# Tree is not scale invariant for simple X transformation?

Theoretically, tree is invariant for X simple transformation, such as “a * X - b”. However, I do some simple tests, and I surprisingly found different version xgboost has different odd behavior, and all simple transformation will lead to unequal results. Here is the R code:

xgboost 0.71.2, change `X` to `X - 8`

``````library(xgboost)
set.seed(111)
N <- 80000
p <- 50
X <- matrix(runif(N * p, 0, 1), ncol = p)
colnames(X) <- paste0("x", 1:p)
beta <- runif(p)
y <- X %*% beta #+ rnorm(N, mean = 0, sd  = 0.1)

tr <- sample.int(N, N * 0.75)

###

param1 <- list(nrounds = 10, num_parallel_tree = 1, nthread = 10L, eta = 0.3, max_depth = 30,
seed = 2018, colsample_bytree = 1, subsample = 1,  min_child_weight = 10,
tree_method = "exact")
param1\$data <- X[tr,]
param1\$label <- y[tr]

set.seed(2019)
bst1 <- do.call(xgboost::xgboost, param1)
test_pred1 <- predict(bst1, newdata = X[-tr,])

newX <- X  - 8

param2 <- list(nrounds = 10, num_parallel_tree = 1, nthread = 10L, eta = 0.3, max_depth = 30,
seed = 2018, colsample_bytree = 1, subsample = 1,  min_child_weight = 10,
tree_method = "exact")
param2\$data <- newX[tr,]
param2\$label <- y[tr]

set.seed(2019)
bst2 <- do.call(xgboost::xgboost, param2)
test_pred2 <- predict(bst2, newdata = newX[-tr,])

summary(test_pred1 - test_pred2)
#     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
#-1.784631 -0.316670 -0.001692  0.002795  0.321040  1.831196
``````

R sessionInfo()

``````> sessionInfo()
R version 3.5.2 (2018-12-20)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 16.04.5 LTS

Matrix products: default
BLAS: /usr/lib/openblas-base/libblas.so.3
LAPACK: /usr/lib/libopenblasp-r0.2.18.so

locale:
[1] LC_CTYPE=C                 LC_NUMERIC=C               LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8     LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8    LC_PAPER=en_US.UTF-8
[8] LC_NAME=C                  LC_ADDRESS=C               LC_TELEPHONE=C             LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] xgboost_0.71.2

loaded via a namespace (and not attached):
[1] compiler_3.5.2    magrittr_1.5      Matrix_1.2-15     tools_3.5.2       stringi_1.2.4     grid_3.5.2        data.table_1.11.8 lattice_0.20-38
``````

xgboost from master compilation, 0.81.0.1, change `X - 8` to `X - 1` or `X / 10`

``````library(xgboost)
set.seed(111)
N <- 80000
p <- 50
X <- matrix(runif(N * p, 0, 1), ncol = p)
colnames(X) <- paste0("x", 1:p)
beta <- runif(p)
y <- X %*% beta #+ rnorm(N, mean = 0, sd  = 0.1)

tr <- sample.int(N, N * 0.75)

###

param1 <- list(nrounds = 10, num_parallel_tree = 1, nthread = 10L, eta = 0.3, max_depth = 30,
seed = 2018, colsample_bytree = 1, subsample = 1,  min_child_weight = 10,
tree_method = "exact")
param1\$data <- X[tr,]
param1\$label <- y[tr]

set.seed(2019)
bst1 <- do.call(xgboost::xgboost, param1)
test_pred1 <- predict(bst1, newdata = X[-tr,])

newX <- X  - 1

param2 <- list(nrounds = 10, num_parallel_tree = 1, nthread = 10L, eta = 0.3, max_depth = 30,
seed = 2018, colsample_bytree = 1, subsample = 1,  min_child_weight = 10,
tree_method = "exact")
param2\$data <- newX[tr,]
param2\$label <- y[tr]

set.seed(2019)
bst2 <- do.call(xgboost::xgboost, param2)
test_pred2 <- predict(bst2, newdata = newX[-tr,])

summary(test_pred1 - test_pred2)
#     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
#-0.714748 -0.109097 -0.003238 -0.002930  0.105858  0.726057
``````
1 Like

Thread has no effect on the result.

did you tested with 1 thread? using same histogram method, or different methods?

Actually I did many tests, with tree method, max_depth and other parameters and found the odd behavior. Do you run my code to reproduce the problem? If not, please try it firstly.

maybe here you can check what changed

two very different versions

Please go over my problem. I don’t compare the two results from the different versions.

if i’m not wrong, at leaf you have a reglin or a logistic that is “x” dependent this give different results using transformations on X

dump both trees and copy paste here, and we can check

for example:

I can reproduce the problem on a single thread on R too. There is a difference even after a single round.

``````> sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Debian GNU/Linux 8 (jessie)

Matrix products: default
BLAS: /usr/lib/openblas-base/libblas.so.3
LAPACK: /usr/lib/libopenblasp-r0.2.12.so

locale:
[1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8    LC_PAPER=en_US.UTF-8       LC_NAME=C