rrrBayes {MultiwayRegression}

Bayesian inference for reduced rank 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,X.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(...).

X.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. (2018). Tensor-on-tensor regression. Journal of Computational and Graphical Statistics, 27 (3): 638-647, 2018.