R/fixedshare.R

In opera: Online Prediction by Expert Aggregation

fixedshare <- function(y, experts, eta, alpha, awake = NULL, loss.type = "square", 
  loss.gradient = TRUE, w0 = NULL, training = NULL, quiet = FALSE) {
  experts <- as.matrix(experts)
  
  N <- ncol(experts)  # Number of experts
  T <- nrow(experts)  # Number of instants
  
  # 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 <- log(w0)/eta
  pred <- rep(0, T)  # Prediction vector
  cumulativeLoss <- 0  # Cumulative loss of the mixture
  weights <- matrix(0, ncol = N, nrow = T)
  
  if (!is.null(training)) {
    R <- training$R
    cumulativeLoss <- training$cumulativeLoss
  }
  
  if (! quiet) steps <- init_progress(T)
  
  for (t in 1:T) {
    if (! quiet) update_progress(t, steps)
    
    # Weight update
    idx <- awake[t,] > 0
    R.aux<- eta * R
    R.max <- max(R.aux[idx])
    weights[t, idx] <- t(exp(R.aux[idx]-R.max)) * t(awake[t, idx])
    weights[t, idx] <- weights[t, idx]/sum(weights[t, idx])
    
    # Prediction and loss
    pred[t] <- experts[t, ] %*% weights[t, ]
    cumulativeLoss <- cumulativeLoss + loss(x = pred[t], y = y[t], loss.type = loss.type)
    lpred <- loss(pred[t], y[t], pred[t], loss.type, loss.gradient)
    lexp <- loss(experts[t, ], y[t], pred[t], loss.type, loss.gradient)
    
    # Regret and weight update
    R <- R + awake[t, ] * (c(c(lpred) - lexp))
    R.aux <- eta * R
    R.max <- max(R.aux)
    v <- exp(R.aux - R.max)/sum(exp(R.aux - R.max))
    R <- log(alpha/N + (1 - alpha) * v)/eta
  }
  if (! quiet) end_progress()
  
  R.aux <- eta * R
  R.max <- max(R.aux)
  w <- t(exp(R.aux - R.max))
  w <- w/sum(w)
  
  object <- list(model = "FS", loss.type = loss.type, loss.gradient = loss.gradient, 
                 coefficients = w)
  
  object$parameters <- list(eta = eta, alpha = alpha)
  object$weights <- weights
  object$prediction <- pred
  
  object$training <- list(R = R, cumulativeLoss = cumulativeLoss)
  
  return(object)
}