| Title: | Perform Tensor-on-Tensor Regression |
|---|---|
| Description: | Functions to predict one multi-way array (i.e., a tensor) from another multi-way array, using a low-rank CANDECOMP/PARAFAC (CP) factorization and a ridge (L_2) penalty [Lock, EF (2018) <doi:10.1080/10618600.2017.1401544>]. Also includes functions to sample from the Bayesian posterior of a tensor-on-tensor model. |
| Authors: | Eric F. Lock |
| Maintainer: | Eric F. Lock <[email protected]> |
| License: | GPL-3 |
| Version: | 1.2 |
| Built: | 2024-12-15 07:21:47 UTC |
| Source: | CRAN |
Functions to predict one multi-way array (i.e., a tensor) from another multi-way array, using a low-rank CANDECOMP/PARAFAC (CP) factorization and a ridge (L_2) penalty. Also includes functions to sample from the Bayesian posterior of a tensor-on-tensor model.
| Package: | MultiwayRegression-package |
| Type: | Package |
| Version: | 1.2 |
| Date: | 2019-05-28 |
| License: | GPL-3 |
Eric F. Lock
Maintainer: Eric F. Lock <[email protected]>
Lock, E. F. (2018). Tensor-on-tensor regression. Journal of Computational and Graphical Statistics, 27 (3): 638-647, 2018.
data(SimData) ##loads simulated X: 100 x 15 x 20 and Y: 100 x 5 x 10 Results <- rrr(X,Y,R=2) ##Fit rank 2 model with no regularization Y_pred <- ctprod(X,Results$B,2) ##Array of fitted valuesdata(SimData) ##loads simulated X: 100 x 15 x 20 and Y: 100 x 5 x 10 Results <- rrr(X,Y,R=2) ##Fit rank 2 model with no regularization Y_pred <- ctprod(X,Results$B,2) ##Array of fitted values
Computes the contracted tensor product between two multiway arrays.
ctprod(A,B,K)ctprod(A,B,K)
A |
An array of dimension P_1 x ... x P_L x R_1 x ... x R_K. |
B |
An array of dimension R_1 x ... x R_K x Q_1 x ... x Q_M. |
K |
A positive integer, giving the number of modes to collapse. |
An array C of dimension P_1 x ... x P_L x Q_1 x ... x Q_M, given by the contracted tensor product of A and B.
Eric F. Lock
Fits a linear model to estimate one multi-way array from another, under the restriction that the coefficient array has given PARAFAC rank. By default, estimates are chosen to minimize a least-squares objective; an optional penalty term allows for $L_2$ regularization of the coefficient array.
rrr(X,Y,R=1,lambda=0,annealIter=0,convThresh=10^(-5), seed=0)rrr(X,Y,R=1,lambda=0,annealIter=0,convThresh=10^(-5), seed=0)
X |
A predictor array of dimension N x P_1 x ... x P_L. |
Y |
An outcome array of dimension N x Q_1 x ... X Q_M. |
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. |
annealIter |
Number of tempering iterations to improve initialization |
convThresh |
Converge threshold for the absolute difference in the objective function between two iterations |
seed |
Random seed for generation of initial values. |
U |
List of length L. U[[l]]: P_l x R gives the coefficient basis for the l'th mode of X. |
V |
List of length M. V[[m]]: Q_m x R gives the coefficient basis for the m'th mode of Y. |
B |
Coefficient array of dimension P_1 x ... x P_L x Q_1 x ... x Q_M. Given by the CP factorization defined by U and V. |
sse |
Vector giving the sum of squared residuals at each iteration. |
sseR |
Vector giving the value of the objective (sse+penalty) at each iteration. |
Eric F. Lock
Lock, E. F. (2018). Tensor-on-tensor regression. Journal of Computational and Graphical Statistics, 27 (3): 638-647, 2018.
data(SimData) ##loads simulated X: 100 x 15 x 20 and Y: 100 x 5 x 10 Results <- rrr(X,Y,R=2) ##Fit rank 2 model with no regularization Y_pred <- ctprod(X,Results$B,2) ##Array of fitted valuesdata(SimData) ##loads simulated X: 100 x 15 x 20 and Y: 100 x 5 x 10 Results <- rrr(X,Y,R=2) ##Fit rank 2 model with no regularization Y_pred <- ctprod(X,Results$B,2) ##Array of fitted values
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.
rrrBayes(X,Y,Inits,X.new,R=1,lambda=0,Samples=1000, thin=1,seed=0)rrrBayes(X,Y,Inits,X.new,R=1,lambda=0,Samples=1000, thin=1,seed=0)
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. |
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.
Eric F. Lock
Lock, E. F. (2018). Tensor-on-tensor regression. Journal of Computational and Graphical Statistics, 27 (3): 638-647, 2018.
Simulated multi-way data for prediction.
X: predictor array of dimension 100 x 15 x 20
Y: outcome array of dimension 100 x 5 x 10
Simulated multi-way data for prediction.
X: predictor array of dimension 100 x 15 x 20
Y: outcome array of dimension 100 x 5 x 10
Simulated multi-way data for prediction.
X: predictor array of dimension 100 x 15 x 20
Y: outcome array of dimension 100 x 5 x 10