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Element-wise cross-validation for nmfkc.net (upper-triangle folds)

Source: R/nmfkc.net.R
nmfkc.net.ecv.Rd

k-fold CV with folds taken over the upper triangle of the symmetric \(Y\) (mirrored to the lower triangle) to prevent information leakage through symmetry. A single entry point covers all three symmetric NMF variants; type selects the fitting function:

Usage

nmfkc.net.ecv(Y, rank = 1:3, type = c("tri", "bi", "signed"), ...)

Arguments

Y

Symmetric N x N non-negative matrix.

rank

Integer vector of ranks to evaluate. Default 1:3.

type

Model type: "tri" (default), "bi", or "signed".

...

Passed to the underlying fitter; also accepts:

  • nfolds (default 5; div alias) and seed (default 123).

  • diag.exclude (default FALSE): leave the diagonal out of the folds and out of every fit (see nmfkc.net), for a network without self-loops. Otherwise its zeros would be scored as edges to predict.

  • folds: the folds to use, as a list of linear indices into \(Y\) – e.g.\ the $folds of an earlier run, so that two models are compared on the same split. A lower-triangle index is read as its upper-triangle mirror. An entry in two folds, or one that cannot be held out (NA, zero weight, or the diagonal under diag.exclude), is an error. nfolds is then length(folds). (Within this function the folds depend only on \(N\), nfolds, seed and the entries that can be held out, so runs that share these already share their folds.)

  • seeds: a vector of seeds (overriding seed), to repeat the CV over different splits. Each split refits with its seed, so the results for seed \(s\) are those of seed = s. objfunc, sigma and r.squared.cv are then averaged over the seeds, with their spread in objfunc.sd and r.squared.cv.sd. Not with folds.

  • pred (default FALSE): also return the held-out predictions (an \(N \times N\) array per rank; kept optional because it is \(N^2\) per rank).

  • Y.weights: as in nmfkc.net. Entries of weight 0 are never held out, every fit keeps the weights, and the held-out loss is the weighted mean. (Before 1.0.0 a Y.weights given here was silently replaced by the fold mask.)

  • cores (getOption("mc.cores", 1L)) to evaluate the rank x fold grid in parallel; results are identical to the sequential run for any cores (PSOCK cluster on Windows, forking elsewhere).

NA entries of \(Y\) are never held out and stay masked in every fit (before 1.0.0 they were fitted as zeros and made objfunc NA).

Value

A list with objfunc, sigma, objfunc.fold, folds, Q.grid, type, and

r.squared.cv

Held-out \(R^2\) per rank, pooled over the folds: \(1 - \sum (y - \hat y)^2 / \sum (y - \bar y)^2\) over all held-out upper-triangle entries (weighted when Y.weights is given). Unlike the r.squared of a fit (a squared correlation), it can be negative.

pred

With pred = TRUE: \(N \times N \times\) (ranks) array of held-out predictions, mirrored to the lower triangle; NA where an entry was never held out.

diag.exclude

TRUE, present only when used.

seeds, objfunc.rep, objfunc.sd, r.squared.cv.rep, r.squared.cv.sd, folds.rep

Present only with two or more seeds: the per-seed values (ranks x seeds), their standard deviations, and each seed's folds. objfunc.fold, folds and pred are those of the first seed.

Lifecycle

This function is experimental. The interface may change in future versions; details are to be described in an upcoming paper.

See also

nmfkc.net