library("gamlss2")
## load data
data("SpirometryUS")
## subset for female
d <- subset(SpirometryUS, gender == "Female")
## note, inner weight are sampled, set
## the seed for reprodicibility
set.seed(1328)
## formula for all 4 parameters
f <- fev1 ~ elm(age,k=100,a="tanh") | . | . | .
## estimate model
m <- gamlss2(f, data = d, family = BCT)
## estimated effects
plot(m)
## predict quantiles
qu <- c(0.025, seq(0.1, 0.9, by = 0.1), 0.975)
fit <- quantile(m, probs = qu)
## plot
plot(fev1 ~ age, data = d)
i <- order(d$age)
matplot(d$age[i], fit[i, ],
type = "l", lty = 1, lwd = 2,
col = c(2, rep(4, ncol(fit) - 1)),
add = TRUE)
## main effects and interactions
f <- fev1 ~ s(age) + s(height) + s(weight) +
elm(~age+height+weight,k=200) | . | . | .
m <- gamlss2(f, data = d, family = BCT)
## summary to inspect effect of interactions
## of the elm()s
summary(m)
## plot main effects
plot(m)
## prediction is handled automatically via
## the special term interface
n <- 50
nd <- with(d, expand.grid(
"age" = seq(min(age), max(age), length = n),
"weight" = seq(min(weight), max(height), length = n)
))
nd$height <- mean(d$height)
## compute lower 2.5
nd$fit <- quantile(m, newdata = nd, probs = 0.025)
## visualize
n <- length(unique(nd$age))
age <- sort(unique(nd$age))
weight <- sort(unique(nd$weight))
z <- matrix(nd$fit, n, n)
image(age, weight, z,
col = hcl.colors(100, "YlOrRd"),
xlab = "age", ylab = "weight")
contour(age, weight, z, add = TRUE)Extreme Learning Machine Model Terms
Description
Constructor function for Extreme Learning Machine (ELM) model terms for GAMLSS.
Usage
## Model term constructor function.
elm(x, k = 50, a = "tanh", ...)
Arguments
x
|
A numeric vector or matrix, a factor, or a formula. If x is a formula, a design matrix is created using model.matrix. See the examples.
|
k
|
Integer, number of hidden units (random features) used to build the ELM design matrix. |
a
|
Character, activation function used for the hidden units. Supported options are “logistic”, “tanh” (default), “relu” and “identity”.
|
…
|
Further control arguments can be passed: criterion = “bic” (default) for shrinkage parameter selection and scale = TRUE (default) for internal scaling of the design matrix. Further arguments are passed to model.matrix if x is specified using a formula.
|
Details
The ELM model term constructs a randomized single-hidden-layer representation of the covariate(s) in x. Internally, a design matrix Z is built from x (including an intercept column). Random weights are sampled and transformed through an activation function to obtain the hidden-layer design matrix X. The columns of X are centered before estimation.
For numerical stability and comparability across terms, the design matrix Z can be scaled internally (scale = TRUE). If x is a factor, a QR-based group scaling is applied; otherwise, a column-wise normal scaling is used. The applied scaling is stored internally and automatically reused during prediction.
The returned object is a special model term used within gamlss2, following the interface described in specials.
Value
The elm() function is used internally within gamlss2 and provides the necessary details for estimating an ELM model term. Essentially, it serves as a special model term, as outlined in specials.
References
Huang GB, Zhu QY, Siew CK (2006). Extreme Learning Machine: Theory and Applications. Neurocomputing, 70(1–3), 489–501. doi:10.1016/j.neucom.2005.12.126
Huang GB, Zhu QY, Siew CK (2004). Extreme Learning Machine: A New Learning Scheme of Feedforward Neural Networks. In: Proceedings of IJCNN 2004, 2, 985–990. doi:10.1109/IJCNN.2004.1380068
See Also
gamlss2, specials.