xwfGridsearch {xwf}

Adaptive grid search

Description

Adaptive grid search to optimize the weighting functions in the extrema-weighted features.

Usage

xwfGridsearch(y, xx, t, n.i, psi.list = default_psi(), F = NULL, z = NULL,
  iter = 3, w = function(t, i, b, left) ifelse(left, min(1, (1 -
  F(xx[[i]](t)))/(1 - b)), min(1, F(xx[[i]](t))/b)), rel.shift = 0.001,
  progressbar = TRUE)

Arguments

y

Vector with binary outcomes data

xx

List of functions for which to compute the XWFs

t

Matrix containing the times at which the functions xx were measured: Element (i,j) contains the time of the j-th measurement of the i-th function.

n.i

Vector containing the number of measurements for each function. The first n.i[i] elements of the i-th row of t should not be NA.

psi.list

List of predefined local features which are functions of a function (first argument) and a measurement time (second argument)

F

CDF of the values of the functions xx. Ignored if weighting function w is not the default.

z

Optional matrix with covariates to be included as linear predictors in the generalized additive model

iter

Number of levels in the adaptive grid search. The resolution in b obtained is 2^-1-iter.

w

Weighting function. The default is the one used in the original paper. See the default for what the roles of its 3 arguments are.

rel.shift

Optional relative reduction of the integration range to avoid instabilities at the end of the integration ranges. Set to 0 if no such correction is desired.

progressbar

Boolean specifying whether a progress bar indicating what level of the adaptive grid has been completed should be displayed.

Value

List containing the final XWFs (wL and wR), the parameters for the optimal weighting functions (b.left and b.right), and the gmcv::gamObject corresponding to the final optimal generalized additive model fit.

Examples

# Data simulation similar to Section 3.2 of the paper

# Sample size
n <- 100

# Length of trajectories
n.i <- rep(5, n)
max.n.i <- max(n.i)

# Times
t <- matrix(NA_integer_, nrow = n, ncol = max.n.i)
for(i in 1:n) t[i, 1:n.i[i]] <- 1:n.i[i]


# Sample periods
phi <- runif(n = n, min = 1, max = 10)

# Sample offsets
m <- 10*runif(n = n)

# Blood pressure measurements
x <- t
for(i in 1:n) x[i, 1:n.i[i]] <- sin(phi[i] * 2*pi/max.n.i * t[i, 1:n.i[i]]) + m[i]

# Matrix with covariates z
q <- 2 # Number of covariates
z <- matrix(rnorm(n = n*q), nrow = n, ncol = q)

# Generate outcomes
temp <- phi*min(m, 7)
temp <- 40*temp
prob <- 1/(1+exp( 2*( median(temp)-temp ) ))
y <- rbinom(n = n, size = 1, prob = prob)

xx <- list()
for(i in 1:n) xx[[i]] <- approxfun(x = t[i,1:n.i[i]], y = x[i,1:n.i[i]], rule = 2)

# Estimate f
weights <- matrix(1/n.i, ncol = max.n.i, nrow = n)[!is.na(t)]
f <- density(
x = t(sapply(X = 1:n, FUN = function(i) c(xx[[i]](t[i,1:n.i[i]]), rep(NA, max.n.i-n.i[i])))),
weights = weights/sum(weights),
na.rm = T
)

# Define CDF of f, F
CDF <- c(0)
for(i in 2:length(f$x)) CDF[i] <- CDF[i-1]+(f$x[i]-f$x[i-1])*(f$y[i]+f$y[i-1])/2
F <- approxfun(x = f$x, y = CDF/max(CDF), yleft = 0, yright = 1)

psi <- list(
  function(x, t) abs(x(t)-x(t-1))
)

XWFresult <- xwfGridsearch(y = y, xx = xx, t = t, n.i = n.i, psi.list = psi, F = F, z = z)

summary(XWFresult$GAMobject)
XWFresult$b.left
XWFresult$b.right