nmf.ffb.ecv: Choose the number of factors for NMF-FFB by element-wise...

In nmfkc: Non-Negative Matrix Factorization with Kernel Covariates

Choose the number of factors for NMF-FFB by element-wise cross-validation

Description

Step 1 of the NMF-FFB workflow: select Q by element-wise cross-validation of the feed-forward fit. Held-out entries of Y_1 are predicted from the remaining ones, so the criterion measures how well a Q-factor non-negative basis describes the outcomes, which is what Q is for.

Usage

nmf.ffb.ecv(
  Y1,
  Y2,
  rank = NULL,
  X.init = "nndsvd",
  X.L2.ortho = 100,
  epsilon = 1e-06,
  maxit = 5000,
  ...
)

Arguments

Y1, Y2	Endogenous and exogenous matrices (variables in rows, units in columns).
rank	Candidate values of Q. Defaults to seq_len(min(3, nrow(Y1))).
X.init	Stage-1 initialization, passed to nmfkc.
X.L2.ortho	Orthogonality penalty on the basis in stage 1. Keep the value that will be used in nmf.ffb: Q and the penalty are not separable.
epsilon, maxit	Convergence tolerance and iteration cap for stage 1.
...	Passed to nmfkc.ecv: nfolds, seed, and cores (or ncores) to evaluate the rank x fold grid in parallel, defaulting to getOption("mc.cores", 1L) as elsewhere in the package.

Details

Feedback cannot be cross-validated, and that is not a limitation of the implementation. By the reduced-form equivalence, the equilibrium mapping M = (I - X\Theta_1)^{-1}X\Theta_2 is reproduced exactly by a feed-forward model with the exogenous matrix L_Q\Theta_2: the two models predict Y_1 from Y_2 identically, so no prediction criterion – column-wise CV, element-wise CV, or a test-sample error – can prefer one over the other. Feedback is identified by the conditional covariance, not by prediction, which is why it is addressed by nmf.ffb.test and not here.

Value

The object returned by nmfkc.ecv: the held-out error by rank, with the selected rank.

Workflow

ecv <- nmf.ffb.ecv(Y1, Y2, rank = 1:5)   # 1. choose Q            <- this function
fit <- nmf.ffb(Y1, Y2, rank = ecv$rank)  # 2. estimate; BIC selects the support
tst <- nmf.ffb.test(fit, Y1, Y2)         # 3. test the feed-forward null
dgn <- nmf.ffb.diagnostics(fit)          # 4. cycles, spectral radius, identifiability
inf <- nmf.ffb.inference(fit, Y1, Y2)    # 5. intervals for the retained entries

See Also

nmf.ffb, nmf.ffb.test, nmfkc.ecv

Examples

set.seed(1)
Y <- t(as.matrix(iris[, 1:4]))
Y1 <- Y[1:2, ]; Y2 <- Y[3:4, ]
ecv <- nmf.ffb.ecv(Y1, Y2, rank = 1:2, nfolds = 3)
ecv$rank

nmfkc documentation built on Oct. 30, 2026, 9:06 a.m.