Using caret to optimize for deviance with binary classification

Question

(example borrowed from Fatal error with train() in caret on Windows 7, R 3.0.2, caret 6.0-21)

I have this example:

library("AppliedPredictiveModeling")
library("caret")

data("AlzheimerDisease")
data <- data.frame(predictors, diagnosis)

tuneGrid <- expand.grid(interaction.depth = 1:2, n.trees = 100, shrinkage = 0.1)
trainControl <- trainControl(method = "cv", number = 5, verboseIter = TRUE)

gbmFit <- train(diagnosis ~ ., data = data, method = "gbm", trControl = trainControl, tuneGrid = tuneGrid)

But let's say I want to optimize with regards to deviance (which is what I believe gbm returns by default) instead of accuracy. I know that trainControl offers a summaryFunction argument. How do I write a summaryFunction that will optimize for deviance?

Answer 1

Deviance is just (minus) twice the log-likelihood. For binomial data with a single trial, that is:

-2 \sum_{i=1}^n y_i log(\pi_i) + (1 - y_i)*log(1-\pi_i)

y_i is a binary indicator for the first class and \pi is the probability of being in the first class.

Here is a simple example to reproduce the deviance in a GLM (by re-calculating the training set deviance):

> library(caret)
> set.seed(1)
> dat <-twoClassSim(200)
> fit1 <- glm(Class ~ ., data = dat, family = binomial)
> ## glm() models the last class level
> prob_class1 <- 1 - predict(fit1, dat[, -ncol(dat)], type = "response")
> is_class1 <- ifelse(dat$Class == "Class1", 1, 0)
> -2*sum(is_class1*log(prob_class1) + ((1-is_class1)*log(1-prob_class1)))
[1] 112.7706
> fit1

Call:  glm(formula = Class ~ ., family = binomial, data = dat)
<snip>  
Degrees of Freedom: 199 Total (i.e. Null);  184 Residual
Null Deviance:      275.3 
Residual Deviance: 112.8    AIC: 144.8

A basic function for train would be:

dev_summary <- function(data, lev = NULL, model = NULL) {
  is_class1 <- ifelse(data$obs == lev[1], 1, 0)
  prob_class1 <- data[, lev[1]]

  c(deviance = -2*sum(is_class1*log(prob_class1) + 
                        ((1-is_class1)*log(1-prob_class1))),
    twoClassSummary(data, lev = lev))
}

ctrl <- trainControl(summaryFunction = dev_summary,
                     classProbs = TRUE)
gbm_grid <- expand.grid(interaction.depth = seq(1, 7, by = 2),
                        n.trees = seq(100, 1000, by = 50),
                        shrinkage = c(0.01, 0.1))
set.seed(1)
fit2 <- train(Class ~ ., data = dat,
              method = "gbm",
              trControl = ctrl,
              tuneGrid = gbm_grid,
              metric = "deviance",
              verbose = FALSE)

Note that you will need to think of something to do if \pi is very near zero or one.

Max