How to compute log loss in machine learning

Question

The following code are used to produce the probability output of binary classification with Random Forest.

library(randomForest) 

rf <- randomForest(train, train_label,importance=TRUE,proximity=TRUE)
prediction<-predict(rf, test, type="prob")

Then the result about prediction is as follows:

The true label about test data are known (named test_label). Now I want to compute logarithmic loss for probability output of binary classification. The function about LogLoss is as follows.

LogLoss=function(actual, predicted)
{
  result=-1/length(actual)*(sum((actual*log(predicted)+(1-actual)*log(1-predicted))))
  return(result)
}

How to compute logarithmic loss with probability output of binary classification. Thank you.

Answer 1

library(randomForest) 

rf <- randomForest(Species~., data = iris, importance=TRUE, proximity=TRUE)
prediction <- predict(rf, iris, type="prob")
#bound the results, otherwise you might get infinity results
prediction <- apply(prediction, c(1,2), function(x) min(max(x, 1E-15), 1-1E-15)) 

#model.matrix generates a true probabilities matrix, where an element is either 1 or 0
#we subtract the prediction, and, if the result is bigger than 0 that's the correct class
logLoss = function(pred, actual){
  -1*mean(log(pred[model.matrix(~ actual + 0) - pred > 0]))
}

logLoss(prediction, iris$Species)

Answer 2

I think the logLoss formula is a little bit wrong.

model <- glm(vs ~ mpg, data = mtcars, family = "binomial")

### OP's formula (Wrong)
logLoss1 <- function(pred, actual){
  -1*mean(log(pred[model.matrix(~ actual + 0) - pred > 0]))
}
logLoss1(actual = model$y, pred = model$fitted.values)
# [1] 0.4466049

### Correct formula in native R 
logLoss2 <- function(pred, actual){
  -mean(actual * log(pred) + (1 - actual) * log(1 - pred))
}
logLoss2(actual = model$y, pred = model$fitted.values)
# [1] 0.3989584

## Results from various packages to verify the correct answer

### From ModelMetrics package
ModelMetrics::logLoss(actual = model$y, pred = model$fitted.values)
# [1] 0.3989584

### From MLmetrics package
MLmetrics::LogLoss(y_pred = model$fitted.values, y_true = model$y)
# [1] 0.3989584

### From reticulate package
sklearn.metrics <- import("sklearn.metrics")
sklearn.metrics$log_loss(y_true = model$y, y_pred = model$fitted.values)
# [1] 0.3989584

I used the R version 4.1.0 (2021-05-18).