# Cross-Validation for cmls Does k-fold or generalized cross-validation to tune the constraint options for `cmls`. Tunes the model with respect to any combination of the arguments `const`, `df`, `degree`, and/or `intercept`. ```r cv.cmls(X, Y, nfolds = 2, foldid = NULL, parameters = NULL, const = "uncons", df = 10, degree = 3, intercept = TRUE, mse = TRUE, parallel = FALSE, cl = NULL, verbose = TRUE, ...) ``` ## Arguments - `X`: Matrix of dimension $n$ x $p$. - `Y`: Matrix of dimension $n$ x $m$. - `nfolds`: Number of folds for k-fold cross-validation. Ignored if `foldid` argument is provided. Set `nfolds=1` for generalized cross-validation (GCV). - `foldid`: Factor or integer vector of length $n$ giving the fold identification for each observation. - `parameters`: Parameters for tuning. Data frame with columns `const`, `df`, `degree`, and `intercept`. See Details. - `const`: Parameters for tuning. Character vector specifying constraints for tuning. See Details. - `df`: Parameters for tuning. Integer vector specifying degrees of freedom for tuning. See Details. - `degree`: Parameters for tuning. Integer vector specifying polynomial degrees for tuning. See Details. - `intercept`: Parameters for tuning. Logical vector specifying intercepts for tuning. See Details. - `mse`: If `TRUE` (default), the mean squared error is used as the CV loss function. Otherwise the mean absolute error is used. - `parallel`: Logical indicating if `parSapply` should be used. See Examples. - `cl`: Cluster created by `makeCluster`. Only used when `parallel = TRUE`. Recommended usage: `cl = makeCluster(detectCores())` - `verbose`: If `TRUE`, tuning progress is printed via `txtProgressBar`. Ignored if `parallel = TRUE`. - `...`: Additional arguments to the `cmls` function, e.g., `z`, `struc`, `backfit`, etc. ## Details The parameters for tuning can be supplied via one of two options: (A) Using the `parameters` argument. In this case, the argument `parameters` must be a data frame with columns `const`, `df`, `degree`, and `intercept`, where each row gives a combination of parameters for the CV tuning. (B) Using the `const`, `df`, `degree`, and `intercept` arguments. In this case, the `expand.grid` function is used to create the `parameters` data frame, which contains all combinations of the arguments `const`, `df`, `degree`, and `intercept`. Duplicates are removed before the CV tuning. ## Returns - **best.parameters**: Best combination of parameters, i.e., the combination that minimizes the `cvloss`. - **top5.parameters**: Top five combinations of parameters, i.e., the combinations that give the five smallest values of the `cvloss`. - **full.parameters**: Full set of parameters. Data frame with `cvloss` (GCV, MSE, or MAE) for each combination of `parameters`. ## References Helwig, N. E. (in prep). Constrained multivariate least squares in R. ## Author(s) Nathaniel E. Helwig ## See Also See the `cmls` and `const` functions for further details on the available constraint options. ## Examples ```r # make X set.seed(1) n <- 50 m <- 20 p <- 2 Xmat <- matrix(rnorm(n*p), nrow = n, ncol = p) # make B (which satisfies all constraints except monotonicity) x <- seq(0, 1, length.out = m) Bmat <- rbind(sin(2*pi*x), sin(2*pi*x+pi)) / sqrt(4.75) struc <- rbind(rep(c(TRUE, FALSE), each = m / 2), rep(c(FALSE, TRUE), each = m / 2)) Bmat <- Bmat * struc # make noisy data Ymat <- Xmat %*% Bmat + rnorm(n*m, sd = 0.5) # 5-fold CV: tune df (5,...,15) for const = "smooth" kcv <- cv.cmls(X = Xmat, Y = Ymat, nfolds = 5, const = "smooth", df = 5:15) kcv$best.parameters kcv$top5.parameters plot(kcv$full.parameters$df, kcv$full.parameters$cvloss, t = "b") ## Not run: # sample foldid for 5-fold CV set.seed(2) foldid <- sample(rep(1:5, length.out = n)) # 5-fold CV: tune df (5,...,15) w/ all 20 relevant constraints (no struc) # using sequential computation (default) myconst <- as.character(const(print = FALSE)$label[-c(13:16)]) system.time({ kcv <- cv.cmls(X = Xmat, Y = Ymat, foldid = foldid, const = myconst, df = 5:15) }) kcv$best.parameters kcv$top5.parameters # 5-fold CV: tune df (5,...,15) w/ all 20 relevant constraints (no struc) # using parallel package for parallel computations myconst <- as.character(const(print = FALSE)$label[-c(13:16)]) system.time({ cl <- makeCluster(2L) # using 2 cores kcv <- cv.cmls(X = Xmat, Y = Ymat, foldid = foldid, const = myconst, df = 5:15, parallel = TRUE, cl = cl) stopCluster(cl) }) kcv$best.parameters kcv$top5.parameters # 5-fold CV: tune df (5,...,15) w/ all 20 relevant constraints (w/ struc) # using sequential computation (default) myconst <- as.character(const(print = FALSE)$label[-c(13:16)]) system.time({ kcv <- cv.cmls(X = Xmat, Y = Ymat, foldid = foldid, const = myconst, df = 5:15, struc = struc) }) kcv$best.parameters kcv$top5.parameters # 5-fold CV: tune df (5,...,15) w/ all 20 relevant constraints (w/ struc) # using parallel package for parallel computations myconst <- as.character(const(print = FALSE)$label[-c(13:16)]) system.time({ cl <- makeCluster(2L) # using 2 cores kcv <- cv.cmls(X = Xmat, Y = Ymat, foldid = foldid, const = myconst, df = 5:15, struc = struc, parallel = TRUE, cl = cl) stopCluster(cl) }) kcv$best.parameters kcv$top5.parameters ## End(Not run) ```

cv.cmls function