Discrete AdaBoost (Geron Ch 6, morie.fn hmadab)

alpha_t = 0.5 log((1 - err)/err); w <- w exp(-alpha y f(x)), renormalised. Default weak learner is a weighted 1-split stump.

Usage

morie_geron_adaboost(
  X,
  y,
  base_estimator = NULL,
  n_estimators = 10,
  eps = 1e-10
)

Arguments

X

Design matrix.

y

Two-class labels.

base_estimator

Optional function(X, y, w) -> predict(X) in {-1, 1}.

n_estimators

Rounds.

eps

Error floor/ceiling in (0, 0.5).

Value

List with alphas, errors, train_errors, predict, decision, margin, weights, classes.

Examples

W1 <- matrix(c(1, -1), 1, 2)
W2 <- matrix(c(2, 3), 2, 1)
morie_geron_backpropagation(matrix(c(1, 2), ncol = 1), matrix(c(0,
    1), ncol = 1), list(W1, W2), c("relu", "identity"))
#> $grads_W
#> $grads_W[[1]]
#>      [,1] [,2]
#> [1,]   16    0
#> 
#> $grads_W[[2]]
#>      [,1]
#> [1,]    8
#> [2,]    0
#> 
#> 
#> $grads_b
#> $grads_b[[1]]
#> [1] 10  0
#> 
#> $grads_b[[2]]
#> [1] 5
#> 
#> 
#> $deltas
#> $deltas[[1]]
#>      [,1] [,2]
#> [1,]    4    0
#> [2,]    6    0
#> 
#> $deltas[[2]]
#>      [,1]
#> [1,]    2
#> [2,]    3
#> 
#> 
#> $loss
#> [1] 6.5
#> 
#> $output
#>      [,1]
#> [1,]    2
#> [2,]    4
#> 
#> $activations_out
#> $activations_out[[1]]
#>      [,1]
#> [1,]    1
#> [2,]    2
#> 
#> $activations_out[[2]]
#>      [,1] [,2]
#> [1,]    1    0
#> [2,]    2    0
#> 
#> $activations_out[[3]]
#>      [,1]
#> [1,]    2
#> [2,]    4
#> 
#> 
#> $pre_activations
#> $pre_activations[[1]]
#>      [,1] [,2]
#> [1,]    1   -1
#> [2,]    2   -2
#> 
#> $pre_activations[[2]]
#>      [,1]
#> [1,]    2
#> [2,]    4
#> 
#> 
#> $estimate
#> [1] 6.5
#> 
#> $n
#> [1] 2
#> 
#> $method
#> [1] "Backpropagation of the mse loss through 2 layers"
#> 
morie_geron_adaboost(X = W2, y = W1)
#> $alphas
#>  [1] 11.51293 11.51293 11.51293 11.51293 11.51293 11.51293 11.51293 11.51293
#>  [9] 11.51293 11.51293
#> 
#> $errors
#>  [1] 0 0 0 0 0 0 0 0 0 0
#> 
#> $train_errors
#>  [1] 0 0 0 0 0 0 0 0 0 0
#> 
#> $predict
#> function (Xnew) 
#> {
#>     Bm <- if (is.matrix(Xnew)) 
#>         Xnew
#>     else matrix(as.numeric(Xnew), ncol = ncol(A))
#>     s <- numeric(nrow(Bm))
#>     for (i in seq_along(predictors)) s <- s + alphas[i] * as.numeric(predictors[[i]](Bm))
#>     ifelse(s >= 0, classes[2], classes[1])
#> }
#> <environment: 0x562178b18d10>
#> 
#> $decision
#> [1]  115.1293 -115.1293
#> 
#> $margin
#> [1] 1 1
#> 
#> $weights
#> [1] 0.5 0.5
#> 
#> $classes
#> [1] -1  1
#> 
#> $estimate
#> [1] 0
#> 
#> $n
#> [1] 2
#> 
#> $method
#> [1] "Discrete AdaBoost with reweighted weak learners"
#>