MLewa <- function(y, experts, awake = NULL, loss.type = "square", loss.gradient = TRUE,
w0 = NULL, training = NULL, quiet = FALSE) {
experts <- as.matrix(experts)
N <- ncol(experts)
T <- nrow(experts)
# Uniform initial weight vector if unspecified
if (is.null(w0)) {
w0 <- rep(1, N)
}
awake <- as.matrix(awake)
idx.na <- which(is.na(experts))
awake[idx.na] <- 0
experts[idx.na] <- 0
R <- rep(0, N) # Regret vector
w <- w0
# weight assigned to each expert
weights <- matrix(0, ncol = N, nrow = T)
prediction <- rep(0, T)
# Initialization or the learning parameter
eta <- matrix(exp(350), ncol = N, nrow = T + 1)
if (!is.null(training)) {
w0 <- training$w0
eta[1, ] <- training$eta
R <- training$R
# Update weights
R.aux <- log(w0) + eta[1, ] * R
R.max <- max(R.aux)
w <- exp(R.aux - R.max)
}
if (! quiet) steps <- init_progress(T)
for (t in 1:T) {
if (! quiet) update_progress(t, steps)
idx <- awake[t,] > 0
R.aux <- log(w0) + eta[t, ] * R
R.max <- max(R.aux[idx])
w <- numeric(N)
w[idx] <- exp(R.aux[idx] - R.max)
# form the each-instant updated mixture and prediction
p <- awake[t, ] * w/sum(awake[t, ] * w)
pred <- experts[t, ] %*% p
# form the operational mixture and the prediction of the aggregation rule
weights[t, ] <- p
prediction[t] <- pred
# observe losses
lpred <- loss(pred, y[t], pred, loss.type = loss.type, loss.gradient = loss.gradient)
lexp <- loss(experts[t, ], y[t], pred, loss.type = loss.type, loss.gradient = loss.gradient)
# update regret and weights
r <- awake[t, ] * (c(c(lpred) - lexp))
R <- R + r
eta[t + 1, ] <- sqrt(log(N)/(log(N)/eta[t, ]^2 + r^2))
idx <- awake[t,] > 0
R.aux <- log(w0) + eta[t + 1, ] * R
R.max <- max(R.aux[idx])
w[idx] <- exp(R.aux[idx] - R.max)
}
if (! quiet) end_progress()
w <- w/sum(w)
object <- list(model = "MLewa", loss.type = loss.type, loss.gradient = loss.gradient,
coefficients = w/sum(w))
object$parameters <- list(eta = eta[1:T, ])
object$weights <- weights
object$prediction <- prediction
object$training <- list(eta = eta[T + 1, ], R = R, w0 = w0)
class(object) <- "mixture"
return(object)
}
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