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add: multivariate Y (aka projective resampling)

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Daniel Kapla 2020-09-17 18:27:31 +02:00
parent 025b9eb2af
commit 05c2aea44a
2 changed files with 121 additions and 54 deletions
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83
CVE/R/CVE.R
View File

@ -163,7 +163,7 @@
#' #'
#' @importFrom stats model.frame #' @importFrom stats model.frame
#' @export #' @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 # check for type of `data` if supplied and set default
if (missing(data)) { if (missing(data)) {
data <- environment(formula) data <- environment(formula)
@ -173,8 +173,11 @@ cve <- function(formula, data, method = "simple", max.dim = 10L, ...) {
# extract `X`, `Y` from `formula` with `data` # extract `X`, `Y` from `formula` with `data`
model <- stats::model.frame(formula, 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()] # pass extracted data on to [cve.call()]
dr <- cve.call(X, Y, method = method, max.dim = max.dim, ...) 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.simple1, k = 1)
#' coef(cve.obj.simple2, k = 1) #' coef(cve.obj.simple2, k = 1)
#' @export #' @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, min.dim = 1L, max.dim = 10L, k = NULL,
momentum = 0.0, tau = 1.0, tol = 1e-3, momentum = 0.0, tau = 1.0, tol = 1e-3,
slack = 0.0, gamma = 0.5, slack = 0.0, gamma = 0.5,
V.init = NULL, 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") # 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)
method_nr <- methods[[tolower(method), exact = FALSE]] if (is.null(func_list)) {
if (!is.integer(method_nr)) { if (endsWith(method, "central")) {
stop('Unable to determine method.') 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) }
)
} else {
func_list <- list(function(Y) Y)
}
} }
method <- names(which(method_nr == methods))
# parameter checking # parameter checking
if (!is.numeric(momentum) || length(momentum) > 1L) { if (!is.numeric(momentum) || length(momentum) > 1L) {
@ -289,10 +306,13 @@ cve.call <- function(X, Y, method = "simple",
if (!is.numeric(Y)) { if (!is.numeric(Y)) {
stop("Parameter 'Y' must be numeric.") 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.") stop("Rows of 'X' and 'Y' elements are not compatible.")
} }
if (ncol(X) < 2) { if (ncol(X) < 2) {
@ -367,6 +387,13 @@ cve.call <- function(X, Y, method = "simple",
stop("Parameter 'max.iter' must be at least 1L.") 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.null(V.init)) {
if (!is.numeric(attempts) || length(attempts) > 1L) { if (!is.numeric(attempts) || length(attempts) > 1L) {
stop("Parameter 'attempts' must be positive integer.") 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)) Fy <- vapply(func_list, do.call, Y, list(Y))
dim(Fy) <- c(nrow(Fy), prod(dim(Fy)[-1]))
# Convert numerical values to "double". # Convert numerical values to "double".
storage.mode(X) <- storage.mode(Fy) <- "double" storage.mode(X) <- storage.mode(Fy) <- "double"

92
cve_tensorflow.R
View File

@ -145,59 +145,91 @@ plot.sim <- function(sim) {
pos = if(diff(stat) > 0) c("2", "4") else c("4", "2")) 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') CVE <- getNamespace('CVE')
X <- matrix(rnorm(n * p), n, p) X <- matrix(rnorm(n * p), n, p)
Delta <- diag(1, q, q)
Delta[1, 2] <- Delta[2, 1] <- -0.5
epsilon <- CVE$rmvnorm(n, sigma = Delta)
B <- matrix(0, p, q)
B[1, 1] <- 1
B[2, 2] <- 2 / sqrt(5)
B[3, 2] <- 1 / sqrt(5)
Y <- X %*% B + epsilon if (dataset == 1) {
Delta <- diag(1, q, q)
Delta[1, 2] <- Delta[2, 1] <- -0.5
epsilon <- CVE$rmvnorm(n, sigma = Delta)
B <- matrix(0, p, q)
B[1, 1] <- 1
B[2, 2] <- 2 / sqrt(5)
B[3, 2] <- 1 / sqrt(5)
list(X = X, Y = Y, B = B[, 1:2]) Y <- X %*% B + epsilon
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$rmvnorm(1, sigma = Delta)
}
Y<-cbind(exp(eps[, 1]), eps[, 2:4])
}
list(X = X, Y = Y, B = B)
} }
set.seed(42) set.seed(42)
reps <- 10L reps <- 5L
sim.cve <- vector("list", reps) sim.cve.m <- vector("list", reps)
sim.cve.c <- vector("list", reps)
sim.cve.wm <- vector("list", reps)
sim.cve.wc <- vector("list", reps)
sim.tf1 <- vector("list", reps) sim.tf1 <- vector("list", reps)
sim.tf2 <- vector("list", reps) sim.tf2 <- vector("list", reps)
start <- Sys.time() start <- Sys.time()
for (i in 1:reps) { for (i in 1:reps) {
# ds <- dataset(1) # ds <- dataset(1)
ds <- multivariate.dataset() ds <- multivariate.dataset(2, n = 400)
# sim.cve[[i]] <- list( sim.cve.m[[i]] <- list(
# B.est = coef(CVE::cve.call(ds$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$B # B.true = ds$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') cat(sprintf("\r%4d/%d -", i, reps), format(Sys.time() - start), '\n')
} }
# pdf('subspace_comp.pdf') # pdf('subspace_comp.pdf')
par(mfrow = c(3, 1))
plot.sim(sim.cve) plot.sim(sim.cve)
plot.sim(sim.tf1) plot.sim(sim.tf1)
plot.sim(sim.tf2) 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() # dev.off()