LatentFactorKernel: Latent Factor Kernel R6 class
In CollinErickson/GauPro: Gaussian Process Fitting
LatentFactorKernel R Documentation
Latent Factor Kernel R6 class
Description
Latent Factor Kernel R6 class
Latent Factor Kernel R6 class
Usage
k_LatentFactorKernel(
s2 = 1,
D,
nlevels,
xindex,
latentdim,
p_lower = 0,
p_upper = 1,
p_est = TRUE,
s2_lower = 1e-08,
s2_upper = 1e+08,
s2_est = TRUE,
useC = TRUE,
offdiagequal = 1 - 1e-06
)
Arguments
s2
Initial variance
D
Number of input dimensions of data
nlevels
Number of levels for the factor
xindex
Index of X to use the kernel on
latentdim
Dimension of embedding space
p_lower
Lower bound for p
p_upper
Upper bound for p
p_est
Should p be estimated?
s2_lower
Lower bound for s2
s2_upper
Upper bound for s2
s2_est
Should s2 be estimated?
useC
Should C code used? Much faster.
offdiagequal
What should offdiagonal values be set to when the
indices are the same? Use to avoid decomposition errors, similar to
adding a nugget.
Format
R6Class object.
Details
Used for factor variables, a single dimension.
Each level of the factor gets mapped into a latent space,
then the distances in that space determine their correlations.
Value
Object of R6Class with methods for fitting GP model.
Super class
GauPro::GauPro_kernel -> GauPro_kernel_LatentFactorKernel
Public fields
pParameter for correlation
p_estShould p be estimated?
p_lowerLower bound of p
p_upperUpper bound of p
p_lengthlength of p
s2variance
s2_estIs s2 estimated?
logs2Log of s2
logs2_lowerLower bound of logs2
logs2_upperUpper bound of logs2
xindexIndex of the factor (which column of X)
nlevelsNumber of levels for the factor
latentdimDimension of embedding space
pf_to_p_logLogical vector used to convert pf to p
p_to_pf_indsVector of indexes used to convert p to pf
offdiagequalWhat should offdiagonal values be set to when the
indices are the same? Use to avoid decomposition errors, similar to
adding a nugget.
Methods
Public methods
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Inherited methods
Method new()
Initialize kernel object
Usage
LatentFactorKernel$new(
s2 = 1,
D,
nlevels,
xindex,
latentdim,
p_lower = 0,
p_upper = 1,
p_est = TRUE,
s2_lower = 1e-08,
s2_upper = 1e+08,
s2_est = TRUE,
useC = TRUE,
offdiagequal = 1 - 1e-06
)
Arguments
s2Initial variance
DNumber of input dimensions of data
nlevelsNumber of levels for the factor
xindexIndex of X to use the kernel on
latentdimDimension of embedding space
p_lowerLower bound for p
p_upperUpper bound for p
p_estShould p be estimated?
s2_lowerLower bound for s2
s2_upperUpper bound for s2
s2_estShould s2 be estimated?
useCShould C code used? Much faster.
offdiagequalWhat should offdiagonal values be set to when the
indices are the same? Use to avoid decomposition errors, similar to
adding a nugget.
Method k()
Calculate covariance between two points
Usage
LatentFactorKernel$k(x, y = NULL, p = self$p, s2 = self$s2, params = NULL)
Arguments
xvector.
yvector, optional. If excluded, find correlation
of x with itself.
pCorrelation parameters.
s2Variance parameter.
paramsparameters to use instead of beta and s2.
Method kone()
Find covariance of two points
Usage
LatentFactorKernel$kone(
x,
y,
pf,
s2,
isdiag = TRUE,
offdiagequal = self$offdiagequal
)
Arguments
xvector
yvector
pfcorrelation parameters on regular scale, includes zeroes
for first level.
s2Variance parameter
isdiagIs this on the diagonal of the covariance?
offdiagequalWhat should offdiagonal values be set to when the
indices are the same? Use to avoid decomposition errors, similar to
adding a nugget.
Method dC_dparams()
Derivative of covariance with respect to parameters
Usage
LatentFactorKernel$dC_dparams(params = NULL, X, C_nonug, C, nug)
Arguments
paramsKernel parameters
Xmatrix of points in rows
C_nonugCovariance without nugget added to diagonal
CCovariance with nugget
nugValue of nugget
Method C_dC_dparams()
Calculate covariance matrix and its derivative
with respect to parameters
Usage
LatentFactorKernel$C_dC_dparams(params = NULL, X, nug)
Arguments
paramsKernel parameters
Xmatrix of points in rows
nugValue of nugget
Method dC_dx()
Derivative of covariance with respect to X
Usage
LatentFactorKernel$dC_dx(XX, X, ...)
Arguments
XXmatrix of points
Xmatrix of points to take derivative with respect to
...Additional args, not used
Method param_optim_start()
Starting point for parameters for optimization
Usage
LatentFactorKernel$param_optim_start(
jitter = F,
y,
p_est = self$p_est,
s2_est = self$s2_est
)
Arguments
jitterShould there be a jitter?
yOutput
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method param_optim_start0()
Starting point for parameters for optimization
Usage
LatentFactorKernel$param_optim_start0(
jitter = F,
y,
p_est = self$p_est,
s2_est = self$s2_est
)
Arguments
jitterShould there be a jitter?
yOutput
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method param_optim_lower()
Lower bounds of parameters for optimization
Usage
LatentFactorKernel$param_optim_lower(p_est = self$p_est, s2_est = self$s2_est)
Arguments
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method param_optim_upper()
Upper bounds of parameters for optimization
Usage
LatentFactorKernel$param_optim_upper(p_est = self$p_est, s2_est = self$s2_est)
Arguments
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method set_params_from_optim()
Set parameters from optimization output
Usage
LatentFactorKernel$set_params_from_optim(
optim_out,
p_est = self$p_est,
s2_est = self$s2_est
)
Arguments
optim_outOutput from optimization
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method p_to_pf()
Convert p (short parameter vector) to pf (long parameter
vector with zeros).
Usage
LatentFactorKernel$p_to_pf(p)
Arguments
pParameter vector
Method s2_from_params()
Get s2 from params vector
Usage
LatentFactorKernel$s2_from_params(params, s2_est = self$s2_est)
Arguments
paramsparameter vector
s2_estIs s2 being estimated?
Method plotLatent()
Plot the points in the latent space
Usage
LatentFactorKernel$plotLatent()
Method print()
Print this object
Usage
LatentFactorKernel$print()
Method clone()
The objects of this class are cloneable with this method.
Usage
LatentFactorKernel$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
https://stackoverflow.com/questions/27086195/linear-index-upper-triangular-matrix
Examples
# Create a new kernel for a single factor with 5 levels,
# mapped into two latent dimensions.
kk <- LatentFactorKernel$new(D=1, nlevels=5, xindex=1, latentdim=2)
# Random initial parameter values
kk$p
# Plots to understand
kk$plotLatent()
kk$plot()
# 5 levels, 1/4 are similar and 2/3/5 are similar
n <- 30
x <- matrix(sample(1:5, n, TRUE))
y <- c(ifelse(x == 1 | x == 4, 4, -3) + rnorm(n,0,.1))
plot(c(x), y)
m5 <- GauPro_kernel_model$new(
X=x, Z=y,
kernel=LatentFactorKernel$new(D=1, nlevels = 5, xindex = 1, latentdim = 2))
m5$kernel$p
# We should see 1/4 and 2/3/4 in separate clusters
m5$kernel$plotLatent()
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 <- LatentFactorKernel$new(D=2, nlevels=3, xind=2, latentdim=2)
k2 <- k2a * k2b
k2b$p_upper <- .65*k2b$p_upper
gp <- GauPro_kernel_model$new(X=X, Z=Z, kernel = k2, verbose = 5,
nug.min=1e-2, restarts=1)
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)
CollinErickson/GauPro documentation built on March 25, 2024, 11:20 p.m.
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| LatentFactorKernel | R Documentation |
Latent Factor Kernel R6 class
Description
Latent Factor Kernel R6 class
Latent Factor Kernel R6 class
Usage
k_LatentFactorKernel(
s2 = 1,
D,
nlevels,
xindex,
latentdim,
p_lower = 0,
p_upper = 1,
p_est = TRUE,
s2_lower = 1e-08,
s2_upper = 1e+08,
s2_est = TRUE,
useC = TRUE,
offdiagequal = 1 - 1e-06
)
Arguments
s2 |
Initial variance |
D |
Number of input dimensions of data |
nlevels |
Number of levels for the factor |
xindex |
Index of X to use the kernel on |
latentdim |
Dimension of embedding space |
p_lower |
Lower bound for p |
p_upper |
Upper bound for p |
p_est |
Should p be estimated? |
s2_lower |
Lower bound for s2 |
s2_upper |
Upper bound for s2 |
s2_est |
Should s2 be estimated? |
useC |
Should C code used? Much faster. |
offdiagequal |
What should offdiagonal values be set to when the indices are the same? Use to avoid decomposition errors, similar to adding a nugget. |
Format
R6Class object.
Details
Used for factor variables, a single dimension. Each level of the factor gets mapped into a latent space, then the distances in that space determine their correlations.
Value
Object of R6Class with methods for fitting GP model.
Super class
GauPro::GauPro_kernel -> GauPro_kernel_LatentFactorKernel
Public fields
pParameter for correlation
p_estShould p be estimated?
p_lowerLower bound of p
p_upperUpper bound of p
p_lengthlength of p
s2variance
s2_estIs s2 estimated?
logs2Log of s2
logs2_lowerLower bound of logs2
logs2_upperUpper bound of logs2
xindexIndex of the factor (which column of X)
nlevelsNumber of levels for the factor
latentdimDimension of embedding space
pf_to_p_logLogical vector used to convert pf to p
p_to_pf_indsVector of indexes used to convert p to pf
offdiagequalWhat should offdiagonal values be set to when the indices are the same? Use to avoid decomposition errors, similar to adding a nugget.
Methods
Public methods
Inherited methods
Method new()
Initialize kernel object
Usage
LatentFactorKernel$new( s2 = 1, D, nlevels, xindex, latentdim, p_lower = 0, p_upper = 1, p_est = TRUE, s2_lower = 1e-08, s2_upper = 1e+08, s2_est = TRUE, useC = TRUE, offdiagequal = 1 - 1e-06 )
Arguments
s2Initial variance
DNumber of input dimensions of data
nlevelsNumber of levels for the factor
xindexIndex of X to use the kernel on
latentdimDimension of embedding space
p_lowerLower bound for p
p_upperUpper bound for p
p_estShould p be estimated?
s2_lowerLower bound for s2
s2_upperUpper bound for s2
s2_estShould s2 be estimated?
useCShould C code used? Much faster.
offdiagequalWhat should offdiagonal values be set to when the indices are the same? Use to avoid decomposition errors, similar to adding a nugget.
Method k()
Calculate covariance between two points
Usage
LatentFactorKernel$k(x, y = NULL, p = self$p, s2 = self$s2, params = NULL)
Arguments
xvector.
yvector, optional. If excluded, find correlation of x with itself.
pCorrelation parameters.
s2Variance parameter.
paramsparameters to use instead of beta and s2.
Method kone()
Find covariance of two points
Usage
LatentFactorKernel$kone( x, y, pf, s2, isdiag = TRUE, offdiagequal = self$offdiagequal )
Arguments
xvector
yvector
pfcorrelation parameters on regular scale, includes zeroes for first level.
s2Variance parameter
isdiagIs this on the diagonal of the covariance?
offdiagequalWhat should offdiagonal values be set to when the indices are the same? Use to avoid decomposition errors, similar to adding a nugget.
Method dC_dparams()
Derivative of covariance with respect to parameters
Usage
LatentFactorKernel$dC_dparams(params = NULL, X, C_nonug, C, nug)
Arguments
paramsKernel parameters
Xmatrix of points in rows
C_nonugCovariance without nugget added to diagonal
CCovariance with nugget
nugValue of nugget
Method C_dC_dparams()
Calculate covariance matrix and its derivative with respect to parameters
Usage
LatentFactorKernel$C_dC_dparams(params = NULL, X, nug)
Arguments
paramsKernel parameters
Xmatrix of points in rows
nugValue of nugget
Method dC_dx()
Derivative of covariance with respect to X
Usage
LatentFactorKernel$dC_dx(XX, X, ...)
Arguments
XXmatrix of points
Xmatrix of points to take derivative with respect to
...Additional args, not used
Method param_optim_start()
Starting point for parameters for optimization
Usage
LatentFactorKernel$param_optim_start( jitter = F, y, p_est = self$p_est, s2_est = self$s2_est )
Arguments
jitterShould there be a jitter?
yOutput
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method param_optim_start0()
Starting point for parameters for optimization
Usage
LatentFactorKernel$param_optim_start0( jitter = F, y, p_est = self$p_est, s2_est = self$s2_est )
Arguments
jitterShould there be a jitter?
yOutput
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method param_optim_lower()
Lower bounds of parameters for optimization
Usage
LatentFactorKernel$param_optim_lower(p_est = self$p_est, s2_est = self$s2_est)
Arguments
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method param_optim_upper()
Upper bounds of parameters for optimization
Usage
LatentFactorKernel$param_optim_upper(p_est = self$p_est, s2_est = self$s2_est)
Arguments
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method set_params_from_optim()
Set parameters from optimization output
Usage
LatentFactorKernel$set_params_from_optim( optim_out, p_est = self$p_est, s2_est = self$s2_est )
Arguments
optim_outOutput from optimization
p_estIs p being estimated?
s2_estIs s2 being estimated?
Method p_to_pf()
Convert p (short parameter vector) to pf (long parameter vector with zeros).
Usage
LatentFactorKernel$p_to_pf(p)
Arguments
pParameter vector
Method s2_from_params()
Get s2 from params vector
Usage
LatentFactorKernel$s2_from_params(params, s2_est = self$s2_est)
Arguments
paramsparameter vector
s2_estIs s2 being estimated?
Method plotLatent()
Plot the points in the latent space
Usage
LatentFactorKernel$plotLatent()
Method print()
Print this object
Usage
LatentFactorKernel$print()
Method clone()
The objects of this class are cloneable with this method.
Usage
LatentFactorKernel$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
https://stackoverflow.com/questions/27086195/linear-index-upper-triangular-matrix
Examples
# Create a new kernel for a single factor with 5 levels,
# mapped into two latent dimensions.
kk <- LatentFactorKernel$new(D=1, nlevels=5, xindex=1, latentdim=2)
# Random initial parameter values
kk$p
# Plots to understand
kk$plotLatent()
kk$plot()
# 5 levels, 1/4 are similar and 2/3/5 are similar
n <- 30
x <- matrix(sample(1:5, n, TRUE))
y <- c(ifelse(x == 1 | x == 4, 4, -3) + rnorm(n,0,.1))
plot(c(x), y)
m5 <- GauPro_kernel_model$new(
X=x, Z=y,
kernel=LatentFactorKernel$new(D=1, nlevels = 5, xindex = 1, latentdim = 2))
m5$kernel$p
# We should see 1/4 and 2/3/4 in separate clusters
m5$kernel$plotLatent()
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 <- LatentFactorKernel$new(D=2, nlevels=3, xind=2, latentdim=2)
k2 <- k2a * k2b
k2b$p_upper <- .65*k2b$p_upper
gp <- GauPro_kernel_model$new(X=X, Z=Z, kernel = k2, verbose = 5,
nug.min=1e-2, restarts=1)
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)
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