pretty plotting for comparing stochastic approximation methods

plot.risk.R

plot.risk <- function(data, est) {
  # Plot estimated biases of the 4 optimization routines performed.
  #
  # Args:
  #   data: List of x, y, A, theta in particular form
  #   est: A list of matrix estimates, one for each set of optimization
  #        methods done on the data.
  #
  # Returns:
  #   A log-log plot with 4 curves, showing excess risk over training size.
  library(dplyr)
  library(ggplot2)

  list.bias <- list()
  for (i in 1:length(est)) {
    values = apply(est[[i]], 2, function(colum) {
      log(
        t(colum-data$theta) %*% data$A %*% (colum-data$theta),
        base=10
        )
      })
    list.bias[[i]] = data.frame(
      t=log(1:length(values), base=10),
      est.bias=values,
      method=names(est)[i]
      )
  }

  # Create a data frame row binding each p x niters matrix for ggplot.
  dat <- rbind(
    list.bias[[1]],
    list.bias[[2]],
    list.bias[[3]],
    list.bias[[4]]
    )
  # Aim to plot only every hundredth one.
  dat <- dat[c(rep(FALSE, 99), TRUE), ]

  # Plot.
  dat %>%
    ggplot(aes(x=t, y=est.bias, group=method, color=method)) +
      geom_line() +
      scale_x_continuous(limits=c(2, 5), breaks=c(2, 3, 4, 5)) +
      ylim(-4, 4) +
      ggtitle("Excess risk over training size")

}