## Functions for computing various performance measures.

## Constructs a confusion matrix given the true labels and
## the predicted labels, FOR BINARY CLASSIFICATION PROBLEMS.
##
## The label of the first class ('negative') is lneg, while
## the label of the other class ('positive') is lpos.

perf.matrix = function(true.y, pred.y, lneg=0, lpos=1)
  {
    if (length(true.y) != length(pred.y))
      stop("The two label vectors must have the same length!")
    
    r = matrix(0, nrow=2, ncol=2)
    colnames(r) = c(paste("true", lpos, sep='.'), paste("true", lneg, sep='.'))
    rownames(r) = c(paste("pred", lpos, sep='.'), paste("pred", lneg, sep='.'))
    
    r[1,1] = sum(pred.y[true.y == lpos] == lpos)  # correct positive predictions
    r[1,2] = sum(pred.y[true.y == lneg] == lpos)  # incorrect pos. predictions
    r[2,1] = sum(pred.y[true.y == lpos] == lneg)  # incorrect neg. predictions
    r[2,2] = sum(pred.y[true.y == lneg] == lneg)  # correct negative predictions
    
    return (r)
  }

perf.sensitivity = function(R)
  {
    return (R[1,1] / (R[1,1]+R[2,1]))
  }

perf.specificity = function(R)
  {
    return (R[2,2] / (R[1,2]+R[2,2]))
  }

perf.error = function(R)
  {
    return ((R[1,2]+R[2,1]) / sum(R))
  }

perf.ppv = function(R)
  {
    return (R[1,1]/(R[1,1]+R[1,2]))
  }

perf.npv = function(R)
  {
    return (R[2,2]/(R[2,1]+R[2,2]))
  }

## AUC: Area under the curve
##
## It assumes that y.true contains the true class posterior probabilities
## as either 0 or 1 (corresponding to the "negative" and "positive" classes
## and that y.prob contains the predicted probabilities that an object
## belongs to the "positive" class (so that all objects having a probability
## higher than a threshold will be labeled as "positive").
perf.auc = function(y.prob, y.true, lneg=0, lpos=1)
  {
    n0  = sum(y.true == lneg)
    n1  = sum(y.true == lpos)
    r   = rank(y.prob, ties.method="random")
    s   = sum(r[y.true==lpos])
    auc = (s - 0.5*n1*(n1+1)) / (n0*n1)

    return (auc)
  }

## Confidence intervals: simple, binomial approximation of the
## error (the textbook approach).
ci.error = function(e, n, alpha)
{
	c = 0.5/n + qnorm(1-alpha/2)*sqrt(e*(1-e)/n)
	return (list(ci.lo=e-c, ci.hi=e+c))
}