add: multivariate Y (aka projective resampling)

CVE/R/CVE.R

@@ -163,7 +163,7 @@
 #'
 #' @importFrom stats model.frame
 #' @export
-cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
+cve <- function(formula, data, method = "mean", max.dim = 10L, ...) {
     # check for type of `data` if supplied and set default
     if (missing(data)) {
         data <- environment(formula)
@@ -173,8 +173,11 @@ cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
 
     # extract `X`, `Y` from `formula` with `data`
     model <- stats::model.frame(formula, data)
-    X <- as.matrix(model[ ,-1L, drop = FALSE])
+    Y <- stats::model.response(model, "double")
-    Y <- as.double(model[ , 1L])
+    X <- stats::model.matrix(model)
+    if ("(Intercept)" %in% colnames(X)) {
+        X <- X[, "(Intercept)" != colnames(X), drop = FALSE]
+    }
 
     # pass extracted data on to [cve.call()]
     dr <- cve.call(X, Y, method = method, max.dim = max.dim, ...)
@@ -252,25 +255,39 @@ cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
 #' coef(cve.obj.simple1, k = 1)
 #' coef(cve.obj.simple2, k = 1)
 #' @export
-cve.call <- function(X, Y, method = "simple",
+cve.call <- function(X, Y,
-                     func_list = list(function (x) x),
+    method = c("mean", "weighted.mean", "central", "weighted.central"),
-                     nObs = sqrt(nrow(X)), h = NULL,
+    func_list = NULL, nObs = sqrt(nrow(X)), h = NULL,
     min.dim = 1L, max.dim = 10L, k = NULL,
     momentum = 0.0, tau = 1.0, tol = 1e-3,
     slack = 0.0, gamma = 0.5,
     V.init = NULL,
-                     max.iter = 50L, attempts = 10L,
+    max.iter = 50L, attempts = 10L, nr.proj = 500L,
-                     logger = NULL) {
+    logger = NULL
+) {
     # Determine method with partial matching (shortcuts: "Weight" -> "weighted")
-    methods <- list(
+    method <- match.arg(method)
-        "simple" = 0L,
+    method_nr <- if(startsWith(method, "weighted")) 1L else 0L
-        "weighted" = 1L
+
+    # Set default functions for ensamble methods (of indentity else)
+    if (is.null(func_list)) {
+        if (endsWith(method, "central")) {
+            func_list <- list(
+                function(Y) { q <- quantile(Y, 0.1); as.double(Y <= q) },
+                function(Y) { q <- quantile(Y, c(0.1, 0.2)); as.double(q[1] < Y & Y <= q[2]) },
+                function(Y) { q <- quantile(Y, c(0.2, 0.3)); as.double(q[1] < Y & Y <= q[2]) },
+                function(Y) { q <- quantile(Y, c(0.3, 0.4)); as.double(q[1] < Y & Y <= q[2]) },
+                function(Y) { q <- quantile(Y, c(0.4, 0.5)); as.double(q[1] < Y & Y <= q[2]) },
+                function(Y) { q <- quantile(Y, c(0.5, 0.6)); as.double(q[1] < Y & Y <= q[2]) },
+                function(Y) { q <- quantile(Y, c(0.6, 0.7)); as.double(q[1] < Y & Y <= q[2]) },
+                function(Y) { q <- quantile(Y, c(0.7, 0.8)); as.double(q[1] < Y & Y <= q[2]) },
+                function(Y) { q <- quantile(Y, c(0.8, 0.9)); as.double(q[1] < Y & Y <= q[2]) },
+                function(Y) { q <- quantile(Y, 0.9); as.double(q < Y) }
             )
-    method_nr <- methods[[tolower(method), exact = FALSE]]
+        } else {
-    if (!is.integer(method_nr)) {
+            func_list <- list(function(Y) Y)
-        stop('Unable to determine method.')
+        }
     }
-    method <- names(which(method_nr == methods))
 
     # parameter checking
     if (!is.numeric(momentum) || length(momentum) > 1L) {
@@ -289,10 +306,13 @@ cve.call <- function(X, Y, method = "simple",
     if (!is.numeric(Y)) {
         stop("Parameter 'Y' must be numeric.")
     }
-    if (is.matrix(Y) || !is.double(Y)) {
+    if (!is.double(Y)) {
-        Y <- as.double(Y)
+        storage.mode(Y) <- "double"
     }
-    if (nrow(X) != length(Y)) {
+    if (!is.matrix(Y)) {
+        Y <- as.matrix(Y)
+    }
+    if (nrow(X) != nrow(Y)) {
         stop("Rows of 'X' and 'Y' elements are not compatible.")
     }
     if (ncol(X) < 2) {
@@ -367,6 +387,13 @@ cve.call <- function(X, Y, method = "simple",
         stop("Parameter 'max.iter' must be at least 1L.")
     }
 
+    if (!is.integer(nr.proj)) {
+        nr.proj <- as.integer(nr.proj)
+    }
+    if (length(nr.proj) > 1 || nr.proj < 1) {
+        stop("Parameter 'nr.proj' must be a single positive integer.")
+    }
+
     if (is.null(V.init)) {
         if (!is.numeric(attempts) || length(attempts) > 1L) {
             stop("Parameter 'attempts' must be positive integer.")
@@ -378,8 +405,16 @@ cve.call <- function(X, Y, method = "simple",
         }
     }
 
-    # Evaluate each function given `Y` and build a `n x |func_list|` matrix.
+    # Projective resampling of the multivariate `Y` as a `n x nr.proj` matrix.
+    if (ncol(Y) > 1) {
+        projections <- matrix(rnorm(ncol(Y) * nr.proj), nr.proj)
+        projections <- projections / sqrt(rowSums(projections^2))
+        Y <- Y %*% t(projections)
+    }
+    # Evaluate each function given (possible projected) `Y` and build a
+    # `n x (|func_list| * nr.proj)` matrix.
     Fy <- vapply(func_list, do.call, Y, list(Y))
+    dim(Fy) <- c(nrow(Fy), prod(dim(Fy)[-1]))
 
     # Convert numerical values to "double".
     storage.mode(X) <- storage.mode(Fy) <- "double"

cve_tensorflow.R

@@ -145,10 +145,11 @@ plot.sim <- function(sim) {
          pos = if(diff(stat) > 0) c("2", "4") else c("4", "2"))
 }
 
-multivariate.dataset <- function(n = 100, p = 6, q = 4) {
+multivariate.dataset <- function(dataset = 1, n = 100, p = 6, q = 4) {
     CVE <- getNamespace('CVE')
-
     X <- matrix(rnorm(n * p), n, p)
+
+    if (dataset == 1) {
         Delta <- diag(1, q, q)
         Delta[1, 2] <- Delta[2, 1] <- -0.5
         epsilon <- CVE$rmvnorm(n, sigma = Delta)
@@ -158,46 +159,77 @@ multivariate.dataset <- function(n = 100, p = 6, q = 4) {
         B[3, 2] <- 1 / sqrt(5)
 
         Y <- X %*% B + epsilon
-
+        B <- B[, 1:2]
-    list(X = X, Y = Y, B = B[, 1:2])
+    }
+    if (dataset == 2) {
+        B <- matrix(c(0.8, 0.6, 0, 0, 0, 0))
+        eps <- matrix(0, n, q)
+        Delta <- diag(1, q, q)
+        for(i in 1:n) {
+        Delta[1, 2] <- Delta[2, 1] <- sin(X[i, ] %*% B)
+        eps[i, ] <- CVE$rmvnorm(1, sigma = Delta)
+        }
+        Y<-cbind(exp(eps[, 1]), eps[, 2:4])
+    }
+    list(X = X, Y = Y, B = B)
 }
 
 
 set.seed(42)
-reps <- 10L
+reps <- 5L
-sim.cve <- vector("list", reps)
+sim.cve.m <- vector("list", reps)
+sim.cve.c <- vector("list", reps)
+sim.cve.wm <- vector("list", reps)
+sim.cve.wc <- vector("list", reps)
 sim.tf1  <- vector("list", reps)
 sim.tf2  <- vector("list", reps)
 
 start <- Sys.time()
 for (i in 1:reps) {
     # ds <- dataset(1)
-    ds <- multivariate.dataset()
+    ds <- multivariate.dataset(2, n = 400)
 
-    # sim.cve[[i]] <- list(
+    sim.cve.m[[i]] <- list(
-    #     B.est = coef(CVE::cve.call(ds$X, ds$Y, k = ncol(ds$B)), ncol(ds$B)),
+        B.est = coef(CVE::cve.call(ds$X, ds$Y, k = ncol(ds$B), method = "mean"), ncol(ds$B)),
+        B.true = ds$B
+    )
+    sim.cve.c[[i]] <- list(
+        B.est = coef(CVE::cve.call(ds$X, ds$Y, k = ncol(ds$B), method = "central"), ncol(ds$B)),
+        B.true = ds$B
+    )
+    sim.cve.wm[[i]] <- list(
+        B.est = coef(CVE::cve.call(ds$X, ds$Y, k = ncol(ds$B), method = "weighted.mean"), ncol(ds$B)),
+        B.true = ds$B
+    )
+    sim.cve.wc[[i]] <- list(
+        B.est = coef(CVE::cve.call(ds$X, ds$Y, k = ncol(ds$B), method = "weighted.central"), ncol(ds$B)),
+        B.true = ds$B
+    )
+
+    # sim.tf1[[i]] <- list(
+    #     B.est = cve.tf(ds$X, ds$Y, ncol(ds$B),
+    #         optimizer_initialier = tf$optimizers$Adam)$B,
+    #     B.true = ds$B
+    # )
+    # sim.tf2[[i]] <- list(
+    #     B.est = cve.tf(ds$X, ds$Y, ncol(ds$B),
+    #         optimizer_initialier = tf$optimizers$Adam,
+    #         method = "weighted")$B,
     #     B.true = ds$B
     # )
-
-    sim.tf1[[i]] <- list(
-        B.est = cve.tf(ds$X, ds$Y, ncol(ds$B),
-            optimizer_initialier = tf$optimizers$Adam)$B,
-        B.true = ds$B
-    )
-
-    sim.tf2[[i]] <- list(
-        B.est = cve.tf(ds$X, ds$Y, ncol(ds$B),
-            optimizer_initialier = tf$optimizers$Adam,
-            method = "weighted")$B,
-        B.true = ds$B
-    )
 
     cat(sprintf("\r%4d/%d -", i, reps), format(Sys.time() - start), '\n')
 }
 
 # pdf('subspace_comp.pdf')
-par(mfrow = c(3, 1))
 plot.sim(sim.cve)
 plot.sim(sim.tf1)
 plot.sim(sim.tf2)
+
+par(mfrow = c(2, 2))
+plot.sim(sim.cve.m)
+plot.sim(sim.cve.c)
+plot.sim(sim.cve.wm)
+plot.sim(sim.cve.wc)
+
 # dev.off()