tosccamm

tosccamm is the package to implement the Thresholded Ordered Sparse CCA for Multiple Measurements (TOSCCA-MM) method described in Senar, et al., ?? (paper not yet available).

Installation

You can install the development version of tosccamm like so:

devtools::install_github("nuria-sv/toscca")    # dependencies
devtools::install_github("nuria-sv/tosccamm")

TOSCCA-MM

TOSCCA-MM is a novel extension of sparse CCA that incorporates time dynamics at the latent variable level through longitudinal models, such as autoregressive models or linear mixed effect models. This approach addresses the correlation of repeated measurements while drawing latent paths, for each component. To aid interpretability and computational efficiency, we implement an $\ell_0$ penalty to enforce fixed sparsity levels. We estimate these trajectories fitting longitudinal models to the low-dimensional latent variables, (i.e.: linear mixed effects model). By leveraging the clustered structure of high-dimensional datasets, we are able to explore the shared longitudinal latent mechanisms. The sparse canonical weights, yield interpretable outcomes on variable contribution to the estimated correlated trajectories. Furthermore, modelling time in the latent space significantly reduces computational burden.

Example

This is a basic example over simulated data of TOSCCA-MM

library(tosccamm)

# for plots
library(grid)
library(ggplot2)
library(gridExtra)

Estimate the canonical weights and latent paths for $K$ components.

res_k = list()

X.temp = XX2
Y.temp = YY2
for (k in 1:K) {
  if(k > 1) {
    # residualise for subsequent components
    X.temp = data.frame(X.temp[,c(1,2)],toscca::residualisation(as.matrix(X.temp[,-c(1,2)]), res_k[[k-1]]$alpha, type = "basic") )
    Y.temp = data.frame(Y.temp[,c(1,2)],toscca::residualisation(as.matrix(Y.temp[,-c(1,2)]), res_k[[k-1]]$beta, type = "basic") )

    nz_a_gen = as.numeric(table(res_k[[k-1]]$alpha != 0)[2])
    nz_b_gen = as.numeric(table(res_k[[k-1]]$beta != 0)[2])
  }

  res_k[[k]] <- tosccamm(X.temp, Y.temp, folds = 2,
                                            nonzero_a = nonz_a, nonzero_b = nonz_b,
                                            model = "lme", lmeformula = " ~ 0 + poly(time,3) + (1|id)")

}
#> Loading required package: Matrix
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo
#>  Common convergence error: 0 & Iterations: 5  Common convergence error: 0 & Iterations: 5 
#> k-fold cv max. cancor 
#>             0.9992169 
#> 
#>  ........................................ 
#>  # nonzero A: 15
#>  # nonzero B: 5
#>  ........................................

#>  Common convergence error: 0.04707 & Iterations: 21  Common convergence error: 0.05388 & Iterations: 21 
#> k-fold cv max. cancor 
#>              0.986778 
#> 
#>  ........................................ 
#>  # nonzero A: 40
#>  # nonzero B: 39
#>  ........................................

#>  Common convergence error: 0.03885 & Iterations: 21  Common convergence error: 0.03053 & Iterations: 21 
#> k-fold cv max. cancor 
#>             0.9577028 
#> 
#>  ........................................ 
#>  # nonzero A: 30
#>  # nonzero B: 5
#>  ........................................

Results

Latent paths for $k=1$ and $k=2$

Canonical weights for $k=1$ and $k=2$

Latent path and canonical weights for $k=3$, noise