R/kernel_OrderedFactor.R
In CollinErickson/GauPro: Gaussian Process Fitting
Defines functions
k_OrderedFactorKernel
Documented in
k_OrderedFactorKernel
#' Ordered Factor Kernel R6 class
#'
#' Use for factor inputs that are considered to have an ordering
#'
#' @docType class
#' @importFrom R6 R6Class
#' @export
#' @useDynLib GauPro, .registration = TRUE
#' @importFrom Rcpp evalCpp
#' @importFrom stats optim
# @keywords data, kriging, Gaussian process, regression
#' @return Object of \code{\link{R6Class}} with methods for fitting GP model.
#' @format \code{\link{R6Class}} object.
#' @field p Parameter for correlation
#' @field p_est Should p be estimated?
#' @field p_lower Lower bound of p
#' @field p_upper Upper bound of p
#' @field p_length length of p
#' @field s2 variance
#' @field s2_est Is s2 estimated?
#' @field logs2 Log of s2
#' @field logs2_lower Lower bound of logs2
#' @field logs2_upper Upper bound of logs2
#' @field xindex Index of the factor (which column of X)
#' @field nlevels Number of levels for the factor
#' @field offdiagequal What should offdiagonal values be set to when the
#' indices are the same? Use to avoid decomposition errors, similar to
#' adding a nugget.
#' @examples
#' kk <- OrderedFactorKernel$new(D=1, nlevels=5, xindex=1)
#' kk$p <- (1:10)/100
#' kmat <- outer(1:5, 1:5, Vectorize(kk$k))
#' kmat
#'
#'
# 2D, Gaussian on 1D, OrderedFactor on 2nd dim
#' library(dplyr)
#' n <- 20
#' X <- cbind(matrix(runif(n,2,6), ncol=1),
#' matrix(sample(1:2, size=n, replace=TRUE), ncol=1))
#' X <- rbind(X, c(3.3,3), c(3.7,3))
#' n <- nrow(X)
#' Z <- X[,1] - (4-X[,2])^2 + rnorm(n,0,.1)
#' plot(X[,1], Z, col=X[,2])
#' tibble(X=X, Z) %>% arrange(X,Z)
#' k2a <- IgnoreIndsKernel$new(k=Gaussian$new(D=1), ignoreinds = 2)
#' k2b <- OrderedFactorKernel$new(D=2, nlevels=3, xind=2)
#' k2 <- k2a * k2b
#' k2b$p_upper <- .65*k2b$p_upper
#' gp <- GauPro_kernel_model$new(X=X, Z=Z, kernel = k2, verbose = 5,
#' nug.min=1e-2, restarts=0)
#' gp$kernel$k1$kernel$beta
#' gp$kernel$k2$p
#' gp$kernel$k(x = gp$X)
#' tibble(X=X, Z=Z, pred=gp$predict(X)) %>% arrange(X, Z)
#' tibble(X=X[,2], Z) %>% group_by(X) %>% summarize(n=n(), mean(Z))
#' curve(gp$pred(cbind(matrix(x,ncol=1),1)),2,6, ylim=c(min(Z), max(Z)))
#' points(X[X[,2]==1,1], Z[X[,2]==1])
#' curve(gp$pred(cbind(matrix(x,ncol=1),2)), add=TRUE, col=2)
#' points(X[X[,2]==2,1], Z[X[,2]==2], col=2)
#' curve(gp$pred(cbind(matrix(x,ncol=1),3)), add=TRUE, col=3)
#' points(X[X[,2]==3,1], Z[X[,2]==3], col=3)
#' legend(legend=1:3, fill=1:3, x="topleft")
#' # See which points affect (5.5, 3 themost)
#' data.frame(X, cov=gp$kernel$k(X, c(5.5,3))) %>% arrange(-cov)
#' plot(k2b)
# OrderedFactorKernel ----
OrderedFactorKernel <- R6::R6Class(
classname = "GauPro_kernel_OrderedFactorKernel",
inherit = GauPro_kernel,
public = list(
p = NULL,
p_est = NULL,
p_lower = NULL,
p_upper = NULL,
p_length = NULL,
s2 = NULL, # variance coefficient to scale correlation matrix to covariance
s2_est = NULL,
logs2 = NULL,
logs2_lower = NULL,
logs2_upper = NULL,
nlevels = NULL,
xindex = NULL,
offdiagequal = NULL,
#' @description Initialize kernel object
#' @param p Vector of distances in latent space
#' @param s2 Initial variance
#' @param D Number of input dimensions of data
#' @param p_lower Lower bound for p
#' @param p_upper Upper bound for p
#' @param p_est Should p be estimated?
#' @param s2_lower Lower bound for s2
#' @param s2_upper Upper bound for s2
#' @param s2_est Should s2 be estimated?
#' @param xindex Index of X to use the kernel on
#' @param nlevels Number of levels for the factor
#' @param useC Should C code used? Much faster.
#' @param offdiagequal What should offdiagonal values be set to when the
#' indices are the same? Use to avoid decomposition errors, similar to
#' adding a nugget.
initialize = function(s2=1, D=NULL, nlevels, xindex,
p_lower=1e-8, p_upper=5, p_est=TRUE,
s2_lower=1e-8, s2_upper=1e8, s2_est=TRUE,
useC=TRUE, offdiagequal=1-1e-6
) {
# Don't require giving in D since it doesn't matter
# stopifnot(is.numeric(D), length(D)==1, D>=1, abs(D-round(D))<1e-16)
stopifnot(is.numeric(nlevels), length(nlevels)==1, nlevels>=2,
abs(nlevels-round(nlevels))<1e-16)
stopifnot(is.numeric(xindex), length(xindex)==1, xindex>=1,
abs(xindex-round(xindex))<1e-16)
# stopifnot(xindex <= D)
self$D <- D
self$nlevels <- nlevels
self$xindex <- xindex
# p <- rep(0, D * (D-1) / 2)
p <- rep(1, nlevels - 1)
self$p <- p
self$p_length <- length(p)
stopifnot(is.numeric(p_lower), length(p_lower)==1, p_lower>=0)
stopifnot(is.numeric(p_upper), length(p_upper)==1, p_upper>=0)
stopifnot(p_lower <= p_upper)
# Ensure separation between levels to avoid instability
self$p_lower <- rep(p_lower, self$p_length)
# Don't give upper 1 since it will give optimization error
self$p_upper <- rep(p_upper, self$p_length)
self$p_est <- p_est
self$s2 <- s2
self$logs2 <- log(s2, 10)
self$logs2_lower <- log(s2_lower, 10)
self$logs2_upper <- log(s2_upper, 10)
self$s2_est <- s2_est
self$useC <- useC
self$offdiagequal <- offdiagequal
},
#' @description Calculate covariance between two points
#' @param x vector.
#' @param y vector, optional. If excluded, find correlation
#' of x with itself.
#' @param p Correlation parameters.
#' @param s2 Variance parameter.
#' @param params parameters to use instead of beta and s2.
k = function(x, y=NULL, p=self$p, s2=self$s2, params=NULL) {
if (!is.null(params)) {
lenparams <- length(params)
if (self$p_est) {
p <- params[1:self$p_length]
} else {
p <- self$p
}
if (self$s2_est) {
logs2 <- params[lenparams]
} else {
logs2 <- self$logs2
}
s2 <- 10^logs2
} else {
if (is.null(p)) {p <- self$p}
if (is.null(s2)) {s2 <- self$s2}
}
if (is.null(y)) {
if (is.matrix(x)) {
if (self$useC) {
val <- s2 * corr_orderedfactor_matrix_symC(x, p, self$xindex,
self$offdiagequal)
} else {
val <- outer(1:nrow(x), 1:nrow(x),
Vectorize(function(i,j){
self$kone(x[i,],x[j,],p=p, s2=s2, isdiag=i==j)
}))
}
return(val)
} else {
return(s2 * 1)
}
}
if (is.matrix(x) & is.matrix(y)) {
if (self$useC) { # Way faster
s2 * corr_orderedfactor_matrixmatrixC(
x=x, y=y, theta=p, xindex=self$xindex,
offdiagequal=self$offdiagequal)
} else {
outer(1:nrow(x), 1:nrow(y),
Vectorize(function(i,j){self$kone(x[i,],y[j,],p=p, s2=s2)}))
}
} else if (is.matrix(x) & !is.matrix(y)) {
apply(x, 1, function(xx) {self$kone(xx, y, p=p, s2=s2)})
} else if (is.matrix(y)) {
apply(y, 1, function(yy) {self$kone(yy, x, p=p, s2=s2)})
} else {
self$kone(x, y, p=p, s2=s2)
}
},
#' @description Find covariance of two points
#' @param x vector
#' @param y vector
#' @param p correlation parameters on regular scale
#' @param s2 Variance parameter
#' @param isdiag Is this on the diagonal of the covariance?
#' @param offdiagequal What should offdiagonal values be set to when the
#' indices are the same? Use to avoid decomposition errors, similar to
#' adding a nugget.
#' @references
#' https://stackoverflow.com/questions/27086195/linear-index-upper-triangular-matrix
kone = function(x, y, p, s2, isdiag=TRUE, offdiagequal=self$offdiagequal) {
x <- x[self$xindex]
y <- y[self$xindex]
stopifnot(x>=1, y>=1, x<=self$nlevels, y<=self$nlevels,
abs(x-as.integer(x)) < 1e-8, abs(y-as.integer(y)) < 1e-8)
if (x==y) {
# out <- s2 * 1
# Trying to avoid singular values
if (isdiag) {
out <- s2 * 1
} else {
out <- s2 * offdiagequal
}
} else {
# i <- x-1
# j <- y-1
i <- min(x,y) #min(x-1, y-1)
j <- max(x,y) - 1 #max(x-1, y-1)
# n <- self$nlevels
p_dist <- sum(p[i:j])
out <- s2 * exp(-p_dist^2)
}
if (any(is.nan(out))) {stop("Error #44011")}
out
},
#' @description Derivative of covariance with respect to parameters
#' @param params Kernel parameters
#' @param X matrix of points in rows
#' @param C_nonug Covariance without nugget added to diagonal
#' @param C Covariance with nugget
#' @param nug Value of nugget
dC_dparams = function(params=NULL, X, C_nonug, C, nug) {
n <- nrow(X)
lenparams <- length(params)
if (lenparams > 0) {
if (self$p_est) {
p <- params[1:self$p_length]
} else {
p <- self$p
}
if (self$s2_est) {
logs2 <- params[lenparams]
} else {
logs2 <- self$logs2
}
} else {
p <- self$p
logs2 <- self$logs2
}
log10 <- log(10)
s2 <- 10 ^ logs2
if (missing(C_nonug)) { # Assume C missing too, must have nug
C_nonug <- self$k(x=X, params=params)
C <- C_nonug + diag(nug*s2, nrow(C_nonug))
}
lenparams_D <- self$p_length*self$p_est + self$s2_est
if (self$useC) {
dC_dparams <- kernel_orderedFactor_dC(X, p, C_nonug, self$s2_est,
self$p_est, lenparams_D, s2*nug,
self$xindex-1,
self$nlevels, s2)
if (any(is.na(dC_dparams))) {
print('bad dcdparams')
browser('fix this')
warning('a;slkdfja;sdlkfj')
}
} else {
dC_dparams <- array(dim=c(lenparams_D, n, n), data=0)
if (self$s2_est) {
dC_dparams[lenparams_D,,] <- C * log10
}
if (self$p_est) {
for (k in 1:length(p)) { # k is index of parameter
for (i in seq(1, n-1, 1)) {
for (j in seq(i+1, n, 1)) {
xx <- X[i, self$xindex]
yy <- X[j, self$xindex]
if (xx == yy) {
# Corr is just 1, parameter has no effect
} else {
# ii <- min(xx-1, yy-1)
# jj <- max(xx-1, yy-1)
# nn <- self$nlevels
# ind <- (nn*(nn-1)/2) - (nn-ii)*((nn-ii)-1)/2 + jj - ii #- 1
ii <- min(xx,yy)
jj <- max(xx,yy) - 1
if (ii <= k && k <= jj) {
# Does correspond to the correct parameter
p_dist <- sum(p[ii:jj])
r <- exp(-p_dist^2)
dC_dparams[k,i,j] <- -2 * p_dist * r * s2
dC_dparams[k,j,i] <- dC_dparams[k,i,j]
} else {
# Parameter has no effect
}
}
}
}
for (i in seq(1, n, 1)) { # Get diagonal set to zero
dC_dparams[k,i,i] <- 0
}
}
}
}
return(dC_dparams)
},
#' @description Calculate covariance matrix and its derivative
#' with respect to parameters
#' @param params Kernel parameters
#' @param X matrix of points in rows
#' @param nug Value of nugget
C_dC_dparams = function(params=NULL, X, nug) {
s2 <- self$s2_from_params(params)
C_nonug <- self$k(x=X, params=params)
C <- C_nonug + diag(s2*nug, nrow(X))
dC_dparams <- self$dC_dparams(params=params, X=X, C_nonug=C_nonug, C=C,
nug=nug)
list(C=C, dC_dparams=dC_dparams)
},
#' @description Derivative of covariance with respect to X
#' @param XX matrix of points
#' @param X matrix of points to take derivative with respect to
#' @param ... Additional args, not used
dC_dx = function(XX, X, ...) {
if (!is.matrix(XX)) {stop()}
d <- ncol(XX)
if (ncol(X) != d) {stop()}
n <- nrow(X)
nn <- nrow(XX)
dC_dx <- array(0, dim=c(nn, d, n))
dC_dx[, self$xindex, ] <- NA
dC_dx
},
#' @description Starting point for parameters for optimization
#' @param jitter Should there be a jitter?
#' @param y Output
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
param_optim_start = function(jitter=F, y, p_est=self$p_est,
s2_est=self$s2_est) {
if (p_est) {
vec <- pmin(pmax(self$p + jitter*rnorm(length(self$p), 0, .5),
self$p_lower), self$p_upper)
} else {
vec <- c()
}
if (s2_est) {
vec <- c(vec,
max(min(self$logs2 + jitter * rnorm(1),
self$logs2_upper),
self$logs2_lower))
}
vec
},
#' @description Starting point for parameters for optimization
#' @param jitter Should there be a jitter?
#' @param y Output
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
param_optim_start0 = function(jitter=F, y, p_est=self$p_est,
s2_est=self$s2_est) {
if (p_est) {
vec <- pmin(pmax(rep(1, length(self$p)) +
jitter*rnorm(length(self$p), 0, .5),
self$p_lower), self$p_upper)
} else {
vec <- c()
}
if (s2_est) {
vec <- c(vec, max(min(self$logs2 + jitter * rnorm(1),
self$logs2_upper),
self$logs2_lower))
}
vec
},
#' @description Lower bounds of parameters for optimization
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
param_optim_lower = function(p_est=self$p_est,
s2_est=self$s2_est) {
if (p_est) {vec <- c(self$p_lower)} else {vec <- c()}
if (s2_est) {vec <- c(vec, self$logs2_lower)} else {}
vec
},
#' @description Upper bounds of parameters for optimization
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
param_optim_upper = function(p_est=self$p_est,
s2_est=self$s2_est) {
if (p_est) {vec <- c(self$p_upper)} else {vec <- c()}
if (s2_est) {vec <- c(vec, self$logs2_upper)} else {}
vec
},
#' @description Set parameters from optimization output
#' @param optim_out Output from optimization
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
set_params_from_optim = function(optim_out, p_est=self$p_est,
s2_est=self$s2_est) {
loo <- length(optim_out)
if (p_est) {
self$p <- optim_out[1:(self$p_length)]
}
if (s2_est) {
self$logs2 <- optim_out[loo]
self$s2 <- 10 ^ self$logs2
}
},
#' @description Get s2 from params vector
#' @param params parameter vector
#' @param s2_est Is s2 being estimated?
s2_from_params = function(params, s2_est=self$s2_est) {
# 10 ^ params[length(params)]
if (s2_est && !is.null(params)) { # Is last if in params
10 ^ params[length(params)]
} else { # Else it is just using set value, not being estimated
self$s2
}
},
#' @description Plot the points in the latent space
plotLatent = function() {
x <- c(0, cumsum(self$p))
pdf <- data.frame(x=x, y=0)
pdf$name <- paste0("x=",1:nrow(pdf))
ggplot2::ggplot(pdf, ggplot2::aes(x, 0, label=name)) +
ggplot2::geom_point() +
ggrepel::geom_label_repel() +
ggplot2::scale_y_continuous(breaks=NULL) +
ggplot2::ylab(NULL)
},
#' @description Print this object
print = function() {
cat('GauPro kernel: Ordered factor\n')
cat('\tD =', self$D, '\n')
cat('\ts2 =', self$s2, '\n')
cat('\ton x-index', self$xindex, 'with', self$nlevels, 'levels\n')
}
)
)
#' @rdname OrderedFactorKernel
#' @export
#' @param s2 Initial variance
#' @param D Number of input dimensions of data
#' @param p_lower Lower bound for p
#' @param p_upper Upper bound for p
#' @param p_est Should p be estimated?
#' @param s2_lower Lower bound for s2
#' @param s2_upper Upper bound for s2
#' @param s2_est Should s2 be estimated?
#' @param xindex Index of the factor (which column of X)
#' @param nlevels Number of levels for the factor
#' @param useC Should C code used? Not implemented for FactorKernel yet.
#' @param offdiagequal What should offdiagonal values be set to when the
#' indices are the same? Use to avoid decomposition errors, similar to
#' adding a nugget.
k_OrderedFactorKernel <- function(s2=1, D, nlevels, xindex,
p_lower=1e-8, p_upper=5, p_est=TRUE,
s2_lower=1e-8, s2_upper=1e8, s2_est=TRUE,
useC=TRUE, offdiagequal=1-1e-6) {
OrderedFactorKernel$new(
s2=s2,
D=D,
nlevels=nlevels,
xindex=xindex,
p_lower=p_lower,
p_upper=p_upper,
p_est=p_est,
s2_lower=s2_lower,
s2_upper=s2_upper,
s2_est=s2_est,
useC=useC,
offdiagequal=offdiagequal
)
}
CollinErickson/GauPro documentation built on March 25, 2024, 11:20 p.m.
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Defines functions k_OrderedFactorKernel
Documented in k_OrderedFactorKernel
#' Ordered Factor Kernel R6 class
#'
#' Use for factor inputs that are considered to have an ordering
#'
#' @docType class
#' @importFrom R6 R6Class
#' @export
#' @useDynLib GauPro, .registration = TRUE
#' @importFrom Rcpp evalCpp
#' @importFrom stats optim
# @keywords data, kriging, Gaussian process, regression
#' @return Object of \code{\link{R6Class}} with methods for fitting GP model.
#' @format \code{\link{R6Class}} object.
#' @field p Parameter for correlation
#' @field p_est Should p be estimated?
#' @field p_lower Lower bound of p
#' @field p_upper Upper bound of p
#' @field p_length length of p
#' @field s2 variance
#' @field s2_est Is s2 estimated?
#' @field logs2 Log of s2
#' @field logs2_lower Lower bound of logs2
#' @field logs2_upper Upper bound of logs2
#' @field xindex Index of the factor (which column of X)
#' @field nlevels Number of levels for the factor
#' @field offdiagequal What should offdiagonal values be set to when the
#' indices are the same? Use to avoid decomposition errors, similar to
#' adding a nugget.
#' @examples
#' kk <- OrderedFactorKernel$new(D=1, nlevels=5, xindex=1)
#' kk$p <- (1:10)/100
#' kmat <- outer(1:5, 1:5, Vectorize(kk$k))
#' kmat
#'
#'
# 2D, Gaussian on 1D, OrderedFactor on 2nd dim
#' library(dplyr)
#' n <- 20
#' X <- cbind(matrix(runif(n,2,6), ncol=1),
#' matrix(sample(1:2, size=n, replace=TRUE), ncol=1))
#' X <- rbind(X, c(3.3,3), c(3.7,3))
#' n <- nrow(X)
#' Z <- X[,1] - (4-X[,2])^2 + rnorm(n,0,.1)
#' plot(X[,1], Z, col=X[,2])
#' tibble(X=X, Z) %>% arrange(X,Z)
#' k2a <- IgnoreIndsKernel$new(k=Gaussian$new(D=1), ignoreinds = 2)
#' k2b <- OrderedFactorKernel$new(D=2, nlevels=3, xind=2)
#' k2 <- k2a * k2b
#' k2b$p_upper <- .65*k2b$p_upper
#' gp <- GauPro_kernel_model$new(X=X, Z=Z, kernel = k2, verbose = 5,
#' nug.min=1e-2, restarts=0)
#' gp$kernel$k1$kernel$beta
#' gp$kernel$k2$p
#' gp$kernel$k(x = gp$X)
#' tibble(X=X, Z=Z, pred=gp$predict(X)) %>% arrange(X, Z)
#' tibble(X=X[,2], Z) %>% group_by(X) %>% summarize(n=n(), mean(Z))
#' curve(gp$pred(cbind(matrix(x,ncol=1),1)),2,6, ylim=c(min(Z), max(Z)))
#' points(X[X[,2]==1,1], Z[X[,2]==1])
#' curve(gp$pred(cbind(matrix(x,ncol=1),2)), add=TRUE, col=2)
#' points(X[X[,2]==2,1], Z[X[,2]==2], col=2)
#' curve(gp$pred(cbind(matrix(x,ncol=1),3)), add=TRUE, col=3)
#' points(X[X[,2]==3,1], Z[X[,2]==3], col=3)
#' legend(legend=1:3, fill=1:3, x="topleft")
#' # See which points affect (5.5, 3 themost)
#' data.frame(X, cov=gp$kernel$k(X, c(5.5,3))) %>% arrange(-cov)
#' plot(k2b)
# OrderedFactorKernel ----
OrderedFactorKernel <- R6::R6Class(
classname = "GauPro_kernel_OrderedFactorKernel",
inherit = GauPro_kernel,
public = list(
p = NULL,
p_est = NULL,
p_lower = NULL,
p_upper = NULL,
p_length = NULL,
s2 = NULL, # variance coefficient to scale correlation matrix to covariance
s2_est = NULL,
logs2 = NULL,
logs2_lower = NULL,
logs2_upper = NULL,
nlevels = NULL,
xindex = NULL,
offdiagequal = NULL,
#' @description Initialize kernel object
#' @param p Vector of distances in latent space
#' @param s2 Initial variance
#' @param D Number of input dimensions of data
#' @param p_lower Lower bound for p
#' @param p_upper Upper bound for p
#' @param p_est Should p be estimated?
#' @param s2_lower Lower bound for s2
#' @param s2_upper Upper bound for s2
#' @param s2_est Should s2 be estimated?
#' @param xindex Index of X to use the kernel on
#' @param nlevels Number of levels for the factor
#' @param useC Should C code used? Much faster.
#' @param offdiagequal What should offdiagonal values be set to when the
#' indices are the same? Use to avoid decomposition errors, similar to
#' adding a nugget.
initialize = function(s2=1, D=NULL, nlevels, xindex,
p_lower=1e-8, p_upper=5, p_est=TRUE,
s2_lower=1e-8, s2_upper=1e8, s2_est=TRUE,
useC=TRUE, offdiagequal=1-1e-6
) {
# Don't require giving in D since it doesn't matter
# stopifnot(is.numeric(D), length(D)==1, D>=1, abs(D-round(D))<1e-16)
stopifnot(is.numeric(nlevels), length(nlevels)==1, nlevels>=2,
abs(nlevels-round(nlevels))<1e-16)
stopifnot(is.numeric(xindex), length(xindex)==1, xindex>=1,
abs(xindex-round(xindex))<1e-16)
# stopifnot(xindex <= D)
self$D <- D
self$nlevels <- nlevels
self$xindex <- xindex
# p <- rep(0, D * (D-1) / 2)
p <- rep(1, nlevels - 1)
self$p <- p
self$p_length <- length(p)
stopifnot(is.numeric(p_lower), length(p_lower)==1, p_lower>=0)
stopifnot(is.numeric(p_upper), length(p_upper)==1, p_upper>=0)
stopifnot(p_lower <= p_upper)
# Ensure separation between levels to avoid instability
self$p_lower <- rep(p_lower, self$p_length)
# Don't give upper 1 since it will give optimization error
self$p_upper <- rep(p_upper, self$p_length)
self$p_est <- p_est
self$s2 <- s2
self$logs2 <- log(s2, 10)
self$logs2_lower <- log(s2_lower, 10)
self$logs2_upper <- log(s2_upper, 10)
self$s2_est <- s2_est
self$useC <- useC
self$offdiagequal <- offdiagequal
},
#' @description Calculate covariance between two points
#' @param x vector.
#' @param y vector, optional. If excluded, find correlation
#' of x with itself.
#' @param p Correlation parameters.
#' @param s2 Variance parameter.
#' @param params parameters to use instead of beta and s2.
k = function(x, y=NULL, p=self$p, s2=self$s2, params=NULL) {
if (!is.null(params)) {
lenparams <- length(params)
if (self$p_est) {
p <- params[1:self$p_length]
} else {
p <- self$p
}
if (self$s2_est) {
logs2 <- params[lenparams]
} else {
logs2 <- self$logs2
}
s2 <- 10^logs2
} else {
if (is.null(p)) {p <- self$p}
if (is.null(s2)) {s2 <- self$s2}
}
if (is.null(y)) {
if (is.matrix(x)) {
if (self$useC) {
val <- s2 * corr_orderedfactor_matrix_symC(x, p, self$xindex,
self$offdiagequal)
} else {
val <- outer(1:nrow(x), 1:nrow(x),
Vectorize(function(i,j){
self$kone(x[i,],x[j,],p=p, s2=s2, isdiag=i==j)
}))
}
return(val)
} else {
return(s2 * 1)
}
}
if (is.matrix(x) & is.matrix(y)) {
if (self$useC) { # Way faster
s2 * corr_orderedfactor_matrixmatrixC(
x=x, y=y, theta=p, xindex=self$xindex,
offdiagequal=self$offdiagequal)
} else {
outer(1:nrow(x), 1:nrow(y),
Vectorize(function(i,j){self$kone(x[i,],y[j,],p=p, s2=s2)}))
}
} else if (is.matrix(x) & !is.matrix(y)) {
apply(x, 1, function(xx) {self$kone(xx, y, p=p, s2=s2)})
} else if (is.matrix(y)) {
apply(y, 1, function(yy) {self$kone(yy, x, p=p, s2=s2)})
} else {
self$kone(x, y, p=p, s2=s2)
}
},
#' @description Find covariance of two points
#' @param x vector
#' @param y vector
#' @param p correlation parameters on regular scale
#' @param s2 Variance parameter
#' @param isdiag Is this on the diagonal of the covariance?
#' @param offdiagequal What should offdiagonal values be set to when the
#' indices are the same? Use to avoid decomposition errors, similar to
#' adding a nugget.
#' @references
#' https://stackoverflow.com/questions/27086195/linear-index-upper-triangular-matrix
kone = function(x, y, p, s2, isdiag=TRUE, offdiagequal=self$offdiagequal) {
x <- x[self$xindex]
y <- y[self$xindex]
stopifnot(x>=1, y>=1, x<=self$nlevels, y<=self$nlevels,
abs(x-as.integer(x)) < 1e-8, abs(y-as.integer(y)) < 1e-8)
if (x==y) {
# out <- s2 * 1
# Trying to avoid singular values
if (isdiag) {
out <- s2 * 1
} else {
out <- s2 * offdiagequal
}
} else {
# i <- x-1
# j <- y-1
i <- min(x,y) #min(x-1, y-1)
j <- max(x,y) - 1 #max(x-1, y-1)
# n <- self$nlevels
p_dist <- sum(p[i:j])
out <- s2 * exp(-p_dist^2)
}
if (any(is.nan(out))) {stop("Error #44011")}
out
},
#' @description Derivative of covariance with respect to parameters
#' @param params Kernel parameters
#' @param X matrix of points in rows
#' @param C_nonug Covariance without nugget added to diagonal
#' @param C Covariance with nugget
#' @param nug Value of nugget
dC_dparams = function(params=NULL, X, C_nonug, C, nug) {
n <- nrow(X)
lenparams <- length(params)
if (lenparams > 0) {
if (self$p_est) {
p <- params[1:self$p_length]
} else {
p <- self$p
}
if (self$s2_est) {
logs2 <- params[lenparams]
} else {
logs2 <- self$logs2
}
} else {
p <- self$p
logs2 <- self$logs2
}
log10 <- log(10)
s2 <- 10 ^ logs2
if (missing(C_nonug)) { # Assume C missing too, must have nug
C_nonug <- self$k(x=X, params=params)
C <- C_nonug + diag(nug*s2, nrow(C_nonug))
}
lenparams_D <- self$p_length*self$p_est + self$s2_est
if (self$useC) {
dC_dparams <- kernel_orderedFactor_dC(X, p, C_nonug, self$s2_est,
self$p_est, lenparams_D, s2*nug,
self$xindex-1,
self$nlevels, s2)
if (any(is.na(dC_dparams))) {
print('bad dcdparams')
browser('fix this')
warning('a;slkdfja;sdlkfj')
}
} else {
dC_dparams <- array(dim=c(lenparams_D, n, n), data=0)
if (self$s2_est) {
dC_dparams[lenparams_D,,] <- C * log10
}
if (self$p_est) {
for (k in 1:length(p)) { # k is index of parameter
for (i in seq(1, n-1, 1)) {
for (j in seq(i+1, n, 1)) {
xx <- X[i, self$xindex]
yy <- X[j, self$xindex]
if (xx == yy) {
# Corr is just 1, parameter has no effect
} else {
# ii <- min(xx-1, yy-1)
# jj <- max(xx-1, yy-1)
# nn <- self$nlevels
# ind <- (nn*(nn-1)/2) - (nn-ii)*((nn-ii)-1)/2 + jj - ii #- 1
ii <- min(xx,yy)
jj <- max(xx,yy) - 1
if (ii <= k && k <= jj) {
# Does correspond to the correct parameter
p_dist <- sum(p[ii:jj])
r <- exp(-p_dist^2)
dC_dparams[k,i,j] <- -2 * p_dist * r * s2
dC_dparams[k,j,i] <- dC_dparams[k,i,j]
} else {
# Parameter has no effect
}
}
}
}
for (i in seq(1, n, 1)) { # Get diagonal set to zero
dC_dparams[k,i,i] <- 0
}
}
}
}
return(dC_dparams)
},
#' @description Calculate covariance matrix and its derivative
#' with respect to parameters
#' @param params Kernel parameters
#' @param X matrix of points in rows
#' @param nug Value of nugget
C_dC_dparams = function(params=NULL, X, nug) {
s2 <- self$s2_from_params(params)
C_nonug <- self$k(x=X, params=params)
C <- C_nonug + diag(s2*nug, nrow(X))
dC_dparams <- self$dC_dparams(params=params, X=X, C_nonug=C_nonug, C=C,
nug=nug)
list(C=C, dC_dparams=dC_dparams)
},
#' @description Derivative of covariance with respect to X
#' @param XX matrix of points
#' @param X matrix of points to take derivative with respect to
#' @param ... Additional args, not used
dC_dx = function(XX, X, ...) {
if (!is.matrix(XX)) {stop()}
d <- ncol(XX)
if (ncol(X) != d) {stop()}
n <- nrow(X)
nn <- nrow(XX)
dC_dx <- array(0, dim=c(nn, d, n))
dC_dx[, self$xindex, ] <- NA
dC_dx
},
#' @description Starting point for parameters for optimization
#' @param jitter Should there be a jitter?
#' @param y Output
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
param_optim_start = function(jitter=F, y, p_est=self$p_est,
s2_est=self$s2_est) {
if (p_est) {
vec <- pmin(pmax(self$p + jitter*rnorm(length(self$p), 0, .5),
self$p_lower), self$p_upper)
} else {
vec <- c()
}
if (s2_est) {
vec <- c(vec,
max(min(self$logs2 + jitter * rnorm(1),
self$logs2_upper),
self$logs2_lower))
}
vec
},
#' @description Starting point for parameters for optimization
#' @param jitter Should there be a jitter?
#' @param y Output
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
param_optim_start0 = function(jitter=F, y, p_est=self$p_est,
s2_est=self$s2_est) {
if (p_est) {
vec <- pmin(pmax(rep(1, length(self$p)) +
jitter*rnorm(length(self$p), 0, .5),
self$p_lower), self$p_upper)
} else {
vec <- c()
}
if (s2_est) {
vec <- c(vec, max(min(self$logs2 + jitter * rnorm(1),
self$logs2_upper),
self$logs2_lower))
}
vec
},
#' @description Lower bounds of parameters for optimization
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
param_optim_lower = function(p_est=self$p_est,
s2_est=self$s2_est) {
if (p_est) {vec <- c(self$p_lower)} else {vec <- c()}
if (s2_est) {vec <- c(vec, self$logs2_lower)} else {}
vec
},
#' @description Upper bounds of parameters for optimization
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
param_optim_upper = function(p_est=self$p_est,
s2_est=self$s2_est) {
if (p_est) {vec <- c(self$p_upper)} else {vec <- c()}
if (s2_est) {vec <- c(vec, self$logs2_upper)} else {}
vec
},
#' @description Set parameters from optimization output
#' @param optim_out Output from optimization
#' @param p_est Is p being estimated?
#' @param s2_est Is s2 being estimated?
set_params_from_optim = function(optim_out, p_est=self$p_est,
s2_est=self$s2_est) {
loo <- length(optim_out)
if (p_est) {
self$p <- optim_out[1:(self$p_length)]
}
if (s2_est) {
self$logs2 <- optim_out[loo]
self$s2 <- 10 ^ self$logs2
}
},
#' @description Get s2 from params vector
#' @param params parameter vector
#' @param s2_est Is s2 being estimated?
s2_from_params = function(params, s2_est=self$s2_est) {
# 10 ^ params[length(params)]
if (s2_est && !is.null(params)) { # Is last if in params
10 ^ params[length(params)]
} else { # Else it is just using set value, not being estimated
self$s2
}
},
#' @description Plot the points in the latent space
plotLatent = function() {
x <- c(0, cumsum(self$p))
pdf <- data.frame(x=x, y=0)
pdf$name <- paste0("x=",1:nrow(pdf))
ggplot2::ggplot(pdf, ggplot2::aes(x, 0, label=name)) +
ggplot2::geom_point() +
ggrepel::geom_label_repel() +
ggplot2::scale_y_continuous(breaks=NULL) +
ggplot2::ylab(NULL)
},
#' @description Print this object
print = function() {
cat('GauPro kernel: Ordered factor\n')
cat('\tD =', self$D, '\n')
cat('\ts2 =', self$s2, '\n')
cat('\ton x-index', self$xindex, 'with', self$nlevels, 'levels\n')
}
)
)
#' @rdname OrderedFactorKernel
#' @export
#' @param s2 Initial variance
#' @param D Number of input dimensions of data
#' @param p_lower Lower bound for p
#' @param p_upper Upper bound for p
#' @param p_est Should p be estimated?
#' @param s2_lower Lower bound for s2
#' @param s2_upper Upper bound for s2
#' @param s2_est Should s2 be estimated?
#' @param xindex Index of the factor (which column of X)
#' @param nlevels Number of levels for the factor
#' @param useC Should C code used? Not implemented for FactorKernel yet.
#' @param offdiagequal What should offdiagonal values be set to when the
#' indices are the same? Use to avoid decomposition errors, similar to
#' adding a nugget.
k_OrderedFactorKernel <- function(s2=1, D, nlevels, xindex,
p_lower=1e-8, p_upper=5, p_est=TRUE,
s2_lower=1e-8, s2_upper=1e8, s2_est=TRUE,
useC=TRUE, offdiagequal=1-1e-6) {
OrderedFactorKernel$new(
s2=s2,
D=D,
nlevels=nlevels,
xindex=xindex,
p_lower=p_lower,
p_upper=p_upper,
p_est=p_est,
s2_lower=s2_lower,
s2_upper=s2_upper,
s2_est=s2_est,
useC=useC,
offdiagequal=offdiagequal
)
}
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