LatentFactorKernel {GauPro}

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

p

Parameter for correlation

p_est

Should p be estimated?

p_lower

Lower bound of p

p_upper

Upper bound of p

p_length

length of p

s2

variance

s2_est

Is s2 estimated?

logs2

Log of s2

logs2_lower

Lower bound of logs2

logs2_upper

Upper bound of logs2

xindex

Index of the factor (which column of X)

nlevels

Number of levels for the factor

latentdim

Dimension of embedding space

pf_to_p_log

Logical vector used to convert pf to p

p_to_pf_inds

Vector of indexes used to convert p to pf

offdiagequal

What 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

• LatentFactorKernel$new()

• LatentFactorKernel$k()

• LatentFactorKernel$kone()

• LatentFactorKernel$dC_dparams()

• LatentFactorKernel$C_dC_dparams()

• LatentFactorKernel$dC_dx()

• LatentFactorKernel$param_optim_start()

• LatentFactorKernel$param_optim_start0()

• LatentFactorKernel$param_optim_lower()

• LatentFactorKernel$param_optim_upper()

• LatentFactorKernel$set_params_from_optim()

• LatentFactorKernel$p_to_pf()

• LatentFactorKernel$s2_from_params()

• LatentFactorKernel$plotLatent()

• LatentFactorKernel$print()

• LatentFactorKernel$clone()

Inherited methods

• GauPro::GauPro_kernel$plot()

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

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.

Method k()

Calculate covariance between two points

Usage

LatentFactorKernel$k(x, y = NULL, p = self$p, s2 = self$s2, params = NULL)

Arguments

x

vector.

y

vector, optional. If excluded, find correlation of x with itself.

p

Correlation parameters.

s2

Variance parameter.

params

parameters 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

x

vector

y

vector

pf

correlation parameters on regular scale, includes zeroes for first level.

s2

Variance parameter

isdiag

Is this on the diagonal of the covariance?

offdiagequal

What 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

params

Kernel parameters

X

matrix of points in rows

C_nonug

Covariance without nugget added to diagonal

C

Covariance with nugget

nug

Value 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

params

Kernel parameters

X

matrix of points in rows

nug

Value of nugget

Method dC_dx()

Derivative of covariance with respect to X

Usage

LatentFactorKernel$dC_dx(XX, X, ...)

Arguments

XX

matrix of points

X

matrix 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

jitter

Should there be a jitter?

y

Output

p_est

Is p being estimated?

s2_est

Is 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

jitter

Should there be a jitter?

y

Output

p_est

Is p being estimated?

s2_est

Is 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_est

Is p being estimated?

s2_est

Is 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_est

Is p being estimated?

s2_est

Is 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_out

Output from optimization

p_est

Is p being estimated?

s2_est

Is 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

p

Parameter vector

Method s2_from_params()

Get s2 from params vector

Usage

LatentFactorKernel$s2_from_params(params, s2_est = self$s2_est)

Arguments

params

parameter vector

s2_est

Is 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

deep

Whether 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)