CausalKinetiX (version 0.2.1)

constrained.smoothspline: constrained.smoothspline

Description

Fit a smoothing spline with constraints on derivatives

Usage

constrained.smoothspline(y, times, pen.degree, constraint = "fixed",
  derivative.values = NA, initial.value = NA, times.new,
  num.folds = "leave-one-out", lambda = "optim")

Arguments

y

a vector of response variables.

times

a vector of time points at which y was measured, same length as y.

pen.degree

desired degree of the derivative in smoothing penalty.

constraint

one of 'none', 'fixed' or 'bounded' depending on whether the derivatives should not be constrained, fixed to a constant or bounded in an interval, respectively.

derivative.values

either a vector with the same length as y if contraint=='fixed' or a matrix with 2 columns conatining the lower and upper bounds on the derivatives if contraint=='bounded'.

initial.value

optional paramter that specifies an initial value of the spline incase it should be fixed.

times.new

optional vector of new time points at which the spline should be evaluated.

num.folds

either a numeric value of the number of folds or the string "leave-one-out" for a leave one out type cross-validation in determining the penalty parameter.

lambda

either a numeric value if the penalty parameter is fixed explicitely or one of the values 'optim' or 'grid.search' depending on the desired optimization procedure.

Value

a list consisting of the following elements

smooth.vals

predicted values at points times

residual

residuals

smooth.vals.new

predicted values at time points times.new

smooth.deriv

predicted derivative values at points times

pen.par

penality parameter used for smoothing

Details

For further details see the references.

References

Pfister, N., S. Bauer, J. Peters (2018). Identifying Causal Structure in Large-Scale Kinetic Systems ArXiv e-prints (arXiv:1810.11776).

Examples

# NOT RUN {
## Example
x <- seq(0,4,length.out=200)
x.long <- seq(0,4,length.out=200)
y <- x^2+rnorm(200,0,2)
dy <- 2*x
dybdd <- cbind(dy-0.5,dy+0.5)
plot(x,y)

ptm <- proc.time()
fit <- constrained.smoothspline(y=y,
                                times=x,
                                pen.degree=2,
                                constraint="none",
                                derivative.values=NA,
                                times.new=x.long,
                                num.folds=5,
                                lambda="optim")
print(proc.time()-ptm)
fit2 <- smooth.spline(x,y)
lines(x.long,fit[[3]],col="blue")
lines(fit2, col="green")
lines(x.long, x.long^2, col="black")
# }