What is wrong with my implementation of AdaBoost? - r

Question

I tried to implement the AdaBoost algorithm of Freund and Schapire as close to the original as possible (see p. 2 here: http://rob.schapire.net/papers/explaining-adaboost.pdf):
library(rpart)
library(OneR)
maxdepth <- 1
T <- 100 # number of rounds
# Given: (x_1, y_1),...,(x_m, y_m) where x_i element of X, y_i element of {-1, +1}
myocarde <- read.table("http://freakonometrics.free.fr/myocarde.csv", head = TRUE, sep = ";")
#myocarde <- read.table("data/myocarde.csv", header = TRUE, sep = ";")
y <- (myocarde[ , "PRONO"] == "SURVIE") * 2 - 1
x <- myocarde[ , 1:7]
m <- nrow(x)
data <- data.frame(x, y)
# Initialize: D_1(i) = 1/m for i = 1,...,m
D <- rep(1/m, m)
H <- replicate(T, list())
a <- vector(mode = "numeric", T)
set.seed(123)
# For t = 1,...,T
for(t in 1:T) {
# Train weak learner using distribution D_t
# Get weak hypothesis h_t: X -> {-1, +1}
data_D_t <- data[sample(m, 10*m, replace = TRUE, prob = D), ]
H[[t]] <- rpart(y ~., data = data_D_t, maxdepth = maxdepth, method = "class")
# Aim: select h_t with low weighted error: e_t = Pr_i~D_t[h_t(x_i) != y_i]
h <- predict(H[[t]], x, type = "class")
e <- sum(h != y) / m
# Choose a_t = 0.5 * log((1-e) / e)
a[t] <- 0.5 * log((1-e) / e)
# Update for i = 1,...,m: D_t+1(i) = (D_t(i) * exp(-a_t * y_i * h_t(x_i))) / Z_t
# where Z_t is a normalization factor (chosen so that Dt+1 will be a distribution)
D <- D * exp(-a[t] * y * as.numeric(h))
D <- D / sum(D)
}
# Output the final hypothesis: H(x) = sign(sum of a_t * h_t(x) for t=1 to T)
newdata <- x
H_x <- sapply(H, function(x) as.numeric(as.character(predict(x, newdata = newdata, type = "class"))))
H_x <- t(a * t(H_x))
pred <- sign(rowSums(H_x))
#H
#a
eval_model(pred, y)
##
## Confusion matrix (absolute):
## Actual
## Prediction -1 1 Sum
## -1 0 1 1
## 1 29 41 70
## Sum 29 42 71
##
## Confusion matrix (relative):
## Actual
## Prediction -1 1 Sum
## -1 0.00 0.01 0.01
## 1 0.41 0.58 0.99
## Sum 0.41 0.59 1.00
##
## Accuracy:
## 0.5775 (41/71)
##
## Error rate:
## 0.4225 (30/71)
##
## Error rate reduction (vs. base rate):
## -0.0345 (p-value = 0.6436)
As can be seen the accuracy of the model is horrible compared to other AdaBoost implementations, e.g.:
library(JOUSBoost)
## JOUSBoost 2.1.0
boost <- adaboost(as.matrix(x), y, tree_depth = maxdepth, n_rounds = T)
pred <- predict(boost, x)
eval_model(pred, y)
##
## Confusion matrix (absolute):
## Actual
## Prediction -1 1 Sum
## -1 29 0 29
## 1 0 42 42
## Sum 29 42 71
##
## Confusion matrix (relative):
## Actual
## Prediction -1 1 Sum
## -1 0.41 0.00 0.41
## 1 0.00 0.59 0.59
## Sum 0.41 0.59 1.00
##
## Accuracy:
## 1 (71/71)
##
## Error rate:
## 0 (0/71)
##
## Error rate reduction (vs. base rate):
## 1 (p-value < 2.2e-16)
My question
Could you please give me a hint what went wrong in my implementation? Thank you
Edit
The final and corrected code can be found in my blog post: Understanding AdaBoost – or how to turn Weakness into Strength

Answer 1

There are quite a few contributing factors as to why your implementation is not working.
You were not using rpart correctly. Adaboost implementation does not mention upsampling with the weights - but rpart itself can accept weights. My example below shows how rpart should be used for this purpose.
Calculation of the weighted error was wrong. You were calculating the error proportion (number of samples calculated incorrectly divided by number of samples). Adaboost uses the sum of the weights that were incorrectly predicted (sum(D[y != yhat])).
Final predictions seemed to be incorrect too, I just ended up doing a simple loop.
Next time I recommend diving into the source code the the other implementations you are comparing against.
https://github.com/cran/JOUSBoost/blob/master/R/adaboost.R uses almost identical code to my below example - and probably would have helped guide you originally.
Additionally using T as a variable could potentially interfere with the logical TRUE and it's shorthand T, so I'd avoid it.
### packages ###
library(rpart)
library(OneR)
### parameters ###
maxdepth <- 1
rounds <- 100
set.seed(123)
### data ###
myocarde <- read.table("http://freakonometrics.free.fr/myocarde.csv", head = TRUE, sep = ";")
y <- (myocarde[ , "PRONO"] == "SURVIE") * 2 - 1
x <- myocarde[ , 1:7]
m <- nrow(x)
dataset <- data.frame(x, y)
### initialisation ###
D <- rep(1/m, m)
H <- list()
a <- vector(mode = "numeric", length = rounds)
for (i in seq.int(rounds)) {
# train weak learner
H[[i]] = rpart(y ~ ., data = dataset, weights = D, maxdepth = maxdepth, method = "class")
# predictions
yhat <- predict(H[[i]], x, type = "class")
yhat <- as.numeric(as.character(yhat))
# weighted error
e <- sum(D[yhat != y])
# alpha coefficient
a[i] <- 0.5 * log((1 - e) / e)
# updating weights (D)
D <- D * exp(-a[i] * y * yhat)
D <- D / sum(D)
}
# predict with each weak learner on dataset
y_hat_final <- vector(mode = "numeric", length = m)
for (i in seq(rounds)) {
pred = predict(H[[i]], dataset, type = "class")
pred = as.numeric(as.character(pred))
y_hat_final = y_hat_final + (a[i] * pred)
}
pred <- sign(y_hat_final)
eval_model(pred, y)
> eval_model(pred, y)
Confusion matrix (absolute):
Actual
Prediction -1 1 Sum
-1 29 0 29
1 0 42 42
Sum 29 42 71
Confusion matrix (relative):
Actual
Prediction -1 1 Sum
-1 0.41 0.00 0.41
1 0.00 0.59 0.59
Sum 0.41 0.59 1.00
Accuracy:
1 (71/71)
Error rate:
0 (0/71)
Error rate reduction (vs. base rate):
1 (p-value < 2.2e-16)