Q_1 x ... x Q_M for the training data.
Inits	Initial values. Inits$U gives a list of length L where Inits$U[[l]]: P_l x R gives the coefficient basis for the l'th mode of X. Inits$V gives a list of length M where Inits$V[[m]]: Q_m x R gives the coefficient basis for the m'th mode of Y. Can be the output of rrr(...).
Xmat.new	Predictor array of dimension M x P_1 x ... x P_L. Each row gives the entries for a new P_1 x ... x P_L predictor observation in vectorized form.
R	Assumed rank of the P_1 x ... x P_L x Q_1 x ... x Q_M coefficient array.
lambda	Ridge ($L_2$) penalty parameter for the coefficient array, inversely proportional to the variance of the coefficients under a Gaussian prior.
Samples	Length of the MCMC sampling chain.
thin	Thinning value, for thin=j, only every j'th observation in the MCMC chain is saved.
seed	Random seed for generation of initial values.

Value

An array of dimension (Samples/thin) x M x Q_1 x ... x Q_M, giving (Samples/thin) samples from the posterior predictive of the outcome array predicted by Xmat.new.

Author(s)

Eric F. Lock

References

Lock, E.F. (2017). Tensor-on-tensor regression. arXiv preprint: https://arxiv.org/abs/1701.01037.

lockEF/MultiwayRegression documentation built on June 20, 2019, 10:04 p.m.