tests/testthat/test_interactions.R

In xgboost: Extreme Gradient Boosting

context('Test prediction of feature interactions')

require(xgboost)
require(magrittr)

set.seed(123)

test_that("predict feature interactions works", {
  # simulate some binary data and a linear outcome with an interaction term
  N <- 1000
  P <- 5
  X <- matrix(rbinom(N * P, 1, 0.5), ncol=P, dimnames = list(NULL, letters[1:P]))
  # center the data (as contributions are computed WRT feature means)
  X <- scale(X, scale=FALSE)

  # outcome without any interactions, without any noise:
  f <- function(x) 2 * x[, 1] - 3 * x[, 2]
  # outcome with interactions, without noise:
  f_int <- function(x) f(x) + 2 * x[, 2] * x[, 3]
  # outcome with interactions, with noise:
  #f_int_noise <- function(x) f_int(x) + rnorm(N, 0, 0.3)

  y <- f_int(X)

  dm <- xgb.DMatrix(X, label = y)
  param <- list(eta=0.1, max_depth=4, base_score=mean(y), lambda=0, nthread=2)
  b <- xgb.train(param, dm, 100)
  
  pred = predict(b, dm, outputmargin=TRUE)

  # SHAP contributions:
  cont <- predict(b, dm, predcontrib=TRUE)
  expect_equal(dim(cont), c(N, P+1))
  # make sure for each row they add up to marginal predictions
  max(abs(rowSums(cont) - pred)) %>% expect_lt(0.001)
  # Hand-construct the 'ground truth' feature contributions:
  gt_cont <- cbind(
      2. * X[, 1],
     -3. * X[, 2] + 1. * X[, 2] * X[, 3], # attribute a HALF of the interaction term to feature #2
      1. * X[, 2] * X[, 3]               # and another HALF of the interaction term to feature #3
     )
  gt_cont <- cbind(gt_cont, matrix(0, nrow=N, ncol=P + 1 - 3))
  # These should be relatively close:
  expect_lt(max(abs(cont - gt_cont)), 0.05)


  # SHAP interaction contributions:
  intr <- predict(b, dm, predinteraction=TRUE)
  expect_equal(dim(intr), c(N, P+1, P+1))
  # check assigned colnames
  cn <- c(letters[1:P], "BIAS")
  expect_equal(dimnames(intr), list(NULL, cn, cn))

  # check the symmetry
  max(abs(aperm(intr, c(1,3,2)) - intr)) %>% expect_lt(0.00001)

  # sums WRT columns must be close to feature contributions
  max(abs(apply(intr, c(1,2), sum) - cont)) %>% expect_lt(0.00001)

  # diagonal terms for features 3,4,5 must be close to zero
  Reduce(max, sapply(3:P, function(i) max(abs(intr[, i, i])))) %>% expect_lt(0.05)

  # BIAS must have no interactions
  max(abs(intr[, 1:P, P+1])) %>% expect_lt(0.00001)

  # interactions other than 2 x 3 must be close to zero
  intr23 <- intr
  intr23[,2,3] <- 0
  Reduce(max, sapply(1:P, function(i) max(abs(intr23[, i, (i+1):(P+1)])))) %>% expect_lt(0.05)

  # Construct the 'ground truth' contributions of interactions directly from the linear terms:
  gt_intr <- array(0, c(N, P+1, P+1))
  gt_intr[,2,3] <- 1. * X[, 2] * X[, 3] # attribute a HALF of the interaction term to each symmetric element
  gt_intr[,3,2] <- gt_intr[, 2, 3]
  # merge-in the diagonal based on 'ground truth' feature contributions
  intr_diag = gt_cont - apply(gt_intr, c(1,2), sum)
  for(j in seq_len(P)) {
    gt_intr[,j,j] = intr_diag[,j]
  }
  # These should be relatively close:
  expect_lt(max(abs(intr - gt_intr)), 0.1)
})

test_that("SHAP contribution values are not NAN", {
  d <- data.frame(
    x1 = c(-2.3, 1.4, 5.9, 2, 2.5, 0.3, -3.6, -0.2, 0.5, -2.8, -4.6, 3.3, -1.2,
           -1.1, -2.3, 0.4, -1.5, -0.2, -1, 3.7),
    x2 = c(291.179171, 269.198331, 289.942097, 283.191669, 269.673332,
           294.158346, 287.255835, 291.530838, 285.899586, 269.290833,
           268.649586, 291.530841, 280.074593, 269.484168, 293.94042,
           294.327506, 296.20709, 295.441669, 283.16792, 270.227085),
    y = c(9, 15, 5.7, 9.2, 22.4, 5, 9, 3.2, 7.2, 13.1, 7.8, 16.9, 6.5, 22.1,
          5.3, 10.4, 11.1, 13.9, 11, 20.5),
    fold = c(2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2))

  ivs <- c("x1", "x2")

  fit <- xgboost(
    verbose = 0,
    params = list(
      objective = "reg:squarederror",
      eval_metric = "rmse"),
    data = as.matrix(subset(d, fold == 2)[, ivs]),
    label = subset(d, fold == 2)$y,
    nthread = 1,
    nrounds = 3)

  shaps <- as.data.frame(predict(fit,
    newdata = as.matrix(subset(d, fold == 1)[, ivs]),
    predcontrib = T))
  result <- cbind(shaps, sum = rowSums(shaps), pred = predict(fit,
      newdata = as.matrix(subset(d, fold == 1)[, ivs])))

  expect_true(identical(TRUE, all.equal(result$sum, result$pred, tol = 1e-6)))
})


test_that("multiclass feature interactions work", {
  dm <- xgb.DMatrix(as.matrix(iris[,-5]), label=as.numeric(iris$Species)-1)
  param <- list(eta=0.1, max_depth=4, objective='multi:softprob', num_class=3)
  b <- xgb.train(param, dm, 40)
  pred = predict(b, dm, outputmargin=TRUE) %>% array(c(3, 150)) %>% t

  # SHAP contributions:
  cont <- predict(b, dm, predcontrib=TRUE)
  expect_length(cont, 3)
  # rewrap them as a 3d array
  cont <- unlist(cont) %>% array(c(150, 5, 3))
  # make sure for each row they add up to marginal predictions
  max(abs(apply(cont, c(1,3), sum) - pred)) %>% expect_lt(0.001)

  # SHAP interaction contributions:
  intr <- predict(b, dm, predinteraction=TRUE)
  expect_length(intr, 3)
  # rewrap them as a 4d array
  intr <- unlist(intr) %>% array(c(150, 5, 5, 3)) %>% aperm(c(4, 1, 2, 3)) # [grp, row, col, col]
  # check the symmetry
  max(abs(aperm(intr, c(1,2,4,3)) - intr)) %>% expect_lt(0.00001)
  # sums WRT columns must be close to feature contributions
  max(abs(apply(intr, c(1,2,3), sum) - aperm(cont, c(3,1,2)))) %>% expect_lt(0.00001)
})