crossEntropy = function(y, yhat){
-(y * log(yhat) + (1 - y) * log(1 - yhat))
}
crossEntropyGrad = function(y, yhat){
(1 - y) / (1 - yhat) - (y / yhat)
}
# Regularized cross entropy: includes a beta prior that the predictions won't
# be less than (a-1) when a==b. Rules out things like billion-to-one odds if
# a==1 + 1E-7
crossEntropyReg = function(y, yhat, a, b){
-(y * log(yhat) + (1 - y) * log(1 - yhat)) - dbeta(yhat, a, b, log = TRUE)
}
crossEntropyRegGrad = function(y, yhat, a, b = a){
(1 - y) / (1 - yhat) - (y / yhat) - ((a - 1)/yhat + (b - 1)/(yhat - 1))
}
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